  Fictitious play does not attribute knowledge of other people’s payoffs or their rationality. It does not depict players as reasoning about the reasoning of others. Instead, it depicts players as performing a mechanical statistical inference that converts an action’s observed historical frequency into a prediction about its future probability of recurrence. For this reason, critics such as Ehud Kalai and Ehud Lehrer (1993) contend that fictitious play attributes to players insufficient recognition that they are engaged in strategic interaction. For instance, a player who reasons in accord with fictitious play implicitly assumes that each opponent plays some stationary (either pure or mixed) strategy. This assumption overlooks that her opponents are themselves updating their beliefs and actions based upon prior interaction. It also prevents players from detecting patterns in the data (such as an opponent who plays one strategy in odd-numbered trials and another strategy in even-numbered trials). Moreover, fictitious play instructs a player to maximize her expected payoff for the current round of play. This “myopic” approach precludes maximizing one’s future expected payoff at the price of lowering one’s current payoff (e.g., playing Hawk rather than Dove even if I expect my opponent to do likewise, since I believe that I can eventually “teach” my opponent to back down and play Dove in future rounds).