Reciprocity and cooperation in repeated coordination games: The principled-player approach
In repeated coordination games, it is known (and obvious) that players will always cooperate if they believe that their opponent will always cooperate. Assuming enough patience, the author derives optimality of cooperation from weaker restrictions on players' beliefs about the opponents' actions (in particular, players may optimally always cooperate even if they begin the game convinced that their opponents will not cooperate). Beliefs are not selected by imposing equilibrium, but the sets of beliefs considered are closed under rational behaviour. The basic intuition is that it should be an optimum for a patient player to cooperate in the attempt to induce the other to do the same if he believes that the attempt will eventually be successfull (i.e.\ if his believes satisfy what the author calls `strict positive influence'). The author shows by a counterexample that this argument fails. Under tight continuity assumptions, he shows that it is however sufficient to require that beliefs also satisfy `negative influence', i.e.\ that the players believe that non-cooperative behaviour will have negative influence on the opponent's inclination to cooperate.
scientific article; zbMATH DE number 1547925