Procedurally Rational Experimentation in Infinite-Horizon Games- Summary for TARK VIII

Standard notions of equilibrium in infinite-horizon interactions support a course of action by the players' beliefs that a deviation will be "punished". Along the equilibrium path, players optimize with respect to their beliefs and thus never realize these punishments. In the case of infinitely repeated games with complete information, this approach often results in "Folk Theorem". Under the solution concept of Nash Equilibrium (NE), for example, every individually rational payoff profile can be approximated arbitrarily closely by a pure-strategy NE, by properly fixing the punishments that sustain equilibrium behavior. This summary proposes an equilibrium concept, which departs from NE in that along the equilibrium path, players do not strictly conform to optimizing behavior. Their departure from best-replying is not arbitrary or random, but systematic. It is based on the following behavioral principle: Every threat that affects optimal response is tested (finitely many times). Not every threat is realized, but only the "relevant" ones, whose existence affects optimal response.