N-Person Bargaining and Strategic Complexity

Abstract

We investigate the effect of introducing costs of complexity in the n -person unanimity bargaining game. In particular, the paper provides a justification for stationary equilibrium strategies in the class of games where complexity costs matter. As is well-known, in this game every individually rational allocation is sustainable as a Nash equilibrium (also as a subgame perfect equilibrium if players are sufficiently patient and if n > 2). Moreover, delays in agreement are also possible in such equilibria. By limiting ourselves to strategies that can be implemented by a machine (automaton) and by suitably modifying the definition of complexity for the purpose of analysing a single extensive form, we find that complexity costs do not reduce the range of possible allocations but they do limit the amount of delay that can occur in any agreement. In particular, we show that in any n-player game, for any allocation z; an agreement on z at any period t can be sustained as a Nash equilibrium of the machine game with complexity costs if and only if t · n: We use the limit on delay result to establish that, in equilibrium, the machines implement stationary strategies. Finally, we also show that noisy Nash equilibrium” with complexity costs sustain only the unique stationary subgame perfect equilibrium allocation.