梯形图上某些二选多人博弈的纳什均衡
Nash Equilibria in certain two-choice multi-player games played on the ladder graph
摘要：
在这篇文章中，我们分析计算纳什均衡（NE）的两个选择游戏（圆形）梯形图上的$2n$的球员。我们考虑了一组具有通用支付参数的游戏，唯一的要求是，如果玩家选择相反的策略（反协调游戏），就会发生NE。结果表明，无论是阶梯还是圆形阶梯，NE的数量都随着$n$的数量（一半）呈指数增长，即$N_{NE}(2n)\sim C(φ)^n$，其中$φ=1.618..$是黄金分割比，$C_{circ}>C_{ladder}$是最大值。此外，比例因子$C_{ladder}$的值取决于支付参数的值。然而，对于循环梯形图（3度图），这不再是真的，即$C_{circ}$是常数，这可能表明图的拓扑结构对于设置NE的数量确实起着重要的作用。
英文摘要：
In this article we compute analytically the number of Nash Equilibria (NE) for a two-choice game played on a (circular) ladder graph with $2n$ players. We consider a set of games with generic payoff parameters, with the only requirement that a NE occurs if the players choose opposite strategies (anti-coordination game). The results show that for both, the ladder and circular ladder, the number of NE grows exponentially with (half) the number of players $n$, as $N_{NE}(2n)\sim C(φ)^n$, where $φ=1.618..$ is the golden ratio and $C_{circ}>C_{ladder}$. In addition, the value of the scaling factor $C_{ladder}$ depends on the value of the payoff parameters. However, that is no longer true for the circular ladder (3-degree graph), that is $C_{circ}$ is constant, which might suggest that the topology of the graph indeed plays an important role for setting the number of NE.
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。
