Cycles versus equilibrium in evolutionary games

Norman, Thomas

doi:10.1007/s11238-009-9190-y

Cited by 4 publications

(2 citation statements)

References 33 publications

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“…In other contexts, a number of other authors have used status-quo bias or switching costs to model insensitivity to negligible payoff improvements: Kuzmics (2011) and Norman (2009Norman ( , 2010 in stochastic evolution with noise; Wang (2000, 2009) in repeated games; Lou, Yin, and Lawphongpanich (2010) and Szeto and Lo (2006) in transportation models. 2 These papers, except Kuzmics (2011), assume a deterministic status-quo bias: an agent maintains a threshold over time, and he revises his action if the payoff improvement exceeds this threshold.…”

Section: Introductionmentioning

confidence: 99%

Tempered best response dynamics

Zusai

2017

Int J Game Theory

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We propose a new deterministic evolutionary dynamic-the tempered best response dynamic (tBRD)-to capture two features of economic decision making: optimization and continuous sensitivity to incentives. That is, in the tBRD, an agent is more likely to revise his action when his current payoff is further from the optimal payoff, and he always switches to an optimal action when revising. The tBRD is a payoff monotone selection like the replicator dynamic, which makes medium and long-run outcomes more consistent with predictions from equilibrium refinement than the BRD in some situations. The technical contribution of the tBRD is continuous sensitivity, which allows us to apply results of a system of piecewise differential equations in order to obtain conditions for uniqueness and stability of solutions.

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Section: Introductionmentioning

confidence: 99%

Tempered best response dynamics

Zusai

2017

Int J Game Theory

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“…Economics is another area where game theory with either pure or mixed strategies has been studied. A series of economics papers focus on modifications of the three-species rock-paper-scissors model (see, for example, [63][64][65][66][67]), whereas others tie three-strategy cyclic domination to the Public Goods game [68][69][70][71][72][73]. Some papers discuss spatial games in an economics setting, but usually only games with two pure strategies (Prisoner's Dilemma, Snowdrift, Hawk and Dove) are considered [74][75][76][77].…”

Section: Introductionmentioning

confidence: 99%

Synchronization and extinction in cyclic games with mixed strategies

Intoy

Pleimling

2015

Phys. Rev. E

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We consider cyclic Lotka-Volterra models with three and four strategies where at every interaction agents play a strategy using a time-dependent probability distribution. Agents learn from a loss by reducing the probability to play a losing strategy at the next interaction. For that, an agent is described as an urn containing β balls of three and four types, respectively, where after a loss one of the balls corresponding to the losing strategy is replaced by a ball representing the winning strategy. Using both mean-field rate equations and numerical simulations, we investigate a range of quantities that allows us to characterize the properties of these cyclic models with time-dependent probability distributions. For the three-strategy case in a spatial setting we observe a transition from neutrally stable to stable when changing the level of discretization of the probability distribution. For large values of β, yielding a good approximation to a continuous distribution, spatially synchronized temporal oscillations dominate the system. For the four-strategy game the system is always neutrally stable, but different regimes emerge, depending on the size of the system and the level of discretization.

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Incentive and stability in the Rock-Paper-Scissors game: an experimental investigation

Wang¹,

Xu²

2014

Preprint

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In a two-person Rock-Paper-Scissors (RPS) game, if we set a loss worth nothing and a tie worth 1, and the payoff of winning (the incentive a) as a variable, this game is called as generalized RPS game. The generalized RPS game is a representative mathematical model to illustrate the game dynamics, appearing widely in textbook. However, how actual motions in these games depend on the incentive has never been report quantitatively. Using the data from 7 games with different incentives, including 84 groups of 6 subjects playing the game in 300-round, with random-pair tournaments and local information recorded, we find that, both on social and individual level, the actual motions are changing continuously with the incentive. More expressively, some representative findings are, (1) in social collective strategy transit views, the forward transition vector field is more and more centripetal as the stability of the system increasing; (2) In the individual behavior of strategy transit view, there exists a phase transformation as the stability of the systems increasing, and the phase transformation point being near the standard RPS;(3) Conditional response behaviors are structurally changing accompanied by the controlled incentive. As a whole, the best response behavior increases and the win-stay lose-shift (WSLS) behavior declines with the incentive. Further, the outcome of win, tie, and lose influence the best response behavior and WSLS behavior. Both as the best response behavior, the win-stay behavior declines with the incentive while the lose-left-shift behavior increase with the incentive. And both as the WSLS behavior, the lose-left-shift behavior increase with the incentive, but the lose-right-shift behaviors declines with the incentive. We hope to learn which one in tens of learning models can interpret the empirical observation above.

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Cycles versus equilibrium in evolutionary games

Abstract: Evolution, Switching costs, Mixed-strategy equilibrium, Cycles, Stochastic stability,

Cited by 4 publications

References 33 publications

Tempered best response dynamics

Tempered best response dynamics

Synchronization and extinction in cyclic games with mixed strategies

Incentive and stability in the Rock-Paper-Scissors game: an experimental investigation

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