Abstract
The ‘irrational’ preference for fairness has attracted increasing attention. Although previous studies have focused on the effects of spitefulness on the evolution of fairness, they did not consider non-monotonic rejections shown in behavioral experiments. In this paper, we introduce a non-monotonic rejection in an evolutionary model of the Ultimatum Game. We propose strategy intervention to study the evolution of fairness in general structured populations. By sequentially adding five strategies into the competition between a fair strategy and a selfish strategy, we arrive at the following conclusions. First, the evolution of fairness is inhibited by altruism, but it is promoted by spitefulness. Second, the non-monotonic rejection helps fairness overcome selfishness. Particularly for group-structured populations, we analytically investigate how fairness, selfishness, altruism, and spitefulness are affected by population size, mutation, and migration in the competition among seven strategies. Our results may provide important insights into understanding the evolutionary origin of fairness.
Highlights
In the last thirty years, there has been substantial progress in understanding the evolution of fairness by studying the Ultimatum Game (UG)
When the altruistic strategy S3 with the fair offer is introduced into the population, the selfish strategy S1 gains an advantage over the fair strategy S2, i.e., f1 > f2
We have focused on the effects of spitefulness and altruism on the evolution of fairness in general structured populations of finite size
Summary
In the last thirty years, there has been substantial progress in understanding the evolution of fairness by studying the Ultimatum Game (UG). The effects of spitefulness on the evolution of fairness have been studied by one evolutionary game model [17] This model has focused on the replicator dynamics of four discrete strategies in infinite populations, which represent selfishness, fairness, altruism, and spitefulness, respectively. We will investigate the impacts of altruism and spitefulness on the evolution of fairness in general structured populations In such case, the unknown parameters Γ1, Γ2, and Γ3 in the Tarnita-σ condition do not have to be calculated. The strategies S2, S7, S4, and S6 have the common behavior as responders, i.e., rejecting the low offer This behavior has been found to be fairness or spitefulness by a behavioral experiment [15].
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