一种惩罚机制下一次性n人囚徒困境的合作性

Cooperation of a One-off n Person Prisoner's Dilemma Under a Punishment System

为解决一次性n人囚徒困境中局中人如何走出困境的问题,引进了背叛惩罚函数及其严厉度和参与人的背叛愿意度等概念,并用数学论证法证明了如下结果:(1)参与人的背叛愿意度都不超过1。(2)背叛愿意度越大,这个参与人越愿意背叛;(3)背叛愿意度为0零时,这个参与人是否背叛其赢得一样;(4)当背叛愿意度取负数时,其绝对值越大,参与人的合作积极性越大。得到博弈结果的判定法:(1)计算各参与人的背叛愿意度。(2)若至少有一个参与人愿意背叛,则全体参与人都背叛。(3)若全体参与人都愿意合作,则合作成功。例子表明,本结果在理论上可有效地解决中局中人如何走出困境和在给定惩罚机制下博弈结果的预测问题。

In order to solve the problem of how players in an n person prisoner＇s dilemma avoid the dilemma,the concepts of a player＇s preferring defection degree（PDD）,and punishment function and its severity are introduced and the following results are proved mathematically：（1）every player＇s PDD is less than or equal to 1;（2）the greater his/her PDD is,the more he/she prefers defection;（3）a player has the same game result if his/her PDD is equal to 0;and（4）when PDD is a negative number,the greater its absolute value is,the greater enthusiasm of cooperation that the player chooses is.Judgement method of game result of a prisoner＇s dilemma is obtained：（1）compute every player＇s PDD;（2）all the players choose defections if at least one of them does so;and（3）they take cooperation if anyone of them likes so.Some examples show that the results can effectively solve the theoretical problems of how the players avoid the dilemma and forecast the situation in a punishment system.