Core equivalence theorems for infinite convex games

We show that the core of a continuous convex game on a measurable space of players is a von Neumann-Morgenstern stable set. We also extend the definition of the Mas-Colell bargaining set to games with a measurable space of players, and show that for continuous convex games the core may be strictly included in the bargaining set but it coincides with the set of all countably additive payoff measures in the bargaining set. We provide examples which show that the continuity assumption is essential to our results

Inner Core, Asymmetric Nash Bargaining Solutions and Competitive Payoffs

We investigate the relationship between the inner core and asymmetric Nash bargaining solutions for n-person bargaining games with complete information. We show that the set of asymmetric Nash bargaining solutions for different strictly positive vectors of weights coincides with the inner core if all points in the underlying bargaining set are strictly positive. Furthermore, we prove that every bargaining game is a market game. By using the results of Qin (1993) we conclude that for every possible vector of weights of the asymmetric Nash bargaining solution there exists an economy that has this asymmetric Nash bargaining solution as its unique competitive payoff vector. We relate the literature of Trockel (1996, 2005) with the ideas of Qin (1993). Our result can be seen as a market foundation for every asymmetric Nash bargaining solution in analogy to the results on non-cooperative foundations of cooperative games.Inner Core, Asymmetric Nash Bargaining Solution, Competitive Payoffs, Market Games

Markov Equilibria in Dynamic Matching and Bargaining Games

Rubinstein and Wolinsky (1990) show that a simple homogeneous market with exogenous matching has continuum of (non-competitive) perfect equilibria, but the unique Markov perfect equilibrium is competitive. By contrast, in the more general case of heterogeneous markets, we show there exists a continuum of (non-competitive) Markov perfect equilibria. However, a refinement of the Markov property, which we call monotonicity, does suffice to guarantee perfectly competitive equilibria, if, and only if, it is monotonic. The monotonicity property is closely related to the concept of Nash equilibrium with complexity costs

Bargaining with an Agenda

We propose a new framework for bargaining in which the process follows an agenda. The agenda is represented by a family, parameterized by time, of increasing sets of joint utilities for possible agreements. This is in contrast to the single set used in the standard framework. The set at each time involves all possible agreements on the issues discussed up to that time. A \emph{bargaining solution} for an agenda specifies a path of agreements, one for each time. We characterize axiomatically a solution that is ordinal, meaning that it is covariant with order- preserving transformations of the utility representations. It can be viewed as the limit of a step-by-step bargaining process in which the agreement point of the last negotiation becomes the disagreement point for the next. The stepwise agreements may follow the Nash solution, the Kalai-Smorodinsky solution or many others, and the ordinal solution will still emerge as the steps tend to zero. Shapley showed that ordinal solutions exist for the standard framework for three players but not for two; the present framework generates an ordinal solution for any number of bargainers, in particular for two.bargaining, ordinal utility

Cores of combined games

This paper studies the core of combined games, obtained by summing two coalitional games. It is shown that the set of balanced transferable utility games can be partitioned into equivalence classes of component games whose core is equal to the core of the combined game. On the other hand, for non balanced games, the binary relation associating two component games whose combination has an empty core is not transitive. However, we identify a class of non balanced games which, combined with any other non balanced game, has an empty core.Cooperative games, Core, Additivity, Issue Linkage, Multi Issue Bargaining

Bargaining over a finite set of alternatives

We analyze bilateral bargaining over a finite set of alternatives. We look for “good” ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that satisfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargaining rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued