Guts扑克的博弈论分析
Game-theoretic analysis of Guts Poker
AI总结：
本文对递归扑克变体Guts进行博弈论分析，给出排除期望赌注不趋于零情形的判据，并据此确定两人博弈的最优纯策略及n人博弈中针对集团玩法的最优策略，同时证明玩家1无法对抗一般协作策略强制获得非负收益。
摘要：
我们对递归博弈“Guts”——一种可能带有不断增长赌注的重复进行的扑克变体——进行了博弈论分析。这类博弈的一个有趣之处在于，如果期望赌注不随游戏轮数趋于零，就需要考虑所有玩家损失的资金。我们提供了一个清晰且易于应用的判据来排除这种情形，在该判据下，可以为此类一般博弈计算出一个值。利用这一判据，我们为两人博弈确定了一个最优“纯”策略，该策略由一个简单的“进行/不进行”判据构成。对于n人博弈（n≥3），我们确定了针对“集团玩法”的最优进行/不进行策略，其中玩家2至n采取相同策略，从而为玩家1带来非负收益。针对玩家2至n的一般协作策略，我们证明玩家1无法强制获得非负收益。由此可知，存在一个非严格对称纳什均衡，但该均衡不是强均衡。
英文摘要：
We carry out a game-theoretic analysis of the recursive game "Guts," a variant of poker featuring repeated play with possibly growing stakes. An interesting aspect of such games is the need to account for funds lost to all players if expected stakes do not go to zero with the number of rounds of play. We provide a sharp, easily applied criterion eliminating this scenario, under which one may compute a value for general games of this type. Using this criterion, we determine an optimal "pure" strategy for the 2-player game consisting of a simple "go/no-go" criterion. For the $n$-player game, $n\geq 3$, we determine an optimal go/no-go strategy against "bloc play" in which players 2-n pursue identical strategies, giving nonnegative return for player 1. Against general collaborative strategies of players 2-n, we show that player 1 cannot force a nonnegative return. It follows that there exists a nonstrict symmetric Nash equilbrium, but this equilibrium is not strong
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。
