MonetaryMechanismDesign.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "  \n",
    "Flexible monetary anchoring \n",
    "============\n",
    "-----\n",
    "\n",
    "### Executive Summary \n",
    "\n",
    "Mundell’s redundancy (or n-1) problem illustrates how international finance can be viewed as a zero-sum game, with many prisoners dilemma problems. Until now, international monetary agreements have relied on specified external anchors (gold, USD, bancor) to facilitate coordination and commitment - indeed, if one views the results of monetary negotiations as a Nash Demand Game with irrevocable commitment from all players to follow, then defining an\n",
    "external anchor is a way to surely enforce this contract. However, that anchoring process creates lengthy, hazardous and always inopportune international negotiations.\n",
    "\n",
    "We will therefore offer in this paper a dynamic upgrade of Mundell’s redundancy problem integrating debts, growth and interest rates, that highlights the process under which a dominant reserve currency emerges, negative incentives it generates in the process, and monetary tools to mitigate such side effects.\n",
    "\n",
    "Indeed, one of the main insight of this model is on how simple forms of privacy- preserving aggregate demand and supply estimation could lead to more flexible forms of anchoring. We thus derive an illustrative example built on currently mature privacy-preserving technologies and provide a concrete implementation of the previously theoretic ”planner” dear to mechanism designers - here to guarantee flexibility in the anchoring, and thus long term monetary stability and equality of opportunities. \n",
    "\n",
    "Our applied protocol, first presented as an extension of the optimal borrowing-lending/insurance literature, is then implemented in simulations of different post Covid-19 debt sustainability scenarii. Finally, some features highlighted by the simulations let us postulate that such flexible monetary anchoring performs better not only facing ”the three inescapable problems” associated with changes and transitions in monetary systems: ”the disruption of foreign exchanges and the collapse of monetary and credit systems”, ”the restoration of foreign trade”, and ”the supply of the capital that will be needed virtually throughout the world for reconstruction, for relief and for economic recovery” (White, 1942), but also during periods of stability, by providing parameters through which analyze and control global natural rates."
   ]
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    "\n",
    "### Why the choice of market design for monetary schemes :\n",
    "\n",
    "- countries’ monetary behaviours encompass many geopolitical, cultural and economical aspects (tendency to save or consume, will to become a reserve currency, control or not of flows...)\n",
    "- thus it is important to work out what incentives combined to what features of the monetary scheme can lead to nefarious behaviours (the Triffin dilemma illustrates one such phenomenon. In our paper we would also like to propose a model to participate in the current debate about the decrease of global natural rates for the past 30 years as a consequence of the post Bretton Woods scheme (quote Borio, 2019) \n",
    "- also the axiomatic approach in market design can provide a better framework to come up with closer to optimal monetary schemes, than ones negotiated within contingent geopo- litical context and dictated by nationalistic and selfish motives\n",
    "\n",
    "### The choice and adaptation of Bogomolnaia and Moulin (2001)\n",
    "\n",
    "We chose this framework first because of its proximity with real life reserve related deci- sions taken by central banks. (a few lines vs common value auctions?) Second because of its good axiomatic properties (”equal treatment of equals”) on which to later build a close to optimal scheme, and third because of its simplicity and versatility suited for calibraton and simulation.\n",
    "\n",
    "Here are the features of our version of the model :\n",
    "\n",
    "- Time is discrete, in rounds.\n",
    "- At the start of each round each country generates one \"cake\" (debt) \n",
    "- Each country simultaneously eats each others' cakes (debt) at different speed and following different rankings (so when a piece of cake is finished the countries that were eating eat move to the item below in their rankings)\n",
    "- Each country stores what he ate in his reserves - the endowments\n",
    "- If at the end of a round a country's cake has not been completed absorbed (by itself and/or by other countries) it suffers a devaluation - i.e. every the value of pieces of cake from this country store in others' endowments is decreased, and its interest rate rises.\n",
    "- Countries' ranking preferences are function of their trading preferences, their trading partners' debts' \"safety\", interest rate, size, and some randomness. See in more details below on how rankings and cakes are generated by each country at each round, and on how endowments change according to countries' behaviours.\n",
    "    "
   ]
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    "\n",
    "    \n",
    "### Mathematical observations - link with Random Growth and power laws (Gabaix, 2008)\n",
    "\n",
    "- to be developped, write the math if number of countries grow. Other examples than power laws ?\n",
    "\n",
    "Note how the gold standard in our model will account for a limitation at each round on the size of the cakes generated by each country and their eating speed, which both have to be smaller than their total reserve. Simulations can show how this reduce the number of deval- uations but growth speed as well, but still naturally leads to a dominant reserve currency and cyclical instabilities.\n",
    "\n",
    "### Some first insights on how the model captures the following features of the current monetary scheme, which produces: \n",
    "\n",
    "(same figures as in the village economy notebook)\n",
    "\n",
    "- naturally one ”safest” reserve currency, not necessarily linked to trade volume or surplus\n",
    "- this tendency of a trade ”winner takes all” is inherent to any groups of trading countries - how good or bad the winner of a trade group will be does not depend only on the size of the trade group - the worse-off countries of a big trading group can be worse than countries’ in smaller trade groups\n",
    "- initial conditions are important in the short-medium term, but not for the long run ; Triffin events do exists here, but are gradual in this model (and in practice).\n",
    "- cycles of decrease in natural real rates occur whenever the sum of countries’ cake eating speed exceed the sum of generated cake (note that this can occur benignly during times of globalization when ”bringing in” new countries to participate in the banquet, or during period of lax macroprudential rules and increase banking leverage).\n",
    "\n",
    "### Toward an optimal monetary scheme design\n",
    "\n",
    "On wars and dominant reserve currency status : because of how our hypothesis crucially relies on countries’ economic rationality, we also explore in our paper how rational situations can lead countries to invest in military expenditures and interventions (for instance in the case of an unwanted reserve currency monopoly other countries might be driven to invest in military to ”force” a shift in reserve currency. Or to recollect debts).\n",
    "\n",
    "**This is also one of the reason why we consider a truly multipolar reserve stabilization scheme - as for us only a truly balanced reserve composition can lead countries to compete fully on economic terms with less incentive to wage war.** \n",
    "\n",
    "Furthermore, such a multipolar scheme will allow for **more variability in countries’ behaviours and cultural differences** (some exporting countries might agree to finance more importing countries), **while casting a global financial safety net** (the rise and fall in one reserve currency can be mitigated by the other reserve currencies).\n"
   ]
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    "\n",
    "\n",
    "### A quick overview of our stabilization scheme :\n",
    "\n",
    "\n",
    "#### In our model and in the simulations :\n",
    "\n",
    "In this model the increased lending and insurance infrastructure we push for are reflected as more willingness from participating countries to accept others' devaluation (as proxy for insurance - see the commented code in the last cells of this notebook), as more lending facilities to \"losers\" from trade countries (implemented as better ranking for these countries during the cake-eating process at each rounds), and extra information given (aggregation of total shocks and needs) at each round - which allows for countries to see how much \"latitude\" they have at each round and share the burden with their trading partners - which reduces global interest rates and augment global output (see 3rd example in the cell below)\n",
    "\n",
    "\n",
    "#### In real life (proposal):\n",
    "\n",
    "At the core of our proposal resides the *multi-currency* nature of the market making activity of international banks, which we aim at replicating at a central bank level. A first underlying reason would be that of *collection of risk* - in the line of bigger risks for higher returns. Additionally (and that is a second reason for emphasizing the multi-currency aspect) in our case the additional risk is that of adding on more exotic currencies such as the South East Asian ones in a reserve basket previously not containing them - that could thus act as an additional cushion to mitigate external shock on them.\n",
    "\n",
    "It is then possible to see that for such a **multi-currency reserve balance sheet** the profit objective of traditional private market maker is here also aligned with the volatility stabilization objective of the central banks involved, and that the mechanisms underlying these forms of interventions would be conceptually the same as the ones through which financiers' alterations to their balance sheets affect both the level and volatility of exchange rates.\n",
    "\n",
    "The design question then, critical to the feasibility of such a multi-currencies account for instance, is on **how to create and foster this form of collaboration among different central banks**.\n",
    "\n",
    "\n",
    "### Computing these multilateral balance sheets, through privacy-preserving methods\n",
    "\n",
    "Privacy-preserving methods like multiparty computation *(referring to the financial adaptation of Abbe, Khandani, Lo, 2012, which build on Yao 1982; Goldreich, Micali, and Wigderson 1987; Ben-Or, Goldwasser, and Wigderson 1988; Chaum, Crépeau, and Damgard 1988; Beaver, Micali, and Rogaway\n",
    "1990; Cramer et al. 1999)* provide a clear and useful framework on which to **reach agreement on the different exchange and interest rate objectives pursued by respective central banks**. This is why this section will build on the language and framework of these privacy-preserving methods - which again don't have to be *actually* implemented for the interventions to be conducted.\n",
    "\n",
    "1. Thus central banks would first each allocate some funds denominated in their national currencies, plus portions of their reserves in each of the currencies they would like to stabilize their exchange rates with. \n",
    "2. They would then set-up the daily volatility bands they want their national currencies to stay in, which proportion of reserves they are ready to commit to the operation, and what amount of risk or leverage they are ready to bear on any derivative instrument used in the process (for convenience let's imagine the updates are only feasible at a regular interval - for instance once a day or once a week. We are then in a discreet time setting). These three points are where privacy-preserving methods might be applied, since participant central banks wouldn't want for instance *the entirety* of the reserves they engaged in that fund to be potentially used to defend the currency of another participating country)\n",
    "3. Thus a daily total amount of reserves committed to each currency could be computed using the aforementioned methods, without individual inputs from each central bank being revealed). Note that the viewing of the results of these computations can also be restrained so that each central bank only sees the pooling of reserves allocated to him - and not that allocated to others. In this fashion, both inputs and outputs of these forms of computations have modular privacy settings, that can be deployed according to participants preferences.\n",
    "\n",
    "The previous paragraph described mostly a pooling of reserves, quite similar to what already exists in the Chiang Mai Initiative, but **applied on a continuous and systematic basis rather than just during times of extreme stress** (in fact one of the goals of this automatic and systematic market smoothing is to potentially provide in-commensurable psychological relief and precious time for governments to *avoid* times of extreme stress). \n",
    "\n",
    "There are also **other benefits to having a common multicurrency account: first, the mechanisms derived to stabilize a currency vs the international currencies part of the reserves portfolio can now also be used to also stabilize more exotic currency pairs** (but among natural trading partners) such as the MYR/IDR. \n",
    "\n",
    "Furthermore, **our scheme would constitute an implementation of the \"optimal capital controls**, that should lean against the wind by requiring a temporary tax on inflows and a subsidy on outflows (if dealing with sudden inflows, the opposite if dealing with a sudden stop)\" from Farhi and Werning (2013).\n",
    "\n",
    "Finally, it would **help by design including more currencies in the global reserve distribution and alleviating the \"safe asset shortage\"** (Caballero, Farhi, Gourinchas, 2017).\n"
   ]
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    "\n",
    "### Methodology for the post-Covid simulations\n",
    "\n",
    "We present here the detailed code used for the simulations. For that we first calibrate the model to match the main trends and events observed from 1945 to now (2020). Being able to capture these features of past history will provide confidence and intuition in the model's inner workings. That lead us to provide several scenarii in how the models' parameters will change following Covid-19's increase in debts *(these parameters from the model being for instance the change in debt levels, while debt absorption speed are maintained roughly constant. Different degrees in shifts in trade and supply chain preferences are also considered)*. We thus generate 50 more rounds after a common departing point, and report here the different outcomes, and the different probabilities of each outcome (since they are intervention of random perturbations in the model the probabilities of each outcome is calculated based on how many of different random sequence generate this specific outcome).\n",
    "\n",
    "### Results\n",
    "\n",
    "The simulations of extra Covid debts show that :\n",
    "\n",
    "- **in the case of everything constant (pre Trump US and China trade relations)** debts are overall sustainable, with adjustements in reserve levels and contraction of countries' economies depending on how affected by the crisis they were.\n",
    "\n",
    "<img src=\"Screen%20Shot%202020-04-06%20at%2010.05.35%20AM.png\" /> \n",
    "\n",
    "- **similar results in the case of everything constant, with just additional reliance on trade with China** (for instance for masks, medical supplies etc). The economic contraction is smaller, and the global reserve contraction as well. This could be interpreted by the fact that the additional trade with China is flushed in its reserve (the increase can be seen in the graph below), used to acquire other countries' debt (inferred from the lowering of global interest rates) and thus sustaining economic activity \n",
    "\n",
    "<img src=\"Screen%20Shot%202020-04-06%20at%2011.13.15%20AM.png\" /> \n",
    "\n",
    "- **in the case of everything constant among all countries except China and US, who in that scenario stop trading with each other**, they are small probabilities of a global contraction (less reserves, less debts, less GDP growth) that preserves the overall shares of each country in the global economy - except for China in the global economy which suffers more. However in these small probability event the US go through an initial bubble fueled by the decrease of China, that then collapses back to the initial level (and note that after this collapse China's share is also back to the initial level - but with the cost of a global contraction, especially for all EM markets). **And with the caveat provided just above that this debt model doesn't take into account other incentives and consequences created by such dynamics - small probabilities in economic contraction in one country might leading to escalating tensions on other dimensions as well*\n",
    "\n",
    "<img src=\"Screen%20Shot%202020-04-04%20at%209.50.20%20PM.png\" /> \n",
    "\n",
    "- **in the case of stopping trade between China and the US AND additional reliance by other countries on China**, there is high probability for a sudden takeover of the role of the US as reserve currency China, accompanied by strong contraction for every other country. **Again, with the previous caveat of unaccounted destabilizing geopolitical consequences**\n",
    "\n",
    "<img src=\"Screen%20Shot%202020-04-04%20at%209.57.55%20PM.png\" /> \n",
    "\n",
    "\n",
    "- **finally, in the case of our proposed stabilization scheme** *(details in the paper - in the model it is just reflected as more willingness from participating countries to accept others' devaluation - see the commented code in the last cells of this notebook. Un-implemented here is also the extra information each country will have on how much latitude they will have at each round on their debt, which should also help in addition of the effects produced here to stabilize debts, interest rates and balance global reserve currencies)* the effects of all above scenarii are smoothen, with much more balanced reserve currencies (at least 3 currencies accounting each more than 20% of the global share of reserves, with the exact currencies - most often Germany ie the Euro, or the JPY - switching depending on the random shocks, but without adverse effects on all countries - including on the US even though the dollar loses its monopoly as reserve currency)\n",
    "\n",
    "Examples from one representative random initialization \n",
    "<img src=\"Screen%20Shot%202020-04-04%20at%2010.12.50%20PM.png\" /> \n",
    "\n",
    "Examples from another representative random initilization\n",
    "<img src=\"Screen%20Shot%202020-04-04%20at%2010.13.52%20PM.png\" /> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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    "# Exogeneous parameters of the simulation to be played with \n",
    "\n",
    "number_of_countries = 12 %total number of countries in the simulation. Here we are running the simulations with the US, UK, France, Germany, Japan, China, plus 6 other randomcountries\n",
    "number_of_rounds = 100 %total number of \"cake eating rounds\" (roughly equals to 1year in real time)\n",
    "\n",
    "interest_rate = (0.03).*ones(number_of_countries,1); %initial interest rates - more below on how interest rates change according to how successfully debt is absorbeb at each round.\n",
    "interest_rate_history = zeros(number_of_countries,number_of_rounds);\n",
    "\n",
    "uni=0.7;%uni is used in the random generation of the trade preference matrix - a number_of_countries x number_of_countries matrix in which the number line i, column j indicates how interconnected the economies of countries i and j are. This random generation is done with the function R = sprandsym(n,density) - in our case n=number_of_countries and density = uni, which returns a symmetric random, n-by-n, sparse matrix with approximately density*n*n nonzeros; each entry is the sum of one or more normally distributed random samples, and (0 <= density <= 1) .For calibration uni=0.3 creates with good probability if there are 6 countries in total 3 trade coalitions, one with 3 countries, one with 2, and 1 in autarky.\n",
    "\n",
    "%If we were in Matlab we would have added the parameter rc=0.02, still for this sprandsym function, which denotes how inequal trade between countries can be (the smaller the more). Indeed,  R = sprandsym(n,density,rc) returns a matrix with a reciprocal condition number equal to rc. The distribution of entries is nonuniform; it is roughly symmetric about 0; all are in [−1,1]. If rc is a vector of length n, then R has eigenvalues rc. Thus, if rc is a positive (nonnegative) vector then R is a positive (nonnegative) definite matrix. In either case, R is generated by random Jacobi rotations applied to a diagonal matrix with the given eigenvalues or condition number. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We initialize here the recording vectors that will collect the history of the simulation, to plot the graphs at the end of this notebook\n",
    "\n",
    "endowments_reserves_history = zeros(number_of_countries,number_of_rounds); %The records of how much cakes in total each country has accumulated at each round (see cell just below for the definition of a cake)\n",
    "endowments_debts_history = zeros(number_of_countries,number_of_rounds); %The records of how much cakes (ie debts) in total each country has generated up to round t (see cell just below for the definition of a cake)\n",
    "sum_cakes_history = zeros(1,number_of_rounds); %The records of each country's cake size for each round (see cell just below for the definition of a cake)\n",
    "sum_of_generated_cakes = 0; %for cumulated\n",
    "\n",
    "abso_speed_history = zeros(number_of_countries,number_of_rounds); %The records of the eating speed of each country for each round (see cell just below for the definition of the eating speed)\n",
    "abso_history = zeros(1,number_of_rounds); \n",
    "sum_of_abso_speed = 0; %for cumulated\n",
    "\n",
    "devaluation_history = zeros(number_of_countries,number_of_rounds); %The records of the cumulated number of times which each country devalued up to round i\n",
    "ranking_history = zeros(number_of_countries,number_of_countries); %The records of the order in which each country ranked other countries' cake to be eaten at each round(see cell just below for the definition of a cake)\n",
    "history_counter = ones(number_of_countries,1); %used in which round to determine sizes of generated cakes and cake eating speeds (see within round cell below)\n",
    "deval_history = zeros(number_of_countries,1); %idem\n",
    "\n",
    "duration_T_updated_history = zeros(1,number_of_rounds); %The records of how long was the timer for each round (see cell just below for the definition of a timer)\n",
    "duration_T = 1; % There's a timer for each round. A round ends when this timer ends, or when countries ate all the cakes if faster than the timer (the timer changes at each round depending on the total cake sizes and total eating speed ratio, so that it increases rather steadily)\n",
    "fraction_ranking = (1/3); % Used for calibration\n",
    "duration_T_updated = duration_T;\n",
    "successfully_loaded_cake_last_round = zeros(number_of_countries,1);\n",
    "successfully_loaded_cake_last_round = zeros(number_of_countries,1);\n",
    "\n",
    "sum_of_generated_cakes = 0;\n",
    "sum_of_abso_speed = 0;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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   "source": [
    "# Now we set up initial conditions to roughly match that of 1945 : i.e. we define the initial endowments (debts owed by each country and detained by which countries) and the initial cake eating speed \n",
    "\n",
    "% We initialize so that the initial numbers here in the endowments matrix corresponds to the initial percentage (0.11 = 11%) of total world GDP. \n",
    "% The endowments matrix is read as reserves accumulated by a country i for lines i of the endowments matrix, and cakes generated by country j for the columns j of the endowments matrix. So the endowments matrix is really just keeping in time record of how much each country i is holding debts from each other country j.\n",
    "\n",
    "endowments = [0.11 0.01 0.001 0.02 ;%0 0 0 0 0 0 0 0; %for the US, its debt in 1945 being of 300 Bdollar ie 43% of US GDP 1945 so 11% of world GDP then\n",
    "    0 0.05 0.001 0.03 ;% 0 0 0 0 0 0 0 0;%for the UK - the UK debt of 1945 being of around 30B$ ie roughly 10% of US debt, of which 3B$ owed by US\n",
    "    0 0 0.001 0.01 ] %0 0 0 0 0 0 0 0];%for France \n",
    "endowments = [endowments rand([3,8]).*0.001]; %random small intialization for the other countries\n",
    "endowments = [endowments ; rand([9,number_of_countries]).*0.001] %random small intialization for the other countries\n",
    "endowments=endowments.*300; %scaling up (see below - we want the values here to avoid being lower than 1 for them to not converge to 0)\n",
    "\n",
    "initial_debts = sum(endowments,1)';"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We now set up initial conditials for the cake eating speed of each country (for that we use as proxy their share in world GDP)\n",
    "\n",
    "abso_speed = [0.25; 0.15; 0.1; 0.01; 0.05; 0.05 ]; %US 1945 GDP being around 25% of 1945 World GDP, UK 15%, France 10%, Germany 1%, Japan 5%, China 5%\n",
    "abso_speed = [abso_speed  ; rand([6,1]).*0.01]; %random small initialization for the other countries\n",
    "abso_speed = abso_speed.*300; %scaling up (see below - we want the values here to avoid being lower than 1 for them to not converge to 0)\n",
    "\n",
    "abso_speed_init = abso_speed;\n",
    "initial_pos = 100.*rand([number_of_countries,1]);\n",
    "initial_pos_init =initial_pos;\n",
    "initial_pos_round = initial_pos;\n",
    "cakes_from_previous_round = initial_pos;\n",
    "abso_speed_from_previous_round = abso_speed;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We initialize now the initial trading preferences of the countries. \n",
    "\n",
    "ranked_list = zeros(number_of_countries,number_of_countries);\n",
    "\n",
    "%at first US, UK and France trading with each other in 1945 (until 1953 - for which see later sections of the code)\n",
    "trading_preferences = [3 2 2 ; %US prefers doing business with others\n",
    "    2 3 2 ; %UK prefers with itself\n",
    "    2 2 3]; %France prefers with itself as well\n",
    "\n",
    "trading_preferences = [trading_preferences ones(3,9)];\n",
    "\n",
    "trading_preferences = [trading_preferences ; ones(9,12)];\n",
    "for j=1:number_of_countries\n",
    "    ranked_list(j,:) = randperm(number_of_countries);\n",
    "    trading_preferences(j,j)=0;\n",
    "    tag{j}=strcat('country ',num2str(j));\n",
    "end\n",
    "tag{1} = 'USA';\n",
    "tag{2} = 'UK';\n",
    "tag{3} = 'France';\n",
    "tag{4} = 'Germany';\n",
    "tag{5} = 'Japan';\n",
    "tag{6} = 'China';\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we go into rounds of cake eating, that are looped over. Everything important happens in this cell !\n",
    "\n",
    "\n",
    "for k=1:number_of_countries\n",
    "    %trading_preferences(k,k)=trading_preferences(k,k)+1;\n",
    "    [~,trading_order]=sort(trading_preferences(k,:).*(ones(1,number_of_countries)+endowments(k,:)),'descend');\n",
    "    %could rank by size of trade and by size of trading partner\n",
    "    res=sum(trading_preferences(k,:)~=0);\n",
    "    if res>0\n",
    "        for l=1:res\n",
    "            ressort_count=find(ranked_list(k,:)==trading_order(l));\n",
    "            if ressort_count>l\n",
    "                for m=1:(ressort_count-l)\n",
    "                    ranked_list(k,ressort_count+1-m)=ranked_list(k,ressort_count-m);\n",
    "                end\n",
    "                ranked_list(k,l)=trading_order(l);\n",
    "            else\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "end\n",
    "ranked_list_true_init = ranked_list;\n",
    "\n",
    "\n",
    "for i=1:number_of_rounds\n",
    "    \n",
    "\n",
    "    %add Marshall %The largest recipient of Marshall Plan money was the United Kingdom (receiving about 26% of the total), followed by France (18%) and West Germany (11%)\n",
    "    %The $17 billion was in the context of a US GDP of $258 billion in 1948,\n",
    "    %that new plan gave away about $7.5 billion annually until 1961 when it was replaced by another program\n",
    "    \n",
    "    if i==8\n",
    "        %initial_debts(4,1)=0;\n",
    "        %initial_debts(5,1)=0;\n",
    "        \n",
    "        successfully_loaded_cake_last_round(4,1)=1;\n",
    "        %history_counter(4,1)=history_counter(4,1)-deval_history(4,1);\n",
    "        deval_history(4,1)=0;\n",
    "        \n",
    "        successfully_loaded_cake_last_round(5,1)=1;\n",
    "        %history_counter(5,1)=history_counter(5,1)-deval_history(5,1);\n",
    "        deval_history(5,1)=0;\n",
    "        \n",
    "        trading_preferences(1,:) = [ 2 2 2 3 3 1 1 1 1 1 1 1 ];\n",
    "        trading_preferences(2,:) = [ 3 2 2 2 2 1 1 1 1 1 1 1 ];\n",
    "        trading_preferences(3,:) = [ 3 2 2 2 2 1 1 1 1 1 1 1 ];\n",
    "        trading_preferences(4,:) = [ 3 2 2 3 3 1 1 1 1 1 1 1 ];\n",
    "        trading_preferences(5,:) = [ 3 3 2 3 3 1 1 1 1 1 1 1 ];\n",
    "    end\n",
    "    \n",
    "    if (i>3 && i<7)\n",
    "        %endowments(2,1)=endowments(2,1)+0.8*mean(mean(endowments));\n",
    "        %endowments(3,1)=endowments(3,1)+0.6*mean(mean(endowments));\n",
    "        endowments(4,1)=endowments(4,1)+0.4*mean(mean(endowments));\n",
    "    end\n",
    "    \n",
    "    if (i>7 && i<10)\n",
    "        endowments(5,1)=endowments(5,1)+0.8*mean(mean(endowments));\n",
    "    end\n",
    "    %add forgiving Germany if i==8 (1953) endowments 8 ==0 and trade. Same\n",
    "    %with Japan\n",
    "    \n",
    "    %China opening FDI vs US GDP ?\n",
    "    if (i>45 && i<75)\n",
    "        endowments(6,1)=endowments(6,1)+(i./1000)*mean(mean(endowments));\n",
    "    end\n",
    "    if i==45\n",
    "        successfully_loaded_cake_last_round(6,1)=1;\n",
    "        %(6,1)=history_counter(6,1)-deval_history(6,1);\n",
    "        deval_history(6,1)=0;\n",
    "        trading_preferences(1,:) = [ 2 2 2 2 2 3 1 1 1 1 1 1 ];\n",
    "        trading_preferences(2,:) = [ 1 1 1 1 2 3 1 1 1 1 1 1 ];\n",
    "        trading_preferences(3,:) = [ 1 1 1 1 2 3 1 1 1 1 1 1 ];\n",
    "        trading_preferences(4,:) = [ 2 2 2 3 2 3 1 1 1 1 1 1 ];\n",
    "        trading_preferences(5,:) = [ 2 2 2 2 3 3 1 1 1 1 1 1 ];\n",
    "        trading_preferences(6,:) = [ 3 3 3 3 3 3 2 2 2 2 2 2 ];\n",
    "        for m=7:12\n",
    "            trading_preferences(m,6) = 3;\n",
    "        end\n",
    "        \n",
    "    end\n",
    "    \n",
    "    cakes = sqrt(sum(endowments,1)'.*(1+rand(number_of_countries,1)));\n",
    "    abso_speed = sqrt((sum(endowments,2)+sum(endowments,1)').*(1+rand(number_of_countries,1)));\n",
    "    \n",
    "    sum_of_generated_cakes = sum_of_generated_cakes + cakes;\n",
    "    sum_of_abso_speed = sum_of_abso_speed + abso_speed;\n",
    "    \n",
    "    initial_pos_round = cakes;    %duration_T_updated = (15+rand(1,1))*sum(cakes)./sum(abso_speed);\n",
    "    duration_T_updated = 50.*(1+rand(1,1))*sum(cakes)./sum(abso_speed);\n",
    "    \n",
    "    cakes_from_previous_round = cakes;\n",
    "    abso_speed_from_previous_round = abso_speed;\n",
    "    \n",
    "    abso_history(1,i)=sum(abso_speed);\n",
    "    sum_cakes_history(1,i)=sum(cakes);\n",
    "    \n",
    "    time_counter=0;\n",
    "    cakes_counter=0;\n",
    "    rank_counter = ones(number_of_countries,1);\n",
    "    removed_cake_row = zeros(number_of_countries,1);\n",
    "    k=1;\n",
    "    latest_finished_cake = 0;\n",
    "    will_be_totally_consumed = zeros(number_of_countries,1);\n",
    "    while (duration_T_updated>0 && cakes_counter<number_of_countries) %&& rank_counter_tot<number_of_countries\n",
    "        initial_pos_updated = cakes;\n",
    "        diff_between_wished_and_offered = zeros(number_of_countries,1);\n",
    "        \n",
    "        for l=1:number_of_countries\n",
    "            if removed_cake_row(ranked_list(l,1))>0\n",
    "                o=1;\n",
    "                u=1;\n",
    "                if  removed_cake_row(ranked_list(l,o+1),1)>0\n",
    "                    u=o+1;\n",
    "                    while ((u<(number_of_countries-1)) && (removed_cake_row(ranked_list(l,u+1),1)>0))\n",
    "                        u=u+1;\n",
    "                    end\n",
    "                    ranked_list(l,o)=ranked_list(l,u+1);\n",
    "                \n",
    "                else\n",
    "                    ranked_list(l,o)=ranked_list(l,o+1);\n",
    "                    \n",
    "                end\n",
    "                rank_counter(j,1)=rank_counter(j,1)+1;\n",
    "            end\n",
    "        end\n",
    "        \n",
    "        for j=1:number_of_countries\n",
    "            if removed_cake_row(j,1)>0\n",
    "            else\n",
    "                if sum(abso_speed(ranked_list(:,1)==j))>cakes(j,1)\n",
    "                    will_be_totally_consumed(j,1)=will_be_totally_consumed(j,1)+1;\n",
    "                    diff_between_wished_and_offered(j,1) = sum(abso_speed(ranked_list(:,1)==j))/initial_pos_updated(j,1);\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "        \n",
    "        if sum(diff_between_wished_and_offered)==0\n",
    "            for j=1:number_of_countries\n",
    "                if removed_cake_row(j,1)>0\n",
    "                else\n",
    "                    diff_between_wished_and_offered(j,1) = sum(abso_speed(ranked_list(:,1)==j))/initial_pos_updated(j,1);\n",
    "                    \n",
    "                    will_be_totally_consumed(j,1)=will_be_totally_consumed(j,1)+1;\n",
    "                end\n",
    "            end\n",
    "        else\n",
    "        end\n",
    "        \n",
    "        [~,consumption_order]=sort(diff_between_wished_and_offered,'descend');\n",
    "        \n",
    "        if sum(diff_between_wished_and_offered)==0\n",
    "            [ii,jj]=find(~removed_cake_row);\n",
    "            if size(ii)==1\n",
    "                consumption_order(1)=ii;\n",
    "            else\n",
    "                for j=1:size(ii)\n",
    "                    consumption_order(j)=ii(j);\n",
    "                end\n",
    "            end\n",
    "        else\n",
    "        end\n",
    "        \n",
    "        if (duration_T_updated-cakes(consumption_order(1),1))>0\n",
    "            duration_T_updated = duration_T_updated - cakes(consumption_order(1),1);\n",
    "            for j=1:number_of_countries\n",
    "                if ranked_list(j,1)==consumption_order(1)\n",
    "                    endowments(j,consumption_order(1)) = endowments(j,consumption_order(1))+(abso_speed(j,1)./(sum(abso_speed(ranked_list(:,1)==consumption_order(1)))))*initial_pos_updated(consumption_order(1),1);\n",
    "                elseif cakes(ranked_list(j,1),1)==0\n",
    "                    removed_cake_row(ranked_list(j,1),1)=removed_cake_row(ranked_list(j,1),1)+1;            \n",
    "                else\n",
    "                    endowments(j,ranked_list(j,1)) = endowments(j,ranked_list(j,1))+(abso_speed(j,1)*cakes(consumption_order(1),1))/(sum(abso_speed(ranked_list(:,1)==consumption_order(1))));\n",
    "                    cakes(ranked_list(j,1),1)=initial_pos_updated(ranked_list(j,1),1)-(sum(abso_speed(ranked_list(:,1)==ranked_list(j,1)))*cakes(consumption_order(1),1))/(sum(abso_speed(ranked_list(:,1)==consumption_order(1))));\n",
    "                end\n",
    "            end\n",
    "            time_counter = time_counter + cakes(consumption_order(1),1);\n",
    "            cakes(consumption_order(1),1) = 0;\n",
    "            removed_cake_row(consumption_order(1),1)=removed_cake_row(consumption_order(1),1)+1;\n",
    "            \n",
    "        else\n",
    "            cakes(consumption_order(1),1) = cakes(consumption_order(1),1) - duration_T_updated;\n",
    "            \n",
    "            time_counter = time_counter + duration_T_updated;\n",
    "            \n",
    "            for j=1:number_of_countries\n",
    "                if ranked_list(j,1)==consumption_order(1)\n",
    "                    endowments(j,consumption_order(1)) = endowments(j,consumption_order(1))+(abso_speed(j,1)./(sum(abso_speed(ranked_list(:,1)==consumption_order(1)))))*duration_T_updated;\n",
    "                    \n",
    "                elseif cakes(ranked_list(j,1),1)==0\n",
    "                    removed_cake_row(ranked_list(j,1),1)=removed_cake_row(ranked_list(j,1),1)+1;\n",
    "                    \n",
    "                else\n",
    "                    endowments(j,ranked_list(j,1)) = endowments(j,ranked_list(j,1))+(abso_speed(j,1)*duration_T_updated)/(sum(abso_speed(ranked_list(:,1)==consumption_order(1))));\n",
    "                    cakes(ranked_list(j,1),1)=cakes(ranked_list(j,1),1)-(abso_speed(j,1)*duration_T_updated)/(sum(abso_speed(ranked_list(:,1)==consumption_order(1))));\n",
    "                end\n",
    "            end\n",
    "            \n",
    "            duration_T_updated = 0;\n",
    "            \n",
    "        end\n",
    "        latest_finished_cake = consumption_order(1);\n",
    "        \n",
    "        cakes_counter = cakes_counter + 1;\n",
    "        k=k+1;\n",
    "        duration_T_updated_history(1,i)=duration_T_updated;\n",
    "    \n",
    "    end\n",
    "    \n",
    "    for j=1:number_of_countries\n",
    "        if (initial_pos_round(j,1)-cakes(j,1))>0\n",
    "            endowments(:,j)=endowments(:,j)*(1-(cakes(j,1)/initial_pos_round(j,1)));   \n",
    "        else\n",
    "        end\n",
    "        if cakes(j,1)==0\n",
    "            history_counter(j,1) = history_counter(j,1) + 1;\n",
    "            successfully_loaded_cake_last_round(j,1) = 1;\n",
    "            interest_rate(j,1)=interest_rate(j,1)./(1+rand(1,1));\n",
    "        else\n",
    "            interest_rate(j,1)=min(1,max(interest_rate_history(j,1),interest_rate(j,1).*(1+rand(1,1))));\n",
    "            deval_history(j,1) = deval_history(j,1)+1 ;\n",
    "        end\n",
    "    end\n",
    "    [~,success_order]=sort(history_counter,'descend');\n",
    "    ranked_list = repmat(success_order',number_of_countries,1);\n",
    "    \n",
    "    \n",
    "    \n",
    "    for k=1:number_of_countries\n",
    "        \n",
    "        r1 = randperm(number_of_countries,2*round(number_of_countries*fraction_ranking));\n",
    "        \n",
    "        \n",
    "        for j=1:round(number_of_countries*fraction_ranking)\n",
    "            inter=ranked_list(k,r1(1,j));\n",
    "            ranked_list(k,r1(1,j))=ranked_list(k,r1(1,2*j));\n",
    "            ranked_list(k,r1(1,2*j))=inter;\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    for k=1:number_of_countries\n",
    "        [~,trading_order]=sort(trading_preferences(k,:).*(ones(1,number_of_countries)+max(0,successfully_loaded_cake_last_round(k,1).*(history_counter(k,1)-deval_history(k,1)).*endowments(k,:)*(interest_rate(k,1)))),'descend');\n",
    "        res=sum(trading_preferences(k,:)~=0);\n",
    "        if res>0\n",
    "            for l=1:res\n",
    "                ressort_count=find(ranked_list(k,:)==trading_order(l));\n",
    "                if ressort_count>l\n",
    "                    for m=1:(ressort_count-l)\n",
    "                        ranked_list(k,ressort_count+1-m)=ranked_list(k,ressort_count-m);\n",
    "                    end\n",
    "                    ranked_list(k,l)=trading_order(l);\n",
    "                else\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "        \n",
    "        interest_rate_history(k,i) = interest_rate(k,1);\n",
    "    end\n",
    "    ranked_list_init = ranked_list;\n",
    "    endowments_reserves_history(:,i) = sum(endowments,2);\n",
    "    endowments_debts_history(:,i) = sum(endowments,1)';\n",
    "    abso_speed_history(:,i) = abso_speed;\n",
    "    devaluation_history(:,i) = deval_history;\n",
    "    ranking_history(:,:,i) = ranked_list_init;\n",
    "end\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Discussion on why we picked this scenario as the baseline calibration for testing the different covid one on top\n",
    "\n",
    "Below is the baseline scenario we chose as calibration before running the different covid scenarii. The reason we chose this one was that given initial conditions close to that of 1945 in debt repartition and trade preferences, and given the Marshall plan, the Germany forgiveness and the Korean war stimulus to Japan, it would give with high frequency approximately correct share of reserves and GDP (using \"absorption speed\" as proxy) now (with high frequency referring to the random initialization - as here we have \"correct\" contemporary outputs more than 80% of the times with random initialization in 1945 and hard coded shocks after).\n",
    "\n",
    "The time_counter parameter is the main one that has been played with - the scaling factor 50 below (one math explanation could be that since there's a total of 100 rounds here a scaling by approximately 100 (as in 50 + 50*(a random number between 0 and 1)) is appropriate.\n",
    "\n",
    "duration_T_updated = 50.*(1+rand(1,1))*sum(cakes)./sum(abso_speed);\n",
    "\n",
    "This graph that represents the calibrated baseline scenario (100 rounds after 1945) is obtained with the code in the cell below -\n",
    "<img src=\"Screen%20Shot%202020-04-06%20at%2012.14.43%20PM.png\" /> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "sum_ranking_history = zeros(number_of_countries,number_of_rounds);\n",
    "i=1;\n",
    "for j=1:number_of_countries\n",
    "    for k=1:number_of_countries\n",
    "        [~,indexes]=sort(ranking_history(k,:,i));\n",
    "        score_for_one_country = ((number_of_countries+1)*ones(1,1)-indexes);\n",
    "        sum_ranking_history(j,1) = sum_ranking_history(j,1)+score_for_one_country(1,j);\n",
    "    end\n",
    "end\n",
    "sum_ranking_history_b = sum_ranking_history;\n",
    "\n",
    "for i=2:number_of_rounds\n",
    "    for j=1:number_of_countries\n",
    "        for k=1:number_of_countries\n",
    "            [~,indexes]=sort(ranking_history(k,:,i));\n",
    "            score_for_one_country = ((number_of_countries+1)*ones(1,1)-indexes);\n",
    "            sum_ranking_history(j,i) = sum_ranking_history(j,i)+score_for_one_country(1,j);\n",
    "        end\n",
    "    end\n",
    "    sum_ranking_history(:,i)=(sum_ranking_history(:,i)+sum_ranking_history(:,i-1));%./(mean(sum_ranking_history(:,i-1)));\n",
    "    sum_ranking_history_b(:,i)=sum_ranking_history(:,i)-sum_ranking_history(:,i-1);%./(mean(sum_ranking_history(:,i-1)));\n",
    "end\n",
    "\n",
    "\n",
    "figure;\n",
    "A=trading_preferences;\n",
    "G = digraph(A);\n",
    "LWidths = 5*G.Edges.Weight/max(G.Edges.Weight);\n",
    "\n",
    "subplot(2,3,1);\n",
    "plot(G,'LineWidth',LWidths)\n",
    "title('Trade preferences among the 12 (numbered) countries graph')\n",
    "\n",
    "\n",
    "subplot(2,3,2);\n",
    "plot(interest_rate_history')\n",
    "title('Interest rate history')\n",
    "legend(tag)\n",
    "    \n",
    "subplot(2,3,3);\n",
    "plot(abso_speed_history')\n",
    "title('Cake eating speed history')\n",
    "%legend(tag)\n",
    "\n",
    "subplot(2,3,4);\n",
    "plot(sum_ranking_history_b')\n",
    "title('Ranking history by country')\n",
    "%legend(tag)\n",
    "\n",
    "subplot(2,3,5);\n",
    "plot(endowments_debts_history')\n",
    "title('Cumulated debts generated by country history')\n",
    "%legend(tag)\n",
    "\n",
    "subplot(2,3,6);\n",
    "plot(endowments_reserves_history')\n",
    "title('Cumulated reserves by country history')\n",
    "%legend(tag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "figure;\n",
    "plot(sum_ranking_history_b')\n",
    "title('Ranking history by country')\n",
    "legend(tag)\n",
    "\n",
    "figure;\n",
    "plot(interest_rate_history')\n",
    "title('Interest rate history')\n",
    "legend(tag)\n",
    "\n",
    "figure;\n",
    "plot(endowments_debts_history')\n",
    "title('Cumulated debts generated by country history')\n",
    "legend(tag)\n",
    "\n",
    "figure;\n",
    "plot(abso_speed_history')\n",
    "title('Cake eating speed history')\n",
    "legend(tag)\n",
    "\n",
    "figure;\n",
    "plot(interest_rate_history')\n",
    "title('Interest rate history')\n",
    "legend(tag)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Post Covid debt simulations\n",
    "\n",
    "Commentated code in the cells below present different tested scenarii, that you can uncomment and adjust at will. Here are a few intuitions behind how these scenarii were designed and what the code represent :\n",
    "\n",
    "- **Scenario 1:** *in the case of everything constant (pre Trump US and China trade relations)*\n",
    "\n",
    "- **Scenario 2:** *similar results in the case of everything constant, with just additional reliance on trade with China*\n",
    "\n",
    "- **Scenario 3:** *in the case of everything constant among all countries except China and US, who in that scenario stop trading with each other*\n",
    "\n",
    "- **Scenario 4:** *in the case of stopping trade between China and the US AND additional reliance by other countries on China* \n",
    " \n",
    "#### Scenarii after our monetary stabilization scheme \n",
    "\n",
    "Some lines on our monetary stabilization scheme. \n",
    "*(details in the paper - in the model it is just reflected as more willingness from participating countries to accept others' devaluation - see the commented code in the last cells of this notebook. Un-implemented here is also the extra information each country will have on how much latitude they will have at each round on their debt, which should also help in addition of the effects produced here to stabilize debts, interest rates and balance global reserve currencies)*\n",
    "\n",
    "Then we run it with all four of the scenarii above.\n",
    "It is basically the same code as the big cell above for one round, with just introduction of the Covid shock"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Introduction of Covid shock\n",
    "\n",
    "number_of_rounds = 150\n",
    "\n",
    "\n",
    "%Scenario 1 : nothing else to be added in this cell\n",
    "\n",
    "\n",
    "%Scenario 2 : add just the following three lines\n",
    "%for p=1:12\n",
    "%    trading_preferences(p,6)=4;\n",
    "%end\n",
    "\n",
    "\n",
    "%Scenario 3 : add just the following two lines\n",
    "%trading_preferences(1,6)=0;\n",
    "%trading_preferences(6,1)=0;\n",
    "\n",
    "\n",
    "%Scenario 4 : add just the following five lines\n",
    "%for p=1:12\n",
    "%    trading_preferences(p,6)=4;\n",
    "%end\n",
    "%trading_preferences(1,6)=0;\n",
    "%trading_preferences(6,1)=0;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Then the same big chunk of code\n",
    "\n",
    "for i=101:number_of_rounds\n",
    "    \n",
    "    cakes = sqrt(sum(endowments,1)'.*(1+rand(number_of_countries,1)));\n",
    "    \n",
    "    if i==101||i==103||i==103\n",
    "        cakes(1,1)\n",
    "        cakes(1,1) = cakes(1,1)+0.2*sum(endowments(:,1))\n",
    "        cakes(2,1) = cakes(2,1)+0.05*sum(endowments(:,2))\n",
    "        \n",
    "        cakes(3,1) = cakes(3,1)+0.1*sum(endowments(:,3))\n",
    "    end\n",
    "        \n",
    "    abso_speed = sqrt((sum(endowments,2)+sum(endowments,1)').*(1+rand(number_of_countries,1)));\n",
    "    \n",
    "    sum_of_generated_cakes = sum_of_generated_cakes + cakes;\n",
    "    sum_of_abso_speed = sum_of_abso_speed + abso_speed;\n",
    "    \n",
    "    initial_pos_round = cakes;\n",
    "    duration_T_updated = 50.*(1+rand(1,1))*sum(cakes)./sum(abso_speed);\n",
    "    \n",
    "    cakes_from_previous_round = cakes;\n",
    "    abso_speed_from_previous_round = abso_speed;\n",
    "    \n",
    "    abso_history(1,i)=sum(abso_speed);\n",
    "    sum_cakes_history(1,i)=sum(cakes);\n",
    "    \n",
    "    %while\n",
    "    time_counter=0;\n",
    "    cakes_counter=0;\n",
    "    %rank_counter_tot=0;\n",
    "    rank_counter = ones(number_of_countries,1);\n",
    "    removed_cake_row = zeros(number_of_countries,1);\n",
    "    k=1;\n",
    "    latest_finished_cake = 0;\n",
    "    will_be_totally_consumed = zeros(number_of_countries,1);\n",
    "    %while (duration_T_updated>0 && cakes_counter<number_of_countries) %&& rank_counter_tot<number_of_countries\n",
    "    while (duration_T_updated>0 && cakes_counter<number_of_countries) %&& rank_counter_tot<number_of_countries\n",
    "        %still_available_rank = 1;\n",
    "        initial_pos_updated = cakes;\n",
    "        diff_between_wished_and_offered = zeros(number_of_countries,1);\n",
    "        \n",
    "        for l=1:number_of_countries\n",
    "            if removed_cake_row(ranked_list(l,1))>0\n",
    "                o=1;\n",
    "                u=1;\n",
    "                %ranked_list(l,1)=ranked_list(l,o);\n",
    "                %while o<number_of_countries && u<(number_of_countries-2)\n",
    "                if  removed_cake_row(ranked_list(l,o+1),1)>0\n",
    "                    u=o+1;\n",
    "                    while ((u<(number_of_countries-1)) && (removed_cake_row(ranked_list(l,u+1),1)>0))\n",
    "                        u=u+1;\n",
    "                    end\n",
    "                    ranked_list(l,o)=ranked_list(l,u+1);\n",
    "                    %o=o+1;\n",
    "                else\n",
    "                    ranked_list(l,o)=ranked_list(l,o+1);\n",
    "                    %o=o+1;\n",
    "                end\n",
    "                %end\n",
    "                rank_counter(j,1)=rank_counter(j,1)+1;\n",
    "            end\n",
    "            %{\n",
    "                for j=1:number_of_countries\n",
    "                    if ranked_list(j,1)==l\n",
    "                        ranked_list(j,1)=ranked_list(j,rank_counter(j,1)+1);\n",
    "                        o=2;\n",
    "                        while o<number_of_countries\n",
    "                            if  removed_cake_row(o,1)==1 && o<(number_of_countries-1)\n",
    "                                ranked_list(j,o)=ranked_list(j,o+2);\n",
    "                                o=o+1;\n",
    "                            else\n",
    "                                ranked_list(j,o)=ranked_list(j,o+1);\n",
    "                                o=o+1;\n",
    "                            end\n",
    "                        end\n",
    "                        rank_counter(j,1)=rank_counter(j,1)+1;\n",
    "                    end\n",
    "                end\n",
    "            %}\n",
    "            %end\n",
    "        end\n",
    "        \n",
    "        for j=1:number_of_countries\n",
    "            if removed_cake_row(j,1)>0\n",
    "            else\n",
    "                if sum(abso_speed(ranked_list(:,1)==j))>cakes(j,1)\n",
    "                    will_be_totally_consumed(j,1)=will_be_totally_consumed(j,1)+1;\n",
    "                    diff_between_wished_and_offered(j,1) = sum(abso_speed(ranked_list(:,1)==j))/initial_pos_updated(j,1);\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "        \n",
    "        if sum(diff_between_wished_and_offered)==0\n",
    "            for j=1:number_of_countries\n",
    "                if removed_cake_row(j,1)>0\n",
    "                else\n",
    "                    diff_between_wished_and_offered(j,1) = sum(abso_speed(ranked_list(:,1)==j))/initial_pos_updated(j,1);\n",
    "                    \n",
    "                    will_be_totally_consumed(j,1)=will_be_totally_consumed(j,1)+1;\n",
    "                end\n",
    "            end\n",
    "        else\n",
    "        end\n",
    "        %{\n",
    "        for j=1:number_of_countries\n",
    "            if removed_cake_row(j,1)==1\n",
    "            else\n",
    "                if sum(abso_speed(ranked_list(:,1)==j))>cakes(j,1)\n",
    "                    will_be_totally_consumed(j,1)=will_be_totally_consumed(j,1)+1;\n",
    "                    diff_between_wished_and_offered(j,1) = sum(abso_speed(ranked_list(:,1)==j))-initial_pos_updated(j,1);\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "        \n",
    "        \n",
    "        %}\n",
    "        \n",
    "        [~,consumption_order]=sort(diff_between_wished_and_offered,'descend');\n",
    "        \n",
    "        if sum(diff_between_wished_and_offered)==0\n",
    "            [ii,jj]=find(~removed_cake_row);\n",
    "            if size(ii)==1\n",
    "                consumption_order(1)=ii;\n",
    "            else\n",
    "                for j=1:size(ii)\n",
    "                    consumption_order(j)=ii(j);\n",
    "                end\n",
    "            end\n",
    "        else\n",
    "        end\n",
    "        \n",
    "        %= cakes - cakes(consumption_order(1),1)*ones(number_of_countries,1);\n",
    "        %cakes(consumption_order(1),1)=1;\n",
    "        \n",
    "        if (duration_T_updated-cakes(consumption_order(1),1))>0\n",
    "            duration_T_updated = duration_T_updated - cakes(consumption_order(1),1);\n",
    "            for j=1:number_of_countries\n",
    "                if ranked_list(j,1)==consumption_order(1)\n",
    "                    endowments(j,consumption_order(1)) = endowments(j,consumption_order(1))+(abso_speed(j,1)./(sum(abso_speed(ranked_list(:,1)==consumption_order(1)))))*initial_pos_updated(consumption_order(1),1);\n",
    "                elseif cakes(ranked_list(j,1),1)==0\n",
    "                    removed_cake_row(ranked_list(j,1),1)=removed_cake_row(ranked_list(j,1),1)+1;\n",
    "                    \n",
    "                else\n",
    "                    %endowments is read as cakes = column, lines = eating\n",
    "                    %country\n",
    "                    endowments(j,ranked_list(j,1)) = endowments(j,ranked_list(j,1))+(abso_speed(j,1)*cakes(consumption_order(1),1))/(sum(abso_speed(ranked_list(:,1)==consumption_order(1))));\n",
    "                    %endowments(j,ranked_list(j,1)) = endowments(j,ranked_list(j,1))+(abso_speed(j,1)./(sum(abso_speed(ranked_list(:,1)==consumption_order(1)))))*initial_pos_updated(ranked_list(j,1),1);\n",
    "                    cakes(ranked_list(j,1),1)=initial_pos_updated(ranked_list(j,1),1)-(sum(abso_speed(ranked_list(:,1)==ranked_list(j,1)))*cakes(consumption_order(1),1))/(sum(abso_speed(ranked_list(:,1)==consumption_order(1))));\n",
    "                    \n",
    "                    %cakes(ranked_list(j,1),1)=initial_pos_updated(ranked_list(j,1),1)*(1-((sum(abso_speed(ranked_list(:,1)==ranked_list(j,1))))./(sum(abso_speed(ranked_list(:,1)==consumption_order(1))))));\n",
    "                    \n",
    "                end\n",
    "                %what about ties ? -> consume half and half ?\n",
    "                %endowment add the others eating their first choice during that\n",
    "                \n",
    "                %time\n",
    "            end\n",
    "            time_counter = time_counter + cakes(consumption_order(1),1);\n",
    "            %cakes\n",
    "            cakes(consumption_order(1),1) = 0;\n",
    "            removed_cake_row(consumption_order(1),1)=removed_cake_row(consumption_order(1),1)+1;\n",
    "            \n",
    "        else\n",
    "            %[~,consumption_order]=sort(diff_between_wished_and_offered,'descend');\n",
    "            cakes(consumption_order(1),1) = cakes(consumption_order(1),1) - duration_T_updated;\n",
    "            \n",
    "            time_counter = time_counter + duration_T_updated;\n",
    "            \n",
    "            for j=1:number_of_countries\n",
    "                if ranked_list(j,1)==consumption_order(1)\n",
    "                    endowments(j,consumption_order(1)) = endowments(j,consumption_order(1))+(abso_speed(j,1)./(sum(abso_speed(ranked_list(:,1)==consumption_order(1)))))*duration_T_updated;\n",
    "                    \n",
    "                elseif cakes(ranked_list(j,1),1)==0\n",
    "                    removed_cake_row(ranked_list(j,1),1)=removed_cake_row(ranked_list(j,1),1)+1;\n",
    "                    \n",
    "                else\n",
    "                    %endowments is read as cakes = column, lines = eating\n",
    "                    %country\n",
    "                    endowments(j,ranked_list(j,1)) = endowments(j,ranked_list(j,1))+(abso_speed(j,1)*duration_T_updated)/(sum(abso_speed(ranked_list(:,1)==consumption_order(1))));\n",
    "                    cakes(ranked_list(j,1),1)=cakes(ranked_list(j,1),1)-(abso_speed(j,1)*duration_T_updated)/(sum(abso_speed(ranked_list(:,1)==consumption_order(1))));\n",
    "                    \n",
    "                    %endowments(j,ranked_list(j,1)) = endowments(j,ranked_list(j,1))+(abso_speed(j,1)./(sum(abso_speed(ranked_list(:,1)==consumption_order(1)))))*duration_T_updated;\n",
    "                    %cakes(ranked_list(j,1),1)=((cakes(consumption_order(1),1) - duration_T_updated)/cakes(consumption_order(1),1))*initial_pos_updated(ranked_list(j,1),1)*(1-((sum(abso_speed(ranked_list(:,1)==ranked_list(j,1))))./(sum(abso_speed(ranked_list(:,1)==consumption_order(1))))));\n",
    "                end\n",
    "                %what about ties ? -> consume half and half ?\n",
    "                %cakes(consumption_order(1),1) = 0;\n",
    "                %endowment add the others eating their first choice during that\n",
    "                %time\n",
    "            end\n",
    "            \n",
    "            duration_T_updated = 0;\n",
    "            \n",
    "        end\n",
    "        latest_finished_cake = consumption_order(1);\n",
    "        \n",
    "        cakes_counter = cakes_counter + 1;\n",
    "        k=k+1;\n",
    "        duration_T_updated_history(1,i)=duration_T_updated;\n",
    "    \n",
    "    %duration_T_updated_history(1,i)=duration_T_updated;\n",
    "    end\n",
    "    \n",
    "    for j=1:number_of_countries\n",
    "        if (initial_pos_round(j,1)-cakes(j,1))>0\n",
    "            %endowments(:,j)=endowments(:,j)*((initial_pos_round(j,1)-cakes(j,1))/initial_pos_round(j,1));\n",
    "            %endowments(:,j)=endowments(:,j)*(1-(cakes(j,1)/(initial_pos_round(j,1).*i)));\n",
    "            endowments(:,j)=endowments(:,j)*(1-(cakes(j,1)/initial_pos_round(j,1)));\n",
    "        else\n",
    "        end\n",
    "        if cakes(j,1)==0\n",
    "            history_counter(j,1) = history_counter(j,1) + 1;\n",
    "            successfully_loaded_cake_last_round(j,1) = 1;\n",
    "            interest_rate(j,1)=interest_rate(j,1)./(1+rand(1,1));\n",
    "        else\n",
    "            %interest_rate(j,1)=min(1,max(interest_rate_history(j,1),interest_rate(j,1).*(1+rand(1,1))));\n",
    "            %deval_history(j,1) = deval_history(j,1)+1 ;\n",
    "            %trading_preferences(j,j)=trading_preferences(j,j)+1;\n",
    "        end\n",
    "    end\n",
    "    %}\n",
    "    [~,success_order]=sort(history_counter,'descend');\n",
    "    %P = perms(success_order);\n",
    "    %ranked_list = P(end-number_of_countries+1:end,:);\n",
    "    \n",
    "    ranked_list = repmat(success_order',number_of_countries,1);\n",
    "    \n",
    "    \n",
    "    \n",
    "    for k=1:number_of_countries\n",
    "        \n",
    "        r1 = randperm(number_of_countries,2*round(number_of_countries*fraction_ranking));\n",
    "        \n",
    "        \n",
    "        for j=1:round(number_of_countries*fraction_ranking)\n",
    "            inter=ranked_list(k,r1(1,j));\n",
    "            ranked_list(k,r1(1,j))=ranked_list(k,r1(1,2*j));\n",
    "            ranked_list(k,r1(1,2*j))=inter;\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    for k=1:number_of_countries\n",
    "        %trading_preferences(k,k)=trading_preferences(k,k)+1;\n",
    "        %[~,trading_order]=sort(trading_preferences(k,:).*(ones(1,number_of_countries)+endowments(k,:)),'descend');\n",
    "        [~,trading_order]=sort(trading_preferences(k,:).*(ones(1,number_of_countries)+max(0,successfully_loaded_cake_last_round(k,1).*(history_counter(k,1)-deval_history(k,1)).*endowments(k,:)*(interest_rate(k,1)))),'descend');\n",
    "        \n",
    "        %could rank by size of trade and by size of trading partner\n",
    "        res=sum(trading_preferences(k,:)~=0);\n",
    "        if res>0\n",
    "            for l=1:res\n",
    "                ressort_count=find(ranked_list(k,:)==trading_order(l));\n",
    "                if ressort_count>l\n",
    "                    for m=1:(ressort_count-l)\n",
    "                        ranked_list(k,ressort_count+1-m)=ranked_list(k,ressort_count-m);\n",
    "                    end\n",
    "                    ranked_list(k,l)=trading_order(l);\n",
    "                else\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "        \n",
    "        interest_rate_history(k,i) = interest_rate(k,1);\n",
    "    end\n",
    "    ranked_list_init = ranked_list;\n",
    "    %total_ranks = total_ranks +\n",
    "    endowments_reserves_history(:,i) = sum(endowments,2);\n",
    "    endowments_debts_history(:,i) = sum(endowments,1)';\n",
    "    abso_speed_history(:,i) = abso_speed;\n",
    "    devaluation_history(:,i) = deval_history;\n",
    "    ranking_history(:,:,i) = ranked_list_init;\n",
    "    \n",
    "    %Graph = digraph(ranking_history);\n",
    "    %LWidths = 5*Graph.Edges.Weight/max(Graph.Edges.Weight);\n",
    "    \n",
    "    %figure\n",
    "    %plot(Graph,'EdgeLabel',Graph.Edges.Weight,'LineWidth',LWidths)\n",
    "end\n",
    "\n",
    "sum_ranking_history = zeros(number_of_countries,number_of_rounds);\n",
    "%sum_ranking_history_b = zeros(number_of_countries,number_of_rounds);\n",
    "i=1;\n",
    "for j=1:number_of_countries\n",
    "    for k=1:number_of_countries\n",
    "        [~,indexes]=sort(ranking_history(k,:,i));\n",
    "        score_for_one_country = ((number_of_countries+1)*ones(1,1)-indexes);\n",
    "        sum_ranking_history(j,1) = sum_ranking_history(j,1)+score_for_one_country(1,j);\n",
    "    end\n",
    "end\n",
    "%sum_ranking_history = sum_ranking_history./(mean(sum_ranking_history(:,1)));\n",
    "sum_ranking_history_b = sum_ranking_history;\n",
    "\n",
    "for i=2:number_of_rounds\n",
    "    for j=1:number_of_countries\n",
    "        for k=1:number_of_countries\n",
    "            [~,indexes]=sort(ranking_history(k,:,i));\n",
    "            score_for_one_country = ((number_of_countries+1)*ones(1,1)-indexes);\n",
    "            sum_ranking_history(j,i) = sum_ranking_history(j,i)+score_for_one_country(1,j);\n",
    "        end\n",
    "    end\n",
    "    sum_ranking_history(:,i)=(sum_ranking_history(:,i)+sum_ranking_history(:,i-1));%./(mean(sum_ranking_history(:,i-1)));\n",
    "    sum_ranking_history_b(:,i)=sum_ranking_history(:,i)-sum_ranking_history(:,i-1);%./(mean(sum_ranking_history(:,i-1)));\n",
    "end\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "figure;\n",
    "A=trading_preferences;\n",
    "G = digraph(A);\n",
    "LWidths = 5*G.Edges.Weight/max(G.Edges.Weight);\n",
    "\n",
    "\n",
    "subplot(2,2,1);\n",
    "\n",
    "plot(devaluation_history')\n",
    "title('Cumulated number of devaluations history')\n",
    "legend(tag)\n",
    "\n",
    "subplot(2,2,2);\n",
    "plot(abso_speed_history')\n",
    "title('Cake eating speed history')\n",
    "%legend(tag)\n",
    "\n",
    "\n",
    "subplot(2,2,3);\n",
    "plot(endowments_debts_history')\n",
    "title('Cumulated debts generated by country history')\n",
    "%legend(tag)\n",
    "\n",
    "subplot(2,2,4);\n",
    "plot(endowments_reserves_history')\n",
    "title('Cumulated reserves by country history')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "figure;\n",
    "plot(endowments_debts_history')\n",
    "title('Cumulated debts generated by country history')\n",
    "legend(tag)\n",
    "\n",
    "figure;\n",
    "plot(abso_speed_history')\n",
    "title('Cake eating speed history')\n",
    "legend(tag)\n",
    "\n",
    "figure;\n",
    "plot(sum_ranking_history_b')\n",
    "title('Ranking history by country')\n",
    "legend(tag)\n",
    "\n",
    "figure;\n",
    "plot(endowments_reserves_history')\n",
    "title('Cumulated reserves by country history')\n",
    "legend(tag)"
   ]
  }
 ],
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