Two support results for the Kalai-Smorodinsky solution in small object division markets

Haake C-J. Two support results for the Kalai-Smorodinsky solution in small object division markets. Working Papers. Institute of Mathematical Economics. Vol 366. Bielefeld: Universität Bielefeld; 2005.We discuss two support results for the Kalai-Smorodinsky bargaining solution in the context of an object division problem involving two agents. Allocations of objects resulting from strategic interaction are obtained as a demand vector in a specific market. For the first support result games in strategic form are derived that exhibit a unique Nash equilibrium. The second result uses subgame perfect equlibria of a game in extensive form. Although there may be multiple equilibria, coordination problems can be removed

Two support results for the Kalai-Smorodinsky solution in small object division markets

We discuss two support results for the Kalai-Smorodinsky bargaining solution in the context of an object division problem involving two agents. Allocations of objects resulting from strategic interaction are obtained as a demand vector in a specific market. For the first support result games in strategic form are derived that exhibit a unique Nash equilibrium. The second result uses subgame perfect equilibria of a game in extensive form. Although there may be multiple equilibria, coordination problems can be removed.support result, object division, market, Kalai-Smorodinsky solution

Monotonicity and Nash implementation in matching markets with contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005) and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.matching with contracts, (Maskin) monotonicity, Nash implementation, stability.

A note on the paradox of smaller coalitions

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy's (1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy's paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy's paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.coalition formation, core, paradox of smaller coalitions, simple games, top coalition property

On Maskin monotonicity of solution based social choice rules

Howard (1992) argues that the Nash bargaining solution is not Nash implementable, as it does not satisfy Maskin monotonicity. His arguments can be extended to other bargaining solutions as well. However, by de.ning a social choice correspondence that is based on the solution rather than on its realizations, one can overcome this shortcoming. We even show that such correspondences satisfy a stronger version of monotonicity that is even su.cient for Nash implementability.Maskin monotonicity, social choice rule, bargaining games, Nash program, mechanism, implementation

Stability and Nash implementation in matching markets with couples

We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a "double stable" matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns all double stable matchings is neither monotonic nor Nash implementable.matching with couples, (Maskin) monotonicity, Nash implementation, stability, weakly responsive preferences

Government versus opposition: Who should be who in the 16th German Bundestag?

We model the process of coalition formation in the 16th German Bundestag as a hedonic coalition formation game. In order to induce players' preferences in the game we apply the Shapley value of the simple game describing all winning coalitions in the Bundestag. Using different stability notions for hedonic games we prove that the "most" stable government is formed by the Union Parties together with the Social Democratic Party.coalition formation, Shapley value, simple games, winning coalitions

An axiomatic approach to composite solutions

We investigate a situation in which gains from cooperation are represented by a cooperative TU-game and a solution proposes a division of coalitional worths. In addition, asymmetries among players outside the game are captured by a vector of exogenous weights. If a solution measures players' payoffs inherent in the game, and a coalition has formed, then the question is how to measure players' overall payoffs in that coalition. For this we introduce the notion of a composite solution. We provide an axiomatic characterization of a specific composite solution, in which exogenous weights enter in a proportional fashion.composite solution, external weights