Multiperson Bargaining and Strategic Complexity

The authors 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, every individually rational allocation is sustainable as a subgame perfect equilibrium in this game if players are sufficiently patient. By limiting ourselves to strategies which can be implemented by a finite-state machine and by suitably modifying the definition of complexity for the purpose of analysing a single extension form, we find that complexity costs do not reduce the range of possible allocations but do limit the amount of delay that can occur in any agreement and also do exclude use of non-stationary strategies in equilibrium. However, a `noisy Nash equilibrium' with complexity costs turns out to sustain on the unique stationary subgame perfect equilibrium allocation