二次投票的纳什均衡
Nash Equilbria for Quadratic Voting
摘要：
投票者做出二元决策，从中央结算所购买选票，支付购买选票数量的平方。购买$v$选票的具有效用$u$的代理的净收益是$Ψ(S_{n+1})u-v^{2}$，其中$Ψ$是取值在-1和+1之间的单调函数，而$S_{n+1}$是参与选举的$n+1$选民购买的所有选票之和。假设选民的效用是从紧支持的概率分布$F_{U}$中随机抽样产生的;每个选民知道她自己的效用，但不知道其他选民的效用，尽管她知道抽样分布$F_{U}$。描述了这个博弈的纳什均衡。这些结果意味着任何纳什均衡的预期无效率像$1/n$一样衰减。
英文摘要：
Voters making a binary decision purchase votes from a centralized clearing house, paying the square of the number of votes purchased. The net payoff to an agent with utility $u$ who purchases $v$ votes is $Ψ(S_{n+1})u-v^{2}$, where $Ψ$ is a monotone function taking values between -1 and +1 and $S_{n+1}$ is the sum of all votes purchased by the $n+1$ voters participating in the election. The utilities of the voters are assumed to arise by random sampling from a probability distribution $F_{U}$ with compact support; each voter knows her own utility, but not those of the other voters, although she does know the sampling distribution $F_{U}$. Nash equilibria for this game are described. These results imply that the expected inefficiency of any Nash equilibrium decays like $1/n$.
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。
