Implementing the Lexicographic Maxmin Bargaining Solution
Implementing the Lexicographic Maxmin Bargaining Solution
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发表时间：
2018-10
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通讯作者：
Ashish Goel;A. Krishnaswamy
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作者：
Ashish Goel;A. Krishnaswamy
已经有很多工作展示机制，实现各种讨价还价的解决方案，特别是，Kalai-Smorodinsky解决方案\cite{moulin 1984 implementing}和纳什讨价还价解决方案。另一个众所周知的公理化的研究解决方案是字典最大最小的解决方案。然而，没有已知的执行机制。为了填补这一空白，我们构建了一个机制，实现字典最大最小的解决方案作为唯一的子博弈完美均衡的结果，在n-玩家设置。作为标准的实施讨价还价的解决方案的文献中，我们使用的假设，任何球员可以抓住整个盈余。我们的机制由二元博弈树组成，每个节点对应于一个子博弈，其中玩家可以在两个结果之间进行选择。我们表征新的组合性质的字典最大最小的解决方案，这是至关重要的设计，我们的机制。
There has been much work on exhibiting mechanisms that implement various bargaining solutions, in particular, the Kalai-Smorodinsky solution \cite{moulin1984implementing} and the Nash Bargaining solution. Another well-known and axiomatically well-studied solution is the lexicographic maxmin solution. However, there is no mechanism known for its implementation. To fill this gap, we construct a mechanism that implements the lexicographic maxmin solution as the unique subgame perfect equilibrium outcome in the n-player setting. As is standard in the literature on implementation of bargaining solutions, we use the assumption that any player can grab the entire surplus. Our mechanism consists of a binary game tree, with each node corresponding to a subgame where the players are allowed to choose between two outcomes. We characterize novel combinatorial properties of the lexicographic maxmin solution which are crucial to the design of our mechanism.