两党选举游戏有多好？
How Good Is a Two-Party Election Game?
摘要：
在本文中，我们提出了一个简单而直观的模型来调查两党选举制度的效率，特别是关于提名过程。两党都有自己的候选人，他们都为人民带来了效用，包括支持者和不支持者。在选举中，每一个政党只提名一名候选人与另一个政党的候选人竞争。如果候选人为所有人带来更多的效用，他或她赢得选举的几率就更高。我们将这种竞争建模为“两党选举博弈”，使得每一方都是具有两个或更多个纯策略的玩家，这些纯策略对应于其潜在的候选人，并且每一方的收益是来自所选择的一对竞争候选人的混合效用。通过研究三种模型，即线性链接，布拉德利-特里，和softmax模型，不同的是如何制定一个候选人的获胜几率对竞争对手的候选人，我们表明，两党选举游戏可能既没有任何纯纳什均衡，也没有一个有界的无政府状态无政府代价。然而，考虑到传统的“利己主义”，即任何候选人的利益，他/她的党的支持者比任何候选人从竞争的政党，我们证明了两党选举博弈的线性链接模型和softmax模型总是有纯纳什均衡，而且，无政府状态的无政府代价是不断有界的。
英文摘要：
In this paper, we propose a simple and intuitive model to investigate the efficiency of the two-party election system, especially regarding the nomination process. Each of the two parties has its own candidates, and each of them brings utilities for the people including the supporters and non-supporters. In an election, each party nominates exactly one of its candidates to compete against the other party's. The candidate wins the election with higher odds if he or she brings more utility for all the people. We model such competition as a "two-party election game" such that each party is a player with two or more pure strategies corresponding to its potential candidates, and the payoff of each party is a mixed utility from a selected pair of competing candidates. By looking into the three models, namely, the linear link, Bradley-Terry, and the softmax models, which differ in how to formulate a candidate's winning odds against the competing candidate, we show that the two-party election game may neither have any pure Nash equilibrium nor a bounded price of anarchy. Nevertheless, by considering the conventional "egoism", which states that any candidate benefits his/her party's supporters more than any candidate from the competing party does, we prove that the two-party election game in both the linear link model and the softmax model always has pure Nash equilibria, and furthermore, the price of anarchy is constantly bounded.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
