Repeated play of families of games by resource-constrained players

This paper studies a repeated play of a family of games by resource-constrained players. To economize on reasoning resources, the family of games is partitioned into subsets of games which players do not distinguish. An example is constructed to show that when games are played a finite number of times, partitioning of the game set according to a coarse exogenously given partition might introduce new symmetric equilibrium payoffs which Pareto dominate best equilibrium outcomes with distinguished games. Moreover, these new equilibrium payoffs are also immune to evolutionary pressure at the partition selection stage.