Multiperson bargaining and strategic complexity

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, d elays in agreement are also possible in such equilibria. By limiting oursel ves 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 doe s 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 co mplexity costs if and only if t less than or equal to n. We use the limit:o n delay result to establish that, in equilibrium, the strategies implement stationary behavior. Finally, Re also show that "noisy Nash equilibrium" wi th complexity costs sustains only the unique stationary subgame perfect equ ilibrium allocation.