Delayed response in the Hawk Dove game

Burridge, James; Gao, Yuan

doi:10.1140/epjb/e2016-70471-1

Cited by 8 publications

(2 citation statements)

References 26 publications

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“…The same study also shows that for smoothed best response dynamics in anti-coordination games, the interior fixed point is stable for low probability of delay and unstable for the large probability of delay. In another work [34] involving a population of finite agents with a specific memory length of past interactions and playing snowdrift game, one notes that the fixed points may become unstable and give way to limit cycles for large memory length.…”

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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Section: Introductionmentioning

confidence: 99%

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

2020

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“…They defined three kind of evolutionary stable strategies and discussed the stability of these ESSs under replicator dynamics with two types of delays. Burridge et al [29] considered a population of agents playing the Hawk-Dove game with a finite memory of past interactions. They showed an instability occurs at a critical memory length.…”

Section: Introductionmentioning

confidence: 99%

Stability of Replicator Dynamics with Bounded Continuously Distributed Time Delay

et al. 2020

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In this paper, we consider evolutionary games and construct a model of replicator dynamics with bounded continuously distributed time delay. In many circumstances, players interact simultaneously while impacts of their choices take place after some time, which implies a time delay exists. We consider the time delay as bounded continuously distributed other than some given constant. Then, we investigate the stability of the evolutionarily stable strategy in the replicator dynamics with bounded continuously distributed time delay in two-player game contexts. Some stability conditions of the unique interior Nash equilibrium are obtained. Finally, the simple but important Hawk–Dove game is used to verify our results.

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