On the centipede game with a social norm

• We present a reformulation of the centipede game.
• The reformulation hinges on a time-dependent social norm and on player proximity.
• We present sufficient conditions for subgame perfection to dictate cooperative outcomes.

In this paper, we present a formulation of the centipede game where inter-subjectivity between players is formalized through random costs that are an increasing function, in the sense of first-order stochastic dominance, of the number of iterations for which the game is played. This injection of a time-dependent social norm, one that also parametrizes player proximity, as an element of each player’s introspective calculations formalizes a setting under which subgame perfection dictates cooperative outcomes.