Rethinking Bargaining Theory
(Lones Smith)
(unpublished manuscript, M.I.T.)

This paper aims for a new approach to bargaining, quite different than Rubinstein (1982), but using his version of the classic bargaining problem: Two impatient individuals wish to agreeably divide a unit pie under complete information. I submit that the players' key motivation is not that offerers enjoy a temporal monopoly, so that spurning any proposal is discretely costly. For that inexorably leads to bargaining game forms like Rubinstein's. Rather, I suppose that players' behaviour is governed solely by their aspiration values (expected payoffs); hence, I simply must consider a continuous time game form.

In a partial reprise of the pre-1970 agenda of bargaining as a concession game, I explore the resulting stationary complete information bargaining game, with endogenous timing and content of offers. When delay occurs, any offer concedes the entire stopping rent --- to wit, players are locked in a war of attrition, awaiting the next concession. Offers are (usually) turned down with positive probability, and aspiration values are a martingale stochastic process.

By tossing out the temporal monopoly, I have done away with any point predictions. Still, there is room here for falsifiable probabilistic implications, as the choice of what and when to offer are stochastically intertwined. An aspired goal of this paper is therefore not the standard deduction that delay occurs or can occur in bargaining, but rather a serious simultaneous consideration of the timing and content of offers. Moreover, I shall investigate how the equilibrium payoff set adjusts with greater patience or risk aversion.

 
Download pdf.