Provides an R package called empiricalGameTheory for analysing heuristic games using empirical game theory (Wellman 2006). Heuristic payoff matrices can be encapsulated in a HeuristicGame object. These can then be analysed as evolutionary games by numerically integrating the replicator dynamics ODE for different initial conditions and then plotting the resulting trajectories in phase space.

Installation

R CMD INSTALL empiricalGameTheory

Example usage

library(empiricalGameTheory)

# Payoff matrix for Rock, Paper, Scissors
payoff.matrix.rps <- matrix( c(
	0, 0, 2,  0,  0,  0,
	0, 1, 1,  0, -1,  1,
	2, 0, 0,  0,  0,  0,
	1, 1, 0, -1,  1,  0,
	0, 2, 0,  0,  0,  0,
	1, 0, 1,  1,  0, -1),
	    ncol = 6, byrow=T)

# Encapsulate in a HeuristicGame object
game.rps <- HeuristicGameFromPayoffMatrix(payoff.matrix.rps, strategies = c('R', 'P', 'S'))

# Generate the initial values for the replicator dynamics ODE
initial.values.random <- GenerateRandomInitialValues()

# Integrate from t=0 to t=100 in steps of delta_t = 1/100
times.rd <- seq(0, 100, by=0.01)

# Integrate the replicator dynamics ODE for each initial value
game.rps.analysed <- Analyse(game.rps, initial.values = initial.values.random, times = times.rd)

# Plot the resulting phase-space
plot(game.rps.analysed)

For a more complete example of analysing an actual agent-based model, see this example in which we analyse a financial market model implemented in the JASA framework.

References

Wellman, M. P. (2006). Methods for Empirical Game-Theoretic Analysis. In Twenty-First National Conference on Artificial Intelligence (AAAI-06) (pp. 1152–1155). Boston, Massachusetts.