损失厌恶型n人非合作博弈Nash均衡

基于参与人是完全理性的期望效用理论是分析经典非合作博弈问题的基本理论,然而越来越多的研究表明,博弈中的参与人往往呈现出有限理性的特点.本文考虑有限理性参与人具有损失厌恶的行为特点,并对此类n人非合作博弈的Nash均衡进行详细研究.首先,根据参与人损失厌恶的行为特点,设置了n人非合作博弈安全水平参照点,并证明此参照点存在且唯一.然后,基于该参照点定义了竹人非合作博弈的损失厌恶Nash均衡,借助Brouwer不动点定理证明了该博弈均衡的存在.最后利用算例进行分析和验证,结果表明参与人的损失厌恶行为会对博弈的均衡策略产生影响,同时参与人的支付效用也会随之发生变化.

An equilibrium of n-person non-cooperative games based on loss aversion

Expectation utility theory based on completely rational players is the mainstream model of analyzing classical non-cooperative game. But more and more studies indicate that players show the characteristics of the bounded rationality. Based on the loss aversion, we study the existence and change of the Nash Equilibrium in n-person non-cooperative games. First, we define a safety level reference point, and prove the existence and uniqueness of the reference point. Then, in this situation, we develop a safety level loss aversion equilibrium in n-person non-cooperative games, and prove the existence of the equilibrium with Brouwer fixed point theorem. Finally, through using a simple case, we find that the loss aversion level of the players has an effect on the equilibrium strategies of the n-person non-cooperative games. At the same time, the utilities are also influenced by the loss aversion.