5,584 research outputs found
On the expected number of equilibria in a multi-player multi-strategy evolutionary game
In this paper, we analyze the mean number of internal equilibria in
a general -player -strategy evolutionary game where the agents' payoffs
are normally distributed. First, we give a computationally implementable
formula for the general case. Next we characterize the asymptotic behavior of
, estimating its lower and upper bounds as increases. Two important
consequences are obtained from this analysis. On the one hand, we show that in
both cases the probability of seeing the maximal possible number of equilibria
tends to zero when or respectively goes to infinity. On the other hand,
we demonstrate that the expected number of stable equilibria is bounded within
a certain interval. Finally, for larger and , numerical results are
provided and discussed.Comment: 26 pages, 1 figure, 1 table. revised versio
Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games
In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the paper are some qualitative and quantitative results on the expected density, fn,dfn,d, and the expected number, E(n, d), of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically as √d−1 as d is sufficiently large. Secondly, we prove that they are monotone functions of d. We also make a conjecture for games with more than two strategies. Thirdly, we provide numerical simulations for our analytical results and to support the conjecture. As consequences of our analysis, some qualitative and quantitative results on the distribution of zeros of a random Bernstein polynomial are also obtained
Approximating n-player behavioural strategy nash equilibria using coevolution
Coevolutionary algorithms are plagued with a set of problems related to intransitivity that make it questionable what the end product of a coevolutionary run can achieve. With the introduction of solution concepts into coevolution, part of the issue was alleviated, however efficiently representing and achieving game theoretic solution concepts is still not a trivial task. In this paper we propose a coevolutionary algorithm that approximates behavioural strategy Nash equilibria in n-player zero sum games, by exploiting the minimax solution concept. In order to support our case we provide a set of experiments in both games of known and unknown equilibria. In the case of known equilibria, we can confirm our algorithm converges to the known solution, while in the case of unknown equilibria we can see a steady progress towards Nash. Copyright 2011 ACM
Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics
A long-running difficulty with conventional game theory has been how to
modify it to accommodate the bounded rationality of all real-world players. A
recurring issue in statistical physics is how best to approximate joint
probability distributions with decoupled (and therefore far more tractable)
distributions. This paper shows that the same information theoretic
mathematical structure, known as Product Distribution (PD) theory, addresses
both issues. In this, PD theory not only provides a principled formulation of
bounded rationality and a set of new types of mean field theory in statistical
physics. It also shows that those topics are fundamentally one and the same.Comment: 17 pages, no figures, accepted for publicatio
A New Mathematical Model for Evolutionary Games on Finite Networks of Players
A new mathematical model for evolutionary games on graphs is proposed to
extend the classical replicator equation to finite populations of players
organized on a network with generic topology. Classical results from game
theory, evolutionary game theory and graph theory are used. More specifically,
each player is placed in a vertex of the graph and he is seen as an infinite
population of replicators which replicate within the vertex. At each time
instant, a game is played by two replicators belonging to different connected
vertices, and the outcome of the game influences their ability of producing
offspring. Then, the behavior of a vertex player is determined by the
distribution of strategies used by the internal replicators. Under suitable
hypotheses, the proposed model is equivalent to the classical replicator
equation. Extended simulations are performed to show the dynamical behavior of
the solutions and the potentialities of the developed model.Comment: 26 pages, 7 figures, 1 tabl
Genome-driven evolutionary game theory helps understand the rise of metabolic interdependencies in microbial communities
Metabolite exchanges in microbial communities give rise to ecological interactions that govern ecosystem diversity and stability. It is unclear, however, how the rise of these interactions varies across metabolites and organisms. Here we address this question by integrating genome-scale models of metabolism with evolutionary game theory. Specifically, we use microbial fitness values estimated by metabolic models to infer evolutionarily stable interactions in multi-species microbial “games”. We first validate our approach using a well-characterized yeast cheater-cooperator system. We next perform over 80,000 in silico experiments to infer how metabolic interdependencies mediated by amino acid leakage in Escherichia coli vary across 189 amino acid pairs. While most pairs display shared patterns of inter-species interactions, multiple deviations are caused by pleiotropy and epistasis in metabolism. Furthermore, simulated invasion experiments reveal possible paths to obligate cross-feeding. Our study provides genomically driven insight into the rise of ecological interactions, with implications for microbiome research and synthetic ecology.We gratefully acknowledge funding from the Defense Advanced Research Projects Agency (Purchase Request No. HR0011515303, Contract No. HR0011-15-C-0091), the U.S. Department of Energy (Grants DE-SC0004962 and DE-SC0012627), the NIH (Grants 5R01DE024468 and R01GM121950), the national Science Foundation (Grants 1457695 and NSFOCE-BSF 1635070), MURI Grant W911NF-12-1-0390, the Human Frontiers Science Program (grant RGP0020/2016), and the Boston University Interdisciplinary Biomedical Research Office ARC grant on Systems Biology Approaches to Microbiome Research. We also thank Dr Kirill Korolev and members of the Segre Lab for their invaluable feedback on this work. (HR0011515303 - Defense Advanced Research Projects Agency; HR0011-15-C-0091 - Defense Advanced Research Projects Agency; DE-SC0004962 - U.S. Department of Energy; DE-SC0012627 - U.S. Department of Energy; 5R01DE024468 - NIH; R01GM121950 - NIH; 1457695 - national Science Foundation; NSFOCE-BSF 1635070 - national Science Foundation; W911NF-12-1-0390 - MURI; RGP0020/2016 - Human Frontiers Science Program; Boston University Interdisciplinary Biomedical Research Office ARC)Published versio
Evolutionary Multiplayer Games
Evolutionary game theory has become one of the most diverse and far reaching
theories in biology. Applications of this theory range from cell dynamics to
social evolution. However, many applications make it clear that inherent
non-linearities of natural systems need to be taken into account. One way of
introducing such non-linearities into evolutionary games is by the inclusion of
multiple players. An example is of social dilemmas, where group benefits could
e.g.\ increase less than linear with the number of cooperators. Such
multiplayer games can be introduced in all the fields where evolutionary game
theory is already well established. However, the inclusion of non-linearities
can help to advance the analysis of systems which are known to be complex, e.g.
in the case of non-Mendelian inheritance. We review the diachronic theory and
applications of multiplayer evolutionary games and present the current state of
the field. Our aim is a summary of the theoretical results from well-mixed
populations in infinite as well as finite populations. We also discuss examples
from three fields where the theory has been successfully applied, ecology,
social sciences and population genetics. In closing, we probe certain future
directions which can be explored using the complexity of multiplayer games
while preserving the promise of simplicity of evolutionary games.Comment: 14 pages, 2 figures, review pape
Recommended from our members
Chris Cannings: A Life in Games
Chris Cannings was one of the pioneers of evolutionary game theory. His early work was inspired by the formulations of John Maynard Smith, Geoff Parker and Geoff Price; Chris recognized the need for a strong mathematical foundation both to validate stated results and to give a basis for extensions of the models. He was responsible for fundamental results on matrix games, as well as much of the theory of the important war of attrition game, patterns of evolutionarily stable strategies, multiplayer games and games on networks. In this paper we describe his work, key insights and their influence on research by others in this increasingly important field. Chris made substantial contributions to other areas such as population genetics and segregation analysis, but it was to games that he always returned. This review is written by three of his students from different stages of his career
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