和光 純

This paper considers von Neumann-Morgenstern (vNM) stable sets in marriage games. Ehlers (Journal of Economic Theory 134: 537-547, 2007) showed that if a vNM stable set exists in a marriage game, the set is a maximal distributive lattice of matchings that includes all core matchings. To determine what matchings form a vNM stable set, we propose a polynomial-time algorithm that finds a man-optimal matching and a woman-optimal matching in a vNM stable set of a given marriage game. This algorithm also generates a modified preference profile such that a vNM stable set is obtained as the core of a marriage game with the modified preference profile. It is well known that cores of marriage games are nonempty. However, the nonemptiness of cores does not imply the existence of a vNM stable set. It is proved using our algorithm that there exists a unique vNM stable set for any marriage game.

This paper considers von Neumann-Morgenstern (vNM) stable sets in marriage games. Ehlers (Journal of Economic Theory 134: 537-547, 2007) showed that if a vNM stable set exists in a marriage game, the set is a maximal distributive lattice of matchings that includes all core matchings. To determine what matchings form a vNM stable set, we propose a polynomial-time algorithm that finds a man-optimal matching and a woman-optimal matching in a vNM stable set of a given marriage game. This algorithm also generates a modified preference profile such that a vNM stable set is obtained as the core of a marriage game with the modified preference profile. It is well known that cores of marriage games are nonempty. However, the nonemptiness of cores does not imply the existence of a vNM stable set. It is proved using our algorithm that there exists a unique vNM stable set for any marriage game. © 2010 Springer Science+Business Media, LLC.

Complementary slackness of a pair of dual linear programming problems implies the remark of Sotomayor (2003) that assignment games have singleton cores only when multiple optimal matchings exist.

Complementary slackness of a pair of dual linear programming problems implies the remark of Sotomayor (2003) that assignment games have singleton cores only when multiple optimal matchings exist.

We consider a barter market with multiple types of indivisible goods. Konishi et al. [J. Math. Econ. 35 (2001) 1-15] showed that the core of this market may be empty. We define a normal form game for this market and consider its equilibrium outcomes. Assuming separable strict preferences, we show that the game has a unique Coalition-proof Nash allocation. This Coalition-proof Nash allocation is precisely the unique commodity-wise competitive allocation of the market, and it may be inefficient. The commodity-wise competitive allocation is implementable in Coalition-proof Nash equilibria but not in Strong Nash equilibria. © 2004 Elsevier B.V. All rights reserved.

We consider a barter market with multiple types of indivisible goods. Konishi et al. [J. Math. Econ. 35 (2001) 1-15] showed that the core of this market may be empty. We define a normal form game for this market and consider its equilibrium outcomes. Assuming separable strict preferences, we show that the game has a unique Coalition-proof Nash allocation. This Coalition-proof Nash allocation is precisely the unique commodity-wise competitive allocation of the market, and it may be inefficient. The commodity-wise competitive allocation is implementable in Coalition-proof Nash equilibria but not in Strong Nash equilibria. (c) 2004 Elsevier B.V. All rights reserved.

We consider the n-player houseswapping game of Shapley and Scarf (1974), with indifferences in preferences allowed. It is well known that the strict core of such a game may be empty, single valued, or multi valued. We define a condition on such games called segmentability, which means that the set of players can be partitioned into a top trading segmentation. It generalizes Gale's well-known idea of the partition of players into top trading cycles (which is used to find the unique strict core allocation in the model with no indifference). We prove that a game has a nonempty strict core if and only if it is segmentable. We then use this result to devise an O(n(3)) algorithm which takes as input any houseswapping game, and returns either a strict core allocation or a report that the strict core is empty. Finally, we are also able to construct a linear inequality system whose feasible region's extreme points precisely correspond to the allocations of the strict core. This last result parallels the results of Vande Vate (1989) and Rothblum (1992) for the marriage game of Gale and Shapley (1962).

We consider the n-player houseswapping game of Shapley and Scarf (1974), with indifferences in preferences allowed. It is well known that the strict core of such a game may be empty, single valued, or multi valued. We define a condition on such games called segmentability, which means that the set of players can be partitioned into a top trading segmentation. It generalizes Gale's well-known idea of the partition of players into top trading cycles (which is used to find the unique strict core allocation in the model with no indifference). We prove that a game has a nonempty strict core if and only if it is segmentable. We then use this result to devise an O(n(3)) algorithm which takes as input any houseswapping game, and returns either a strict core allocation or a report that the strict core is empty. Finally, we are also able to construct a linear inequality system whose feasible region's extreme points precisely correspond to the allocations of the strict core. This last result parallels the results of Vande Vate (1989) and Rothblum (1992) for the marriage game of Gale and Shapley (1962).

We study a generalization of Shapley-Scarfs [Journal of Mathematical Economics 1 (1974) 23-37] economy in which multiple types of indivisible goods are traded, We show that many of the distinctive results from the Shapley-Scarf economy do not carry over to this model, even if agents' preferences are strict and can be represented by additively separable utility functions. The core may be empty. The strict core, if nonempty, may be multi-valued, and might not coincide with the set of competitive allocations, Furthermore, there is no Pareto efficient, individually rational, and strategy-proof social choice rule. We also show that the core may be empty in the class of economies with a single type of indivisible good and agents consuming multiple units, even if no complementarity exists among the goods. (C) 2001 Elsevier Science B.V. All rights reserved.