Dynamics of Three-Strategy Symmetric Games
This Demonstration shows the phase portrait in the 2D simplex of the single-sampling "imitate if better" dynamics in three-strategy symmetric games for large populations.[more]
Consider a population of agents (players) who, in every time step, are randomly matched in pairs for an interaction that can be modeled as a symmetric game. The ordinal preferences over outcomes for the row agent are summarized in the payoff matrix , where a higher number indicates a higher preference. At the end of every time step, after all individuals have played the game, one randomly selected player revises their strategy according to the following rule: I look at another (randomly selected) individual and adopt their strategy if and only if they got a higher payoff than I did. (This is the so-called "single-sampling imitate if better" rule.) With probability , the revising agent adopts a random strategy rather than the one prescribed by the previous rule.
This Demonstration shows the mean dynamic for the agent-based model described. One time unit in the mean dynamic corresponds to one revision for each agent in the population on average. The program also provides a numerical approximation to the critical points of the system and to their corresponding eigenvalues, which are helpful in assessing the dynamic stability of the critical point.[less]
This model is analyzed in detail in .
Snapshot 1: a game with seven critical points
Snapshot 2: rock paper scissors game without noise
Snapshot 3: rock paper scissors game with small noise
Snapshot 4: a game with one critical point and critical regions
Snapshot 5: a game with an internal critical region
Snapshot 6: a game with critical regions only
 S. S. Izquierdo and L. R. Izquierdo, "Stochastic Approximation to Understand Simple Simulation Models," Journal of Statistical Physics, 151(1–2), 2013 pp. 254–276. doi:10.1007/s10955-012-0654-z.