Reactive Strategies: An Inch of Memory, a Mile of Equilibria

We explore how an incremental change in complexity of strategies (“an inch memory”) repeated interactions influences the sets Nash equilibrium (NE) strategy and payoff profiles. For this, we introduce two most basic setups games, where players are allowed to use only reactive for which a probability players’ actions depends on opponent’s preceding move. The first game is trivial inherits equilibria stage since have unconditional (memory-less) Reactive Strategies (RSs); second one, also conditional stochastic RSs. This extension can be understood as result evolution or learning that increases strategies. with RSs, characterize all possible NE profiles RSs find symmetric games admitting these equilibria. By setting benchmark least profile memory-less demonstrate classes infinitely many (“a mile equilibria”) Pareto dominate benchmark. Since there no folk theorem improvement over best one gain memory.