Fast convergence in evolutionary equilibrium selection

Kreindler, Gabriel; Young, H. Peyton

doi:10.1016/j.geb.2013.02.004

Cited by 85 publications

(73 citation statements)

References 27 publications

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“…It is assumed, however, that everyone knows the potential payoffs from alternative strategies. 12 10 This is the standard approach in the literature; see, among others, Hart and Mansour (2010), Shah and Shin (2010), Kreindler and Young (2013), Babichenko (2014), Marden and Shamma (2014).…”

Section: Nash Population Gamesmentioning

confidence: 99%

Stochastic Learning Dynamics and Speed of Convergence in Population Games

Arieli

Young²

2016

Econometrica

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We study how long it takes for large populations of interacting agents to come close to Nash equilibrium when they adapt their behavior using a stochastic better reply dynamic. Prior work considers this question mainly for 2 × 2 games and potential games; here we characterize convergence times for general weakly acyclic games, including coordination games, dominance solvable games, games with strategic complementarities, potential games, and many others with applications in economics, biology, and distributed control. If players' better replies are governed by idiosyncratic shocks, the convergence time can grow exponentially in the population size; moreover, this is true even in games with very simple payoff structures. However, if their responses are sufficiently correlated due to aggregate shocks, the convergence time is greatly accelerated; in fact, it is bounded for all sufficiently large populations. We provide explicit bounds on the speed of convergence as a function of key structural parameters including the number of strategies, the length of the better reply paths, the extent to which players can influence the payoffs of others, and the desired degree of approximation to Nash equilibrium.

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Section: Nash Population Gamesmentioning

confidence: 99%

Stochastic Learning Dynamics and Speed of Convergence in Population Games

Arieli

Young²

2016

Econometrica

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“…The case where players revise their decisions following noisy best-response dynamics was considered in [3]- [7], i.e., players prefer their best response, but do not always follow it. Reference [3] showed that noisy best-response dynamics with global interaction result in every player choosing the risk-dominant strategy.…”

Section: Related Workmentioning

confidence: 99%

“…Reference [6] characterized the expected waiting time until all players choose the risk-dominant strategy under noisy best-response dynamics on random graphs. When the degree of risk-dominance exceeds a threshold, the riskdominant strategy spreads under noisy best-response dynamics and gobal interaction, and the expected time for this to happen is bounded independently of the system size [7].…”

Section: Related Workmentioning

confidence: 99%

Diffusion of innovation in two-sided markets

Hui

Subramanian

Guo

et al. 2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-We consider the diffusion of innovation in twosided markets where both sides choose between an incumbent technology and an innovation. Each player chooses whether to adopt the innovation or not, and repeatedly learns how many players on the other side of the market adopted the innovation and revises her decision accordingly. Using largesystem analysis, we characterize the dynamics of the market, and show a phase transition result: If the initial proportion of adoptors on both sides are sufficiently large, then the innovation will spread to the entire market; otherwise, no one will adopt the innovation. Assuming the innovator can select the proportion of initial adoptors on both sides of the market by advertisements, we study the following three economic problems that are of interest to the innovator: 1) minimizing the advertisement cost while allowing the innovation to spread, 2) minimizing the total cost of advertising and technology improvement while allowing the innovation to spread, and 3) maximizing the total revenue less advertisement cost, where the innovator derives revenue per unit time from each player adopting the innovation. Our analysis provides insight into the types of advertising strategies that can lead to the successful adoption of an innovation.

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“…[7] Interesting simulation results have been conducted for heterogeneous populations in [11], [12] and [13] where the agents are associated with different payoff matrices. Some mathematical statements have been provided in [14] and [15] The work was supported in part by the European Research Council (ERCStG-307207).…”

Section: Introductionmentioning

confidence: 99%

“…Ramazi and M. Cao are with ENTEG, Faculty of Mathematics and Natural Sciences, University of Groningen, The Netherlands, {p.ramazi, m.cao}@rug.nl for the myopic best response update rule [15] but only for the case when the population is homogeneous and the game is symmetric. Some researchers have studied the stochastic stability of different strategies in the population when the update rule is noisy [16] [14]. Besides the results addressing the stability issue of strategically interacting populations, there is an emerging trend to investigate how to control such populations.…”

Section: Introductionmentioning

confidence: 99%

Analysis and control of strategic interactions in finite heterogeneous populations under best-response update rule

Ramazi

Cao

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-For a finite, well-mixed population of heterogeneous agents playing evolutionary games choosing to cooperate or defect in each round of the game, we investigate, when agents update their strategies in each round using the myopic best-response rule, how the number of cooperating agents changes over time and demonstrate how to control that number by changing the agents' payoff matrices. The agents are heterogeneous in that their payoff matrices may differ from one another; we focus on the specific case when the payoff matrices, fixed throughout the evolution, correspond to prisoner's dilemma or snowdrift games. To carry out stability analysis, we identify the system's absorbing states when taking the number of cooperating agents as a random variable of interest. It is proven that when all the agents update frequently enough, the reachable final states are completely determined by the available types of payoff matrices. As a further step, we show how to control the final state by changing at the beginning of the evolution, the types of the payoff matrices of a group of agents.

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Fast convergence in evolutionary equilibrium selection

Cited by 85 publications

References 27 publications

Stochastic Learning Dynamics and Speed of Convergence in Population Games

Stochastic Learning Dynamics and Speed of Convergence in Population Games

Diffusion of innovation in two-sided markets

Analysis and control of strategic interactions in finite heterogeneous populations under best-response update rule

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