以演化方法探討不公平趨避行為之形成

Abstract

本文透過最後通牒賽局 (ultimatum game) 與演化方法, 探討不公平趨避行為的形成。根據 Fehr & Schmidt(1999)(1), 人的效用函數除了包含自己的報償以外, 還會考慮對手與自己報償的差距, 而不相等的報償會產生一個負效用 (disutility), 負效用的大小因每個賽局的參與者對於報償不相等的敏感程度而有差異, 此敏感程度會傳遞給賽局參與者的後代。賽局的參與者在考慮自己與對手的報償後, 做出極大化自己效用的策略, 透過在賽局中採取此策略得到的報償, 會影響其後代產生的數量。我們首先在不考慮突變 (mutation) 力量之下, 找出所有的均衡狀態, 接著加入突變, 分析在不同均衡狀態之間移動的難易程度。透過計算阻力──使系統永久脫離各個均衡狀態所需要的最少突變次數──以分析不同均衡狀態之間相對穩定程度, 進而找出演化位能最低、相對最穩定的均衡狀態。

This article explores how evolution may shape inequity aversion, using ultimatumgame. Based on Fehr & Schmidt(1999)(1), in addition to payoff, utility is also affectedby the difference between own and other’s payoff. If the difference in payoffs may producedisutility, the degree of this disutility could depend on how inequity averse eachparticipant is. This sensitivity of inequity aversion may pass on to the offspring. Considering own and other’s payoff, the participant chooses a strategy which maximizes his utility. The payoff associated with his strategy then influences how many offspring he has. We first find out all equilibria before adding mutations. Then analyse how difficult to move from one equilibrium to another. By calculating resistance, the least number of mutations required to make the system escape from the basin of an equilibrium, we analyse the relative stability among different equilibria first, and the find out the most stable equilibrium.