Sequential Bargaining Mechanisms

Peter Cramton , Game-Theoretic Models of Bargaining, Alvin Roth (ed.), Cambridge University Press, Chapter 8, 149–179 , January 1985.

The introductory discussion presented in this chapter considers the simplest type of sequential bargaining games in which the players’ time preferences are described by known and fixed discount rates. I begin by characterizing the class of perfect bargaining mechanisms, which satisfy the desirable properties of incentive compatibility (i.e., each player reports his type truthfully), individual rationality (i.e., every potential player wishes to play the game), and sequential rationality (i.e., it is never common knowledge that the mechanism induced over time is dominated by an alternative mechanism). It is shown that ex post efficiency is unobtainable by any incentive-compatible and individually rational mechanism when the bargainers are uncertain about whether or not they should trade immediately. I conclude by finding those mechanisms that maximize the players’ ex ante utility, and show that such mechanisms violate sequential rationality. Thus, the bargainers would be better off ex ante if they could commit to a mechanism before they knew their private information. In terms of their ex ante payoffs, if the seller’s delay costs are higher than those of the buyer, then the bargainers are better off adopting a sequential bargaining game rather than a static mechanism; however, when the buyer’s delay costs are higher, then a static mechanism is optimal.

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