Far-sighted equilibria in 2 × 2, non-cooperative,repeated games

Consider a two-person simultaneous-move game in strategic form. Suppose this game is played over and over at discrete points in time. Suppose, furthermore, that communication is not possible, but nevertheless we observe some regularity in the sequence of outcomes. The aim of this paper is to provide an explanation for the question why such regularity might persist for many (i.e., infinite) periods.Each player, when contemplating a deviation, considers a sequential-move game, roughly speaking of the following form: if I change my strategy this period, then in the next my opponent will take his strategy b and afterwards I can switch to my strategy a, but then I am worse off since at that outcome my opponent has no incentive to change anymore, whatever I do. Theoretically, however, there is no end to such reaction chains. In case that deviating by some player gives him less utility in the long run than before deviation, we say that the original regular sequence of outcomes is far-sighted stable for that player. It is a far-sighted equilibrium if it is far-sighted stable for both players.     

A choice for ‘me’ or for ‘us’? Using we-reasoning to predict cooperation and coordination in games

Cooperation is the foundation of human social life, but it sometimes requires individuals to choose against their individual self-interest. How then is cooperation sustained? How do we decide when instead to follow our own goals? I develop a model that builds on Bacharach (in: Gold, Sugden (eds) Beyond individual choice: teams and frames in game theory, 2006) ??circumspect we-reasoning?? to address these questions. The model produces a threshold cost/benefit ratio to describe when we-reasoning players should choose cooperatively. After assumptions regarding player types and beliefs, we predict how the extent of cooperation varies across games. Results from two experiments offer strong support to the models and predictions herein.