Random allocation of pies promotes the evolution of fairness in the Ultimatum Game

Abstract

In the Ultimatum Game, two players are offered a chance to win a pie. The proposer suggests how to split the pie. The responder can either accept or reject the deal. If an agreement is not reached, neither player gets anything. Both game theory and evolutionary game theory predict the rational solution that the proposer offers the smallest possible share and the responder accepts it. Fairness thus requires additional mechanisms for natural selection to favor it. Studies to date assumed that individuals have competed for the fixed size of pies, in sharp contrast with real situations, where randomness is ubiquitous. Here we study the impact of random allocation of pies on the evolution of fairness in the Ultimatum Game. Interestingly, we find that the evolution of fairness can be promoted by the randomness associated with the size of pies, without the support of any additional evolutionary mechanisms.

Evolutionary dynamics of fairness on graphs with migration

“…This is because individuals with self-incompatible strategies obtain nothing when interacting with themselves. Consequently, they have little chance of surviving in the structured population (Wang et al, 2014). Furthermore, we notice that the most common selfcompatible strategies first move towards the right, and then the left of the concrete strategy space, as the increment of node degree k. The offer and acceptance level calculated by both computer simulations and theoretical analysis support our naked-eye observation (see Fig.…”

“…4 can be provided as follows. In a previous study (Wang et al, 2014), we have shown that the tradeoff between rejecting unfair offers (achieving by maintaining high a) and making more successful deals (achieving by decreasing a) results in the best acceptance thresholds for individuals in structured populations. When node degree k is low, the former factor (i.e., rejecting unfair offers) is much more important than the latter one (i.e., making more successful deals), which leads to the maintenance of high acceptance level a.…”

“…However, this evolutionary mechanism is inapplicable for the explanation of the evolution of fairness in the networked ultimatum game, as clusters of individuals with different self-compatible strategies (either fair or selfish) receive the same average payoff. On the contrary, the evolutionary fate of a self-compatible strategy in the ultimatum game lies in its performance against other ones (Wang et al, 2014). This is the reason that induces the paradox evolutionary phenomenon between the ultimatum game and the prisoner's dilemma game or the public goods game on graphs.…”

“…In the framework of evolutionary game theory, theoretical studies indicate that reputation , empathy (Page and Nowak, 2002;Sánchez and Cuesta, 2005), randomness (Rand et al, 2013;Wang et al, 2014), population structure Killingback and Studer, 2001;Sinatra et al, 2009;Li and Cao, 2009;Duan and Stanley, 2010;Gao et al, 2011;Iranzo et al, 2011;Szolnoki et al, 2012bSzolnoki et al, , 2012a and heterogeneity (da Silva and Kellerman, 2007) play a vital role in the evolution of fairness in the ultimatum game. In particular, Nowak et al (2000) have shown that natural selection favors the rational solution in well-mixed populations, while much fairer evolutionary outcomes can be resulted on spatial networks .…”

Leaving bads provides better outcome than approaching goods in a social dilemma

“…It has been demonstrated that the mode of individual mobility does influence the evolutionary dynamics of cooperation among unrelated individuals, which has attracted intensive research activity in recent years [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Theoretical and experimental studies have shown that individual mobility can promote the evolution of cooperation [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. In particular, Meloniet al considered random migration for individuals playing the prisoner's dilemma game on a twodimensional plane and found that cooperation can be maintained when the moving velocity of individuals is not too high [28].…”