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

A comparison of the average prekernel and the prekernel

We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral setting

Competitive Outcomes and the Inner Core of NTU Market Games

We consider the inner core as a solution concept for cooperative games with non-transferable utility (NTU) and its relationship to competitive equilibria of markets that are induced by an NTU game. We investigate the relationship between certain subsets of the inner core for NTU market games and competitive payoff vectors of markets linked to the NTU market game. This can be considered as the case in between the two extreme cases of Qin (1993). We extend the results of Qin (1993) to a large class of closed subsets of the inner core: Given an NTU market game we construct a market depending on a given closed subset of its inner core. This market represents the game and further has the given set as the set of payoffs of competitive equilibria. It turns out that this market is not determined uniquely and thus we obtain a class of markets with the desired property.Market Games, Competitive Payoffs, Inner Core

Coalitional Bargaining Equilibria

This paper takes up the foundational issue of existence of stationary subgame perfect equi- libria in a general class of coalitional bargaining games that includes many known bargaining models and models of coalition formation. General sufficient conditions for existence of equilib- ria are currently lacking in many interesting environments: bargaining models with non-concave stage utility functions, models with a Pareto optimal status quo alternative and heterogeneous discount factors, and models of coalition formation in public good economies with consumption lower bounds. This paper establishes existence of stationary equilibrium under compactness and continuity conditions, without the structure of convexity or comprehensiveness used in the extant literature. The proof requires a precise selection of voting equilibria following different proposals. The result is applied to obtain equilibria in models of bargaining over taxes, coalition formation in NTU environments, and collective dynamic programming problems.

A COMPARISON OF THE AVERAGE PREKERNEL AND THE PREKERNEL

We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral settings

Game theory

game theory

A Dual Model of Cooperative Value

An expanded model of value in cooperative games is presented in which value has either a linear or a proportional mode, and NTU value has either an input or an output basis. In TU games, the modes correspond to the Shapley (1953) and proportional (Feldman (1999) and Ortmann (2000)) values. In NTU games, the Nash (1950) bargaining solution and the Owen- Maschler (1989, 1992) value have a linear mode and an input basis. The egalitarian value (Kalai and Samet (1985)) has a linear mode and an output basis. The output-basis NTU proportional value (Feldman (1999)) and the input-basis variant, identified here, complete the model. The TU proportional value is shown to have a random marginal contribution representation and to be in the core of a positive convex game. The output-basis NTU variant is shown to be the unique efficient Hart and Mas-Colell consistent NTU value based on equal proportional gain in two-player TU games. Both NTU proportional values are shown to be equilibrium payoffs in variations of the bargaining game of Hart and Mas-Colell (1996). In these variations, players' probabilities of participation at any point in the game are a function of their expected payoff at that time. Limit results determine conditions under which players with zero individual worth receive zero value. Further results show the distinctive nature of proportional allocations to players with small individual worths. In an example with a continuum of players bargaining with a monopolist, the monopolist obtains the entire surplus.cooperative game, value, mode, basis, bilateral cooperation, endogenous bargaining power, potential, equal proportional gain, consistency, noncooperative bargaining, zero players, monopoly

A comparison of the average prekernel and the prekernel.

We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is approximated by the set of equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average prekernel as the unique solution that satisfies a set of Nash-like axioms for two-person games, and versions of average consistency and its converse for multilateral settings

On Convexity for NTU-Games

For cooperative games with transferable utility, convexity has turned out to be an important and widely applicable concept.Convexity can be defined in a number of ways, each having its own specific attractions.Basically, these definitions fall into two categories, namely those based on a supermodular interpretation and those based on a marginalistic interpretation.For games with non-transferable utility, however, the literature only offers two kinds of convexity, ordinal and cardinal convexity, which both extend the supermodular interpretation.In this paper, we introduce and analyse three new types of convexity for NTU-games that generalise the marginalistic interpretation of convexity.game theory