Loss of skills in coordination games

This paper deals with 2‐player coordination games with vanishing actions, which are repeated games where all diagonal payoffs are strictly positive and all non‐diagonal payoffs are zero with the following additional property: At any stage beyond r, if a player has not played a certain action for the last r stages, then he unlearns this action and it disappears from his action set. Such a game is called an r‐restricted game. To evaluate the stream of payoffs we use the average reward. For r = 1 the game strategically reduces to a one‐shot game and for r ≥ 3 in Schoenmakers (Int Game Theory Rev 4:119–126, 2002) it is shown that all payoffs in the convex hull of the diagonal payoffs are equilibrium rewards. In this paper for the case r = 2 we provide a characterization of the set of equilibrium rewards for 2 × 2 games of this type and a technique to find the equilibrium rewards in m × m games. We also discuss subgame perfection.