论文标题
在随机回报的游戏中平衡的效率
Efficiency of equilibria in games with random payoffs
论文作者
论文摘要
我们考虑使用$ n $玩家的正常形式游戏和每个玩家的两种策略，而收益为I.I.D.随机变量具有某些发行版$ f $，我们将游戏中与纯平的问题视为玩家的数量分歧。众所周知，如果分销$ f $没有原子，那么纯平的随机数是渐近的泊松$（1）$。在存在原子的情况下，它有分歧。对于每个策略概况，我们考虑玩家的（随机）平均收益，称为平均社会公用事业（ASU）。特别是，我们研究了最佳ASU的渐近行为以及与最佳和最差的纯纳什平衡相关的行为，我们表明，尽管这些数量是随机的，但它们会汇聚为$ n \ to \ infty $，以确定性数量。
We consider normal-form games with $n$ players and two strategies for each player, where the payoffs are i.i.d. random variables with some distribution $F$ and we consider issues related to the pure equilibria in the game as the number of players diverges. It is well-known that, if the distribution $F$ has no atoms, the random number of pure equilibria is asymptotically Poisson$(1)$. In the presence of atoms, it diverges. For each strategy profile, we consider the (random) average payoff of the players, called Average Social Utility (ASU). In particular, we examine the asymptotic behavior of the optimum ASU and the one associated to the best and worst pure Nash equilibria and we show that, although these quantities are random, they converge, as $n\to\infty$ to some deterministic quantities.
