Rubinstein and Wolinsky (1990b) consider a simple decentralized market in which agents either meet randomly or choose their partners volunatarily and bargain over the terms on which they are willing to trade. Intuition suggests that if there are no transaction costs, the outcome of this matching and bargaining game should be the unique competitive equilibrium. This does not happen. In fact, Rubinstein and Wolinsky show that any price can be sustained as a sequential equilibrium of this game. In this paper, I consider Rubinstein and Wolinsky’s model and show that if the complexity costs of implementing strategies enter players’ preferences (lexicographically), together with the standard payoﬀ in the game, then the only equilibrium that survives is the unique competitive outcome. This will be done both for the random matching and for the voluntary matching models. Thus the paper demonstrates that complexity costs might have a role in providing a justiﬁcation for the competitive outcome.
Sabourian, Hamid, "Bargaining and Markets: Complexity and the Walrasian Outcome" (2000). Cowles Foundation Discussion Papers. 1499.