  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.
