【摘要】：零行列式策略不僅可以單方面設(shè)置對手收益,而且可以對雙方的收益施加一個線性關(guān)系,從而達(dá)到敲詐對手的目的.本文針對零行列式策略博弈前期與穩(wěn)態(tài)期的收益存在偏差,基于Markov鏈理論給出零行列式策略與全合作策略博弈的瞬態(tài)分布、瞬態(tài)收益及達(dá)到穩(wěn)態(tài)所需時間.發(fā)現(xiàn)在小的敲詐因子下,敲詐者前期收益高于穩(wěn)態(tài)期收益,敲詐因子較大時,情況截然相反,并且敲詐因子越大,越不利于雙方合作,達(dá)到穩(wěn)態(tài)也越慢.這為現(xiàn)實(shí)生活中頻繁更新策略的博弈提供了一種計算實(shí)時收益的方法.此外針對敲詐策略與進(jìn)化人的博弈,論證了雙方均背叛狀態(tài)下,進(jìn)化人下次博弈時一定進(jìn)化為全合作策略.通過對所有狀態(tài)下策略更新過程仿真,發(fā)現(xiàn)進(jìn)化人在四種情況下的進(jìn)化速度有顯著差異,并最終演化為全合作策略,表明零行列式策略是合作產(chǎn)生的催化劑.
[Abstract]:The zero-determinant strategy can not only set up the opponent's income unilaterally, but also impose a linear relation to the profit of both parties, so as to achieve the purpose of extorting the opponent. Based on the Markov chain theory, this paper gives the transient distribution, transient income and the time to reach the steady state of the zero-determinant strategy game and the total cooperative strategy game. It is found that under the small extortion factor, the earlier income of the blackmailer is higher than that of the steady period. When the extortion factor is larger, the situation is opposite, and the bigger the extortion factor is, the more unfavorable the cooperation between the two parties is, and the slower the steady state is. This provides a method to calculate real-time income for the game of frequent update strategy in real life. In addition, for the game between extortion strategy and evolutionist, it is proved that the evolutionary person will evolve into a full cooperation strategy in the next game under the state of betrayal by both sides. Through the simulation of the strategy updating process in all states, it is found that there are significant differences in the evolutionary speed of the evolutionary human under the four conditions, and the ultimate evolution is the full cooperation strategy, which indicates that the zero-determinant strategy is the catalyst for the generation of cooperation.
【作者單位】： 上海理工大學(xué)管理學(xué)院;華北水利水電大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院;西京學(xué)院商貿(mào)技術(shù)系;
【基金】：國家自然科學(xué)基金(批準(zhǔn)號:71571119)和國家自然科學(xué)基金青年科學(xué)基金(批準(zhǔn)號:11501199)資助的課題~~
【分類號】：O225

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