Defense Mechanisms of Empathetic Players in the Spatial Ultimatum Game

Szolnoki, Attila; Perc, Matjaž; Szabó, György

doi:10.1103/physrevlett.109.078701

Cited by 206 publications

(135 citation statements)

References 27 publications

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“…That is to say, these cooperators are impervious to defector attacks, and at the same time let more agents penetrate into the clusters, which eventually causes cooperation spreading across the whole network. Therefore, this fig provides a direct proof that cooperators possessing heterogeneous noise play a significant role for the effective expansion of cooperation behavior, which can be regarded as a valuable clue to explaining more social dilemmas [58,59,60]. …”

Section: Results and Analysismentioning

confidence: 99%

Multiplicative noise enhances spatial reciprocity

Yao¹,

Chen²

2014

Physica A: Statistical Mechanics and its Applications

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Recent research has identified the heterogeneity as crucial for the evolution of cooperation in spatial population. However, the influence of heterogeneous noise is still lack. Inspired by this interesting question, in this work, we try to incorporate heterogeneous noise into the evaluation of utility, where only a proportion of population possesses noise, whose range can also be tuned. We find that increasing heterogeneous noise monotonously promotes cooperation and even translates the full defection phase (of the homogeneous version) into the complete cooperation phase. Moreover, the promotion effect of this mechanism can be attributed to the leading role of cooperators who have the heterogeneous noise. These type of cooperators can attract more agents penetrating into the robust cooperator clusters, which is beyond the text of traditional spatial reciprocity. We hope that our work may shed light on the understanding of the cooperative behavior in the society.

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Section: Results and Analysismentioning

confidence: 99%

Multiplicative noise enhances spatial reciprocity

Yao¹,

Chen²

2014

Physica A: Statistical Mechanics and its Applications

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“…Thus, qualitatively similar results may be obtained if the experiments are conducted in other countries. Third, most theoretical models for networked UG assume that a subject can act as both a proposer and a responder (18)(19)(20). Thus we may ask how the two identities of subjects influence each other and affect the formation of local communities predicted by theoretical models.…”

Section: Discussionmentioning

confidence: 99%

“…All of the proposers' neighbors are responders and vice versa. To be consistent with theoretical models, in each round all subjects must use one decision behavior as they interact with their neighbors; that is, a proposer must make the same offer p (0 ≤ p ≤ 100) to all of his or her neighboring responders, and a responder must indicate the same minimum acceptance level q (0 ≤ q ≤ 100) to all of his or her neighboring proposers (18)(19)(20). For T1 we construct a regular bipartite network in which each node has four neighbors.…”

Section: Methodsmentioning

confidence: 99%

“…Game theory and models have offered powerful tools for exploring collective behaviors in animal and human society and our evolutionary origins (6-10). Recent theoretical studies found that network structure is significant in the emergence of mutually reinforcing communities among altruistic subjects in social games, such as the prisoner's dilemma (PD) game, the public goods game (PGG), and the ultimatum game (UG) (11)(12)(13)(14)(15)(16)(17)(18)(19)(20). Although some experiments found that cooperation is stabilized in dynamical networks (21-24), stable communities have been rarely observed in laboratory experiments on a variety of static networks (25-32).…”

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confidence: 99%

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Emergence of Communities and Diversity in Social Networks

et al. 2016

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“…In order to consider a simple evolutionary probabilistic model where unsatisfactory proposals are refused, in this paper we propose to study a model where accepting depends on proposal. 1 Although it is rationally better for the responder to accept any offer, offers below one third of the available amount to be shared are often rejected [6]. The responder punishes the proposer up to the balance between proposal and acceptance in the iterated game.…”

mentioning

confidence: 99%

Randomness and arbitrary coordination in the reactive ultimatum game

Silva

Valverde

Lamb

2016

Communications in Nonlinear Science and Numerical Simulation

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The ultimatum game explains and is a useful model in the analysis of several effects of bargaining in population dynamics. Darwin's theory of evolution -as introduced in game theory by Maynard Smith -is not the only important evolutionary aspect in a evolutionary dynamics, since complex interdependencies, competition, and growth should be modeled by, for example, reactive aspects. In biological models, computationally or analytically considered, several authors have been able to show the emergence of cooperation with stochastic or deterministic dynamics based on the mechanism of copying the best strategies. On the other hand, in the ultimatum game the reciprocity and the fifty-fifty partition seems to be a deviation from rational behavior of the players under the light of the Nash equilibrium concept. Such equilibrium emerges from the punishment of the responder who generally tends to refuse unfair proposals. In the iterated version of the game, the proposers are able to improve their proposals by adding an amount thus making fairer proposals. Such evolutionary aspects are not properly Darwinian-motivated, but they are endowed with a fundamental aspect: they reflect their actions according to value of the offers. Recently, a reactive version of the ultimatum game where the acceptance occurs with fixed probability was proposed. In this paper, we aim at exploring this reactive version of the ultimatum game where the acceptance by the players depends on the offer. In order to do so, we analyze two situations: (i) mean field and (ii) by considering the players inserted within the networks with arbitrary coordinations. In the proposed model we not only explore situations of occurrence of the fifty-fifty steady-state, in both homogeneous and heterogeneous populations, but also explore the fluctuations and payoff distribution characterized by the Gini coefficient of the population. We then show that the reactive aspect, here studied, thus far not analyzed in the evolutionary game theory literature can unveil an essential feature for the convergence to fifty-fifty split. Our approach concerns four different policies to be adopted by the players. In such policies the evolutionary aspects do not work through a Darwinian copying mechanism, but by following a policy that governs the increase or decrease of their offers according to the response of the result -i.e. acceptance or refusal. Moreover, we present results where the acceptance occurs with fixed probability. Our contribution is twofold: we present both analytical results and MC simulations which in turn are useful to design new controlled experiments in the ultimatum game in stochastic and deterministic scenarios.

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Defense Mechanisms of Empathetic Players in the Spatial Ultimatum Game

Cited by 206 publications

References 27 publications

Multiplicative noise enhances spatial reciprocity

Multiplicative noise enhances spatial reciprocity

Emergence of Communities and Diversity in Social Networks

Randomness and arbitrary coordination in the reactive ultimatum game

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