Evolutionary Strategies with Analogy Partitions in p-guessing Games

In Keynesian Beauty Contests notably modeled by p-guessing games, players try to guess the average of guesses multiplied by p. Convergence of plays to Nash equilibrium has often been justified by agents' learning. However, interrogations remain on the origin of reasoning types and equilibrium behavior when learning takes place in unstable environments. When successive values of p can take values above and below 1, bounded rational agents may learn about their environment through simplified representations of the game, reasoning with analogies and constructing expectations about the behavior of other players. We introduce an evolutionary process of learning to investigate the dynamics of learning and the resulting optimal strategies in unstable p-guessing games environments with analogy partitions. As a validation of the approach, we first show that our genetic algorithm behaves consistently with previous results in persistent environments, converging to the Nash equilibrium. We characterize strategic behavior in mixed regimes with unstable values of p. Varying the number of iterations given to the genetic algorithm to learn about the game replicates the behavior of agents with different levels of reasoning of the level k approach. This evolutionary process hence proposes a learning foundation for endogenizing existence and transitions between levels of reasoning in cognitive hierarchy models.