论文标题
稳定的匹配游戏
Stable Matching Games
论文作者
论文摘要
Gale和Shapley引入了两组代理之间的匹配问题，其中一侧的每个代理在另一侧的代理上都有外源性偏好排序。他们将匹配定义为稳定，如果没有无与伦比的一对可以通过形成新对来改善其实用程序。从算法上，他们证明了稳定匹配的存在。 Shapley和Shubik，Demange和Gale以及许多其他人通过允许货币转移扩展了模型。我们通过假设匹配的夫妻在通常的非合作意义（无承诺）或半合作的方式（承诺，作为双边绑定合同的结果，每个玩家都负责她的合同的一部分）。根据玩家是否可以提交的不同，我们在每种情况下定义了一个解决方案概念，该解决方案概念将大风 - 夏普利成对稳定性与（广义）NASH平衡稳定性相结合。在每种情况下，我们都为解决方案集提供了必要和充分的条件，并提供了计算解决方案的算法。
Gale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both improve their utility by forming a new pair. They proved, algorithmically, the existence of a stable matching. Shapley and Shubik, Demange and Gale, and many others extended the model by allowing monetary transfers. We offer a further extension by assuming that matched couples obtain their payoff endogenously as the outcome of a strategic game they have to play in a usual non-cooperative sense (without commitment) or in a semi-cooperative way (with commitment, as the outcome of a bilateral binding contract in which each player is responsible for her part of the contract). Depending on whether the players can commit or not, we define in each case a solution concept that combines Gale-Shapley pairwise stability with a (generalized) Nash equilibrium stability. In each case we give necessary and sufficient conditions for the set of solutions to be non-empty and provide an algorithm to compute a solution.
