SFB 303 Discussion Paper No. B - 125

Author: Moldovanu, Benny
Title: Bargained Equilibria For Assignment Games Without Side Payments
Abstract: The intersection of the core and the kernel of games with side payments has a very interesting property: A payoff vector is in this intersection if and only if each pair obtains the standard solution in its reduced game, where the standard solution is the only efficient, symmetric and covariant solution to a two-person bargaining problem with side payments. A set with similar properties for general games without side payments is shown not to exist. The equations leading to such a solution may be inconsistent. We show the existence of a set of equilibria for assignment games without side payments, which naturally generalize the intersection of the core and the kernel of similar games with side payments. All the main properties of the old solution are preserved. In the model, bargaining between members of a matched pair is modelled using the paradigms of axiomatic bargaining theory. The disagreement point is endogenuously determined, taking in account outside options which are based on the current payoff of other players. An allocation is in equilibrium if and only if each pair is in equilibrium (obtains a "standard" solution to its reduced game). Existence of equilibria is established via a bargaining process which converge to the set of equilibria. We generalize also the results and approach pionereed by Rochford(1984) for the side-payments case. Our main tools are reduced games and consistency properties: The main idea is one of stability of solutions under partial implementation by subgroups of players which form expectations about outside options. This relates the results to other recent works (Peleg(1985,1986), Hart, Mas-Collel(1989), Thomson, Lensberg(1989)).
Creation-Date: October 1989
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