Evolutionary game dynamics of combining the imitation and aspiration-driven update rules

Wang, Xianjia; Gu, Cuiling; Zhao, Jinhua; Quan, Ji

doi:10.1103/physreve.100.022411

Cited by 31 publications

(21 citation statements)

References 50 publications

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“…To implement such a setting, we took an instance of the vaccination game presented in [23]. Previous works (such as [37–40]) on combining aspiration and imitation mechanisms for social dilemma games demonstrated that aspiration protocols possess a positive probability to improve the cooperation level in a situation where imitative rules favour defection. Such a phenomenon is also observed in the vaccination game.…”

Section: Discussionmentioning

confidence: 99%

“…In such a scenario, an individual may adopt the imitation rule, to change the vaccinating strategy, with probability α and the aspiration rule with probability 1 − α . Notably, this type of mixing mechanism has already been studied in some previous works (such as [40,52]), but for classical social dilemma games. Furthermore, the inclusion of adaptive aspirations in structured populations may capture a more realistic picture than the current setting because the learning rate of aspirations and update rules will be significantly influenced by neighbouring agents.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, the inclusion of heterogeneous updating is much needed to reflect a more realistic scenario. In fact, some of the previous studies [39,40] have already explored the presence of heterogenous updating in classical social dilemma games, such as dyadic games. In those cases, the existence of aspiration-led updating in addition to the imitation rule has seemed to ensure the survival of cooperation, even in a defective milieu (such as the Prisoner's Dilemma; PD) [37,38].…”

Section: Introductionmentioning

confidence: 99%

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Vaccinating behaviour guided by imitation and aspiration

2020

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Vaccinating decisions can be influenced by imitation as well as self-evaluation or aspiration. This work analyses vaccinating behaviours by coupling both imitation and aspiration update rules, adopting an existing set-up of the mean-field vaccination game. We incorporate the imitation mechanism with several variants of the aspiration protocol, encompassing constant and adaptive aspirations. Equations of the combined dynamics have been derived by grouping the population according to (i) vaccinating strategies and (ii) healthy and infected status within each strategy. If aspiration levels are fixed but differentiated by vaccinating strategies, then vaccinators aspiring less than non-vaccinators are found to ameliorate the vaccination coverage, thereby yielding a less infectious state. The adaptive aspirations maintain a positive correlation with the vaccine efficacy while keeping the opposite relation with vaccination cost. When vaccinating strategies, aspirations and update rules are allowed to evolve synchronously, then either the imitation or aspiration process takes over the entire population. If aspiration rules prevail, then vaccinees and non-vaccinees coexist equally (according to (i)) or vaccine uptake follows a non-monotonic trend with the efficacy (according to (ii)). The imitative rule performs better when vaccination is less expensive or cheap, while aspiration updating safeguards the tenacity of vaccinees despite vaccination being expensive.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vaccinating behaviour guided by imitation and aspiration

2020

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“…Evolutionary models have allowed identifying additional mechanisms that could play a role to sustain cooperation among humans, including memory effects [23,24], strategy diversity [25,26], diverse forms of reputation [27,28] and aspiration [29,30] and onymity [31]. Central to our work, there have been many advances in the study of how interactions among humans are structured.…”

Section: Snowdrift Gamementioning

confidence: 99%

Evolutionary games on simplicial complexes

Guo,

Jia,

Sendiña-Nadal

et al. 2021

Preprint

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“…Analysis of nonlinear dynamical equations modelling arXiv:2102.10103v1 [nlin.AO] 17 Feb 2021 various aspects [11][12][13][14][15][16][17][18][19][20][21][22] of evolutionary games is an exciting modern interdisciplinary research area that encompasses problems from biophysics, mathematics, economics, and sociology. In its simplest form, a strategic interaction in a game is supposed to lead to realization of payoff/fitness instantaneously.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation

2020

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Game theory deals with strategic interactions among players and evolutionary game dynamics tracks the fate of the players' populations under selection. In this paper, we consider the replicator equation for two-player-two-strategy games involving cooperators and defectors. We modify the equation to include the effect of mutation and also delay that corresponds either to the delayed information about the population state or in realizing the effect of interaction among players. By focusing on the four exhaustive classes of symmetrical games-the Stag Hunt game, the Snowdrift game, the Prisoners' Dilemma game, and the Harmony game-we analytically and numerically analyze delayed replicator-mutator equation to find the explicit condition for the Hopf bifurcation bringing forth stable limit cycle. The existence of the asymptotically stable limit cycle imply the coexistence of the cooperators and the defectors; and in the games, where defection is a stable Nash strategy, a stable limit cycle does provide a mechanism for evolution of cooperation. We find that while mutation alone can never lead to oscillatory cooperation state in two-player-two-strategy games, the delay can change the scenario. On the other hand, there are situations when delay alone cannot lead to the Hopf bifurcation in the absence of mutation in the selection dynamics.

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Evolutionary game dynamics of combining the imitation and aspiration-driven update rules

Cited by 31 publications

References 50 publications

Vaccinating behaviour guided by imitation and aspiration

Vaccinating behaviour guided by imitation and aspiration

Evolutionary games on simplicial complexes

Evolutionary dynamics of the delayed replicator-mutator equation: Limit cycle and cooperation

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