The spatial Ultimatum game revisited

Abstract

a b s t r a c tWe revisit the issue of the emergence of fair behavior in the framework of the spatial Ultimatum game, adding many important results and insights to the pioneering work by The spatial Ultimatum game. Proc. R. Soc. London B 267, 2177], who showed in a specific example that on a two dimensional setup evolution may lead to strategies with some degree of fairness. Within this spatial framework, we carry out a thorough simulation study and show that the emergence of altruism is a very generic phenomenon whose details depend on the dynamics considered. A very frequent feature is the spontaneous emergence and fixation of quasiempathetic individuals, whose offers are very close to their acceptance thresholds. We present analytical arguments that allow an understanding of our results and give insights on the manner in which local effects in evolution may lead to such non rational or apparently maladaptive behaviors.

Evolution of fairness in the dictator game by multilevel selection

“…(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fairness could evolve genetically, but structured populations are also highly conducive to the cultural evolution of beneficial traits (Boyd and Richerson, 2002;Traulsen and Nowak, 2006;Iranzo et al, 2011).…”

“…Fairness could evolve if agents aggregate with agents with the same strategy and rejection levels just below offer levels. Although recipients in the DG cannot reject offers, Page et al (2000)'s results suggest that space may be important for the DG (Page et al, 2000;Iranzo et al, 2011). Kuperman and Risau-Gusman (2008), Sinatra et al (2009), Eguíluz and Tessone (2009), and Iranzo et al (2012) reported theoretical results that support the importance of clusters of agents (in networks) in the evolution of fairness.…”

Evolutionary dynamics of fairness on graphs with migration

“…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 .…”

“…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 . Following the line of this pioneering work, the evolutionary ultimatum game on networks has aroused great concerns from researchers (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. Although the differences in their model setups, all of these studies have confirmed that network structure promotes the evolution of fairness in the ultimatum game.…”

“…Although the differences in their model setups, all of these studies have confirmed that network structure promotes the evolution of fairness in the ultimatum game. Iranzo et al (2011) have revisited the spatial ultimatum game in detail, and found that the quasiempathetic individuals, whose offer levels are very close to their acceptance thresholds, can spontaneously emerge and fixate in the structured population. Gao et al (2011) have explored how fairness evolves if individuals are able to adjust both strategies and social ties.…”