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On the support size of stable strategies in random games

Spyros C. Kontogiannis, Paul G. Spirakis
2009 Theoretical Computer Science  
In this paper we study the support sizes of evolutionary stable strategies (ESS) in random evolutionary games.  ...  We prove that, when the elements of the payoff matrix behave either as uniform, or normally distributed random variables, almost all ESS have support sizes o (n), where n is the number of possible types  ...  In the next section we shall use this to calculate an upper bound on the support sizes of almost all ESS in a random game.  ... 
doi:10.1016/j.tcs.2008.12.056 fatcat:tljwuwm2knfxjfmk5hje7ejgei

Optimization-Based Algorithm for Evolutionarily Stable Strategies against Pure Mutations [article]

Sam Ganzfried
2019 arXiv   pre-print
It turns out that the vast majority of the games included in the experiments contain ESS with small support, and our algorithm is outperformed by a support-enumeration based approach.  ...  However we suspect our algorithm may be useful in the future as games are studied that have ESS with potentially larger and unknown support size.  ...  n k total supports of size k in a game with n pure strategies which is exponential.  ... 
arXiv:1803.00607v2 fatcat:dtzdwftocja6vbozwzeisq4gbe

The Complexity of Genetic Diversity [article]

Ruta Mehta and Ioannis Panageas and Georgios Piliouras and Sadra Yazdanbod
2015 arXiv   pre-print
variant of the well known multiplicative weights update algorithm in symmetric coordination games which could be of independent interest.  ...  Technically, our results exploit connections between game theory, nonlinear dynamical systems, complexity theory and biology and establish hardness results for predicting the evolution of a deterministic  ...  If there exists a clique of size at least k in graph G, then the game (A, A) has a mixed strategy p that is strict Nash stable.  ... 
arXiv:1411.6322v2 fatcat:swp5wyc7pncvvkbj3ufl447viy

Counting Stable Strategies in Random Evolutionary Games [chapter]

Spyros Kontogiannis, Paul Spirakis
2005 Lecture Notes in Computer Science  
In this paper we study the notion of the Evolutionary Stable Strategies (ESS) in evolutionary games and we demonstrate their qualitative difference from the Nash Equilibria, by showing that a random evolutionary  ...  game has on average exponentially less number of ESS than the number of Nash Equilibria in the underlying symmetric 2-person game with random payoffs.  ...  The authors wish to thank an anonymous referee for some nice remarks on their structural argument, in an earlier version of the paper.  ... 
doi:10.1007/11602613_84 fatcat:5wsjifcqvvddnjf3hyuf6epofe

Competition of tolerant strategies in the spatial public goods game

Attila Szolnoki, Matjaž Perc
2016 New Journal of Physics  
Depending on the number of defectors within a group, a tolerant player can either cooperate in or abstain from a particular instance of the game.  ...  We observe complex pattern formation that gives rise to an intricate phase diagram, where invisible yet stable strategy alliances require outmost care lest they are overlooked.  ...  This research was supported by the Hungarian National Research Fund (Grant K-120785) and the Slovenian Research Agency (Grants P5-0027 and J1-7009).  ... 
doi:10.1088/1367-2630/18/8/083021 fatcat:l7filq3ocvgmfnjjzu2r2dmjei

The distribution of optimal strategies in symmetric zero-sum games

Florian Brandl
2017 Games and Economic Behavior  
A randomized strategy is optimal if it guarantees an expected payoff of at least 0 for a player independently of the strategy of the other player.  ...  We determine the probability that an optimal strategy randomizes over a given set of actions when the game is drawn from a distribution that satisfies certain regularity conditions.  ...  An earlier version of this paper has been presented at the 5th World Congress of the Game Theory Society in Maastricht (July 2016).  ... 
doi:10.1016/j.geb.2017.06.017 fatcat:ojwa77ma3jgn7nrnj7sducc3ba

Evolutionary Voluntary Prisoner's Dilemma Game under Deterministic and Stochastic Dynamics

Qian Yu, Ran Chen, Xiaoyan Wen
2015 Entropy  
Current studies show that the inherent cyclic dominance of the strategies of the VPD game results in periodic oscillations in population.  ...  This paper investigated the influence of the level of individual rationality and the size of a population on the evolutionary dynamics of the VPD game.  ...  Acknowledgments This work was supported by the National Natural Science Foundation of China (71373198, 71233006), the Soft Science Research Project of Hubei Province, China (2014BDF103) and the National  ... 
doi:10.3390/e17041660 fatcat:7ltma2b4vbgldlxvigm657x3i4

On the geometric structures in evolutionary games on square and triangular lattices [article]

Evgeni Burovski, Aleksandr Malyutin, Lev Shchur
2018 arXiv   pre-print
We study a model of a spatial evolutionary game, based on the Prisoner's dilemma for two regular arrangements of players, on a square lattice and on a triangular lattice.  ...  We analyze steady state distributions of players which evolve from irregular, random initial configurations.  ...  A.M. acknowledges the support of the Academic Fund Program at the National Research University Higher School of Economics (HSE) in 2018-2019 (grant No 18-05-0024) and by the Russian Academic Excellence  ... 
arXiv:1811.08784v1 fatcat:laagla3h6bbsxcleajjwfkhwli

The replicator equation and other game dynamics

R. Cressman, Y. Tao
2014 Proceedings of the National Academy of Sciences of the United States of America  
An early success of evolutionary game theory is then the result that an evolutionarily stable strategy (ESS) is dynamically stable for the single species replicator equation described above (1, 5).  ...  may depend on what choices were made in earlier ones) as well as asymmetric population games and games with continuous strategy spaces.  ...  This work was partially supported by the Natural Sciences and Engineering Research Council of Canada, the National Science Foundation of China (Grant 31270439), and the National Basic Research Program  ... 
doi:10.1073/pnas.1400823111 pmid:25024202 pmcid:PMC4113915 fatcat:ewlsq4dn4facjci3bhsoxdqghm

Research on Cooperative Innovation Behavior of Industrial Cluster Based on Subject Adaptability

Xiaohui Jia, Minghui Jiang, Lei Shi
2016 Discrete Dynamics in Nature and Society  
On this basis, the subject's own adaptability is introduced, which is regarded as the system noise in the stochastic evolutionary game model so as to analyze the impact of adaptability on the game strategy  ...  Through the utilization of two key tools, evolutionary stable strategy and replicator dynamics equations, this paper considers the cost and gains of cooperative innovation and the amount of government  ...  The results show that the introduction of random factors did not impact on the game strategy selection.  ... 
doi:10.1155/2016/3069065 fatcat:cktosybgzrdzjeufqjmtbp6tjq

Cyclic Game Dynamics Driven by Iterated Reasoning

Seth Frey, Robert L. Goldstone, Attila Szolnoki
2013 PLoS ONE  
We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors.  ...  The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept.  ...  Wrote the paper: SF RLG.  ... 
doi:10.1371/journal.pone.0056416 pmid:23441191 pmcid:PMC3575333 fatcat:q27rjdbyjvbojl5ubzuqutcvce

Algorithms for Closed Under Rational Behavior (CURB) Sets

M. Benisch, G. B. Davis, T. Sandholm
2010 The Journal of Artificial Intelligence Research  
We then show that the complexity of finding a Nash equilibrium can be exponential only in the size of a game's smallest CURB set.  ...  First, we describe an algorithm that identifies all of a player's best responses conditioned on the belief that the other player will play from within a given subset of its strategy space.  ...  Acknowledgments This material is based upon work supported by National Science Foundation ITR grant 0205435, IGERT grant 9972762, and IIS grants 0121678, 0427858, and 0905390, as well as Office of Naval  ... 
doi:10.1613/jair.3070 fatcat:v3bj2fhtzjcbfjlpntv66gt66e

Constrained School Choice with Incomplete Information [article]

Hugo Gimbert and Claire Mathieu and Simon Mauras
2021 arXiv   pre-print
We focus on symmetric equilibria, in which all students play the same strategy.  ...  Most often in practice, notably when the process is implemented by a national clearinghouse and thousands of schools enter the market, there is a quota on the number of applications that a student can  ...  The game G µ is a k-players game in normal form, where the payoff function V is given by a matrix of size k · |A| k .  ... 
arXiv:2109.09089v1 fatcat:mo4zzftoe5dwhfg6zyno2p7pai

Page 5115 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
If discounting is small, cycles of stable equilibria occur that can be invaded by pure strategies not in the support of their face.  ...  After sufficient time has elapsed, each player selects a random sample of fixed size s, from the strategies historically used by his opponent, and chooses his own play according to whichever strategy has  ... 

Aggregation Dynamics in Service Overlay Networks

Pietro Michiardi, Paul Marrow, Richard Tateson, Fabrice Saffre
2007 First International Conference on Self-Adaptive and Self-Organizing Systems (SASO 2007)  
Hindered by the computational complexity of finding stable wirings, we propose a simple distributed heuristic that allows the study of overlay networks with a realistic size and with several service instances  ...  We show the ability of our re-wiring strategy to promote the emergence of a clustered global topology whilst running locally.  ...  by clients using the overlay; • we propose a game theoretic model of service overlay construction wherein the uncoordinated strategic actions of nodes result in a stable wiring of an initially random  ... 
doi:10.1109/saso.2007.7 dblp:conf/saso/MichiardiMTS07 fatcat:hc2hjawjyfedvokmlqou6adwlm
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