通过财富再分配的Parrondo悖论
Parrondo's paradox via redistribution of wealth
摘要：
Toral（2002）考虑了N \geq 2个参与者的合奏。在博弈B中，玩家被随机选择参与Parrondo最初的资本依赖博弈。在游戏A中，两个玩家被随机选择，没有替换，第一个转移一个单位的资本给第二个。游戏A'是公平的（相对于总资本），游戏B是失败的（或公平的），随机混合物γ A'+（1-γ）B是胜利的，正如Toral使用计算机模拟γ=1/2所证明的那样。我们证明了这一点，建立了一个强大数律和一个中心极限定理的序列的合奏的球员为每个γ \in（0，1）的利润。我们对非随机博弈模式（A '）^r B^s做同样的事情，对所有整数r，s \geq 1。随机混合情况和非随机模式情况之间的意外关系出现在极限N \rightarrow \infty中。
英文摘要：
Toral (2002) considered an ensemble of N\geq2 players. In game B a player is randomly selected to play Parrondo's original capital-dependent game. In game A' two players are randomly selected without replacement, and the first transfers one unit of capital to the second. Game A' is fair (with respect to total capital), game B is losing (or fair), and the random mixture γA'+(1-γ)B is winning, as was demonstrated by Toral for γ=1/2 using computer simulation. We prove this, establishing a strong law of large numbers and a central limit theorem for the sequence of profits of the ensemble of players for each γ\in(0,1). We do the same for the nonrandom pattern of games (A')^r B^s for all integers r,s\geq1. An unexpected relationship between the random-mixture case and the nonrandom-pattern case occurs in the limit as N\rightarrow\infty.
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