Intro to Game Theory Assignment 1 Question 2

Find all weakly dominant strategy equilibria for an n-person game given nfg file.

Language and modules

Language: python3 Modules imported:

• sys

##Displays all dominant strategy equilibria for a n-player game

To run the file ./run

sample command: ./run Example1.nfg output1

Input Format

If file is not provided it will throw error "Please pass the name of the game file to be analyzed"

Input file should be in NFG format line 1: Static Content with Title line 2: { Space seperated, double quoted player names } { space seperated integers of #strategies in respect to the players } line 3: line 4: space seperated integers of payoffs to all players for each stratgies combination.

line 1: NFG 1 R "Example1" line 2: { "Player 1" "Player 2" } { 3 3 } line 3: line 4: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3

Solution approach

The approach uses brute-force method. It iterates over each player one by one. In the i^th iteration it finds the best action s_i for all possible values of the strategy S_-i of all other players. If the interesction of s_i for all possible S_-i is null for any player then no dominant strategy equilibrium exists else atleast one exists.

Time Complexity

The complexity is O(N * A). where N is the number of players and A is the product of the number of actions available to each player