Multiperson bargaining and strategic complexity

We investigate the effect of introducing costs of complexity in the n-person unanimity bargaining game. 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 a plausible notion of complexity that captures length of memory, we find that the introduction of complexity costs (lexicographically with the standard payoffs) does not reduce the range of possible allocations but does 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 game with complexity costs if and only if t ≤ n. We use the limit on delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, we also show that "noisy Nash equilibrium" with complexity costs sustains only the unique stationary subgame perfect equilibrium allocation.