迭代公共物品博弈中的零决定策略
Zero-Determinant Strategies in the Iterated Public Goods Game
摘要：
最近，Press和Dyson针对两人迭代囚徒困境提出了一类新的概率策略和条件策略，即所谓的零决定策略。采用零决定性策略的参与者能够以单边的方式固定对手的预期收益或强制自己的收益与对手的收益之间的线性关系。本文研究了迭代公共物品博弈中的零决定策略，迭代公共物品博弈是一种典型的多人进化博弈，在每一轮中，每个人都将选择是否将自己的代币放入公共罐中，罐中的代币乘以一个大于1的因子，然后在所有参与者中平均分配。分析和数值结果显示了与二人博弈相似但又不同的情形：（i）在参与人较少或乘法因子较小的情况下，一个参与人可以单方面地固定所有其他参与人的期望总收益;（ii）一个参与者能够设定他的收益与所有其他参与者的总收益之间的比率，但是如果倍增因子超过取决于玩家数量的阈值，则该比率受到上限的限制。
英文摘要：
Recently, Press and Dyson have proposed a new class of probabilistic and conditional strategies for the two-player iterated Prisoner's Dilemma, so-called zero-determinant strategies. A player adopting zero-determinant strategies is able to pin the expected payoff of the opponents or to enforce a linear relationship between his own payoff and the opponents' payoff, in a unilateral way. This paper considers zero-determinant strategies in the iterated public goods game, a representative multi-player evolutionary game where in each round each player will choose whether or not put his tokens into a public pot, and the tokens in this pot are multiplied by a factor larger than one and then evenly divided among all players. The analytical and numerical results exhibit a similar yet different scenario to the case of two-player games: (i) with small number of players or a small multiplication factor, a player is able to unilaterally pin the expected total payoff of all other players; (ii) a player is able to set the ratio between his payoff and the total payoff of all other players, but this ratio is limited by an upper bound if the multiplication factor exceeds a threshold that depends on the number of players.
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