Analogy-based expectation equilibrium

Abstract

It is assumed that players bundle nodes in which other players must move into analogy classes, and players only have expectations about the average behavior in every class. A solution concept is proposed for multi-stage games with perfect information: at every node players choose best-responses to their analogy-based expectations, and expectations are correct on average over those various nodes pooled together into the same analogy classes. The approach is applied to a variety of games. It is shown that a player may beneÞt from having a coarse analogy partitioning. And for simple analogy partitioning,(1) initial cooperation followed by an end opportunistic behavior may emerge in the Þnitely repeated prisoner's dilemma (or in the centipede game), (2) an agreement need not be reached immediately in bargaining games with complete information.

Subgame perfection in ultimatum bargaining trees

“…Gale et al (1995) argue that learning is especially difficult in the ultimatum game and that subgame perfection may be observed in the very long run (see also Roth and Erev, 1995). Jehiel (2005) proposed an analogy-based approach in which first movers discretize their own action space into analogy classes and offer the lower extreme point of the analogy class that would result in acceptance. The reader, undoubtedly, can add to this list.…”

Categorizing others in a large game

“…Such a refinement leads to a special case of Jehiel's (2005) analogy based expectation equilibrium (ABEE). The scope of ABEE is much wider since it is defined for extensive form games and for any partition of opponents' nodes in the game tree.…”

Paying attention to payoffs in analogy-based learning

“…Analogy-based expectations equilibrium, or simply analogy equilibrium, Jehiel 2005;Jehiel and Koessler 2008) provides a powerful tool to understand how steady-state-like equilibrium behavior may differ from Nash equilibrium behavior when players use stereotypical classifications, analogy classes, in learning about others. Stereotypes must be confirmed by experience.…”