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Multiperson Bargaining and Strategic Complexity
Author(s) -
Chatterjee Kalyan,
Sabourian Hamid
Publication year - 2000
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00169
Subject(s) - subgame perfect equilibrium , unanimity , mathematical economics , nash equilibrium , trembling hand perfect equilibrium , economics , limit (mathematics) , epsilon equilibrium , bargaining problem , lexicographical order , equilibrium selection , normal form game , best response , correlated equilibrium , solution concept , subgame , repeated game , mathematical optimization , game theory , mathematics , combinatorics , mathematical analysis , political science , law
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.