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如您所说,我这个设定,甚至整个讨论,对实战意义不大,无论双方什么立场,不影响我们在各自得场地里赢钱。
但是如果就爱研究理论中的各种极端情况,非要叫这个真的话,Bill Chen在《The Mathematics of Poker》的第29章里举的例子几乎跟我这个设定一模一样,见Example29.1,361页。非要说不一样的话,是陈教授把这个游戏简化又简化了。
结论是:如果有疯子发疯,另一人用石头打法剥削他,则我们最好的结果也是-EV。
又比如他的Example29.4, 367页, 某一个正常打,第二个发疯,最后一个行动的人可以决定他要跟谁一起+EV。
陈教授如此结束这一章:
We have considered just a few multiplayer games here; the pattern should hopefully be clear. We can always find a Nash equilibrium for a game, where all the players cannot unilaterally improve their equity. (说的是:纳什平衡总是存在)Often, however, one or more players can disturb the equilibrium by changing strategies. (但纳什平衡会被一个或多人的偏离而打破) When the other players move to maximize their equity by exploiting the disturbance, alliances are formed, and often the disturber can gain equity from the shift, without counter-exploiting at all. (偏离者会得到+EV, 别人拿他没招儿) This is of course impossible in two-player zero-sum games, ( 俩人单挑则不可能) as any equity that one player gains must be lost by the other player. (因为偏离者丢掉的EV总是被未偏离者捡到) It is this idea that leads us to refrain from using the term "optimal" in regard to multiplayer strategies. (正因为如此,我们不建议在多人策略中使用“Optimal”最优这个词)。
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