Results 1  10
of
95
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
Abstract

Cited by 144 (0 self)
 Add to MetaCart
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Active linking in evolutionary games
, 2006
"... In the traditional approach to evolutionary game theory, the individuals of a population meet each other at random, and they have no control over the frequency or duration of interactions. Here we remove these simplifying assumptions. We introduce a new model, where individuals differ in the rate at ..."
Abstract

Cited by 33 (10 self)
 Add to MetaCart
In the traditional approach to evolutionary game theory, the individuals of a population meet each other at random, and they have no control over the frequency or duration of interactions. Here we remove these simplifying assumptions. We introduce a new model, where individuals differ in the rate at which they seek new interactions. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. In a limiting case, the linking dynamics introduces a simple transformation of the payoff matrix. We outline conditions for evolutionary stability. As a specific example, we study the interaction between cooperators and defectors. We find a simple relationship that characterizes those linking dynamics which allow natural selection to favour cooperation over defection.
Calculating Evolutionary Dynamics in Structured Populations
, 2009
"... Evolution is shaping the world around us. At the core of every evolutionary process is a population of reproducing individuals. The outcome of an evolutionary process depends on population structure. Here we provide a general formula for calculating evolutionary dynamics in a wide class of structure ..."
Abstract

Cited by 26 (3 self)
 Add to MetaCart
(Show Context)
Evolution is shaping the world around us. At the core of every evolutionary process is a population of reproducing individuals. The outcome of an evolutionary process depends on population structure. Here we provide a general formula for calculating evolutionary dynamics in a wide class of structured populations. This class includes the recently introduced ‘‘games in phenotype space’ ’ and ‘‘evolutionary set theory.’ ’ There can be local interactions for determining the relative fitness of individuals, but we require global updating, which means all individuals compete uniformly for reproduction. We study the competition of two strategies in the context of an evolutionary game and determine which strategy is favored in the limit of weak selection. We derive an intuitive formula for the structure coefficient, s, and provide a method for efficient numerical calculation.
Evolutionary game theory: temporal and spatial effects beyond replicator dynamics
, 2009
"... Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the socalled replicator equation, that describes mathematically the idea that those indiv ..."
Abstract

Cited by 23 (1 self)
 Add to MetaCart
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the socalled replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of nonmean field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the nontrivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.
Analytical Results for Individual and Group Selection of Any Intensity
 BULLETIN OF MATHEMATICAL BIOLOGY (2008)
, 2007
"... The idea of evolutionary game theory is to relate the payoff of a game to reproductive success ( = fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in th ..."
Abstract

Cited by 22 (5 self)
 Add to MetaCart
The idea of evolutionary game theory is to relate the payoff of a game to reproductive success ( = fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection ( = multilevel selection). We discuss the difference between our approach and that of inclusive fitness theory.
Stochastic evolutionary game dynamics
 In Reviews of Nonlinear Dynamics and Complexity
, 2009
"... Game theory and evolution Modern game theory goes back to a series of papers by the mathematician John von Neumann in the 1920s. This program started a completely new branch of social sciences and applied mathematics. This early work on game theory is summarized in the seminal book “The Theory of Ga ..."
Abstract

Cited by 20 (4 self)
 Add to MetaCart
Game theory and evolution Modern game theory goes back to a series of papers by the mathematician John von Neumann in the 1920s. This program started a completely new branch of social sciences and applied mathematics. This early work on game theory is summarized in the seminal book “The Theory of Games and Economic Behavior ” by John von Neumann and Oskar Morgenstern [115]. Initially, game theory was primarily focused on cooperative game theory, which analyzes optimal strategies assuming that individuals stick to previous agreements. In the 1950’s, the focus shifted to noncooperative games in which individuals act selfish to get the most out of an interaction. At that time, game theory had matured from a theoretical concept to a scientific field influencing political decision making, mainly in the context of the arms race of the cold war. The basic assumption was that individuals act rationally and take into account that their interaction partners know that their decisions are rational and
Spatial effects in social dilemmas
, 2006
"... Social dilemmas and the evolutionary conundrum of cooperation are traditionally studied through various kinds of game theoretical models such as the prisoner’s dilemma, public goods games, snowdrift games or byproduct mutualism. All of them exemplify situations which are characterized by different ..."
Abstract

Cited by 17 (2 self)
 Add to MetaCart
Social dilemmas and the evolutionary conundrum of cooperation are traditionally studied through various kinds of game theoretical models such as the prisoner’s dilemma, public goods games, snowdrift games or byproduct mutualism. All of them exemplify situations which are characterized by different degrees of conflicting interests between the individuals and the community. In groups of interacting individuals, cooperators produce a common good benefitting the entire group at some cost to themselves, whereas defectors attempt to exploit the resource by avoiding the costly contributions. Based on synergistic or discounted accumulation of cooperative benefits a unifying theoretical framework was recently introduced that encompasses all games that have traditionally been studied separately (Hauert, Michor, Nowak, Doebeli, 2005. Synergy and discounting of cooperation in social dilemmas. J. Theor. Biol., in press.). Within this framework we investigate the effects of spatial structure with limited local interactions on the evolutionary fate of cooperators and defectors. The quantitative effects of space turn out to be quite sensitive to the underlying microscopic update mechanisms but, more general, we demonstrate that in prisoner’s dilemma type interactions spatial structure benefits cooperation—although the parameter range is quite limited—whereas in snowdrift type interactions spatial structure may be beneficial too, but often turns out to be detrimental to cooperation.
Evolutionary game dynamics with nonuniform interaction rates
, 2006
"... The classical setting of evolutionary game theory, the replicator equation, assumes uniform interaction rates. The rate at which individuals meet and interact is independent of their strategies. Here we extend this framework by allowing the interaction rates to depend on the strategies. This extensi ..."
Abstract

Cited by 16 (1 self)
 Add to MetaCart
The classical setting of evolutionary game theory, the replicator equation, assumes uniform interaction rates. The rate at which individuals meet and interact is independent of their strategies. Here we extend this framework by allowing the interaction rates to depend on the strategies. This extension leads to nonlinear fitness functions. We show that a strict Nash equilibrium remains uninvadable for nonuniform interaction rates, but the conditions for evolutionary stability need to be modified. We analyze all games between two strategies. If the two strategies coexist or exclude each other, then the evolutionary dynamics do not change qualitatively, only the location of the equilibrium point changes. If, however, one strategy dominates the other in the classical setting, then the introduction of nonuniform interaction rates can lead to a pair of interior equilibria. For the Prisoner’s Dilemma, nonuniform interaction rates allow the coexistence between cooperators and defectors. For the snowdrift game, nonuniform interaction rates change the equilibrium frequency of cooperators.
Direct reciprocity on graphs
, 2007
"... Direct reciprocity is a mechanism for the evolution of cooperation based on the idea of repeated encounters between the same two individuals. Here we examine direct reciprocity in structured populations, where individuals occupy the vertices of a graph. The edges denote who interacts with whom. The ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
Direct reciprocity is a mechanism for the evolution of cooperation based on the idea of repeated encounters between the same two individuals. Here we examine direct reciprocity in structured populations, where individuals occupy the vertices of a graph. The edges denote who interacts with whom. The graph represents spatial structure or a social network. For birth–death or pairwise comparison updating, we find that evolutionary stability of direct reciprocity is more restrictive on a graph than in a wellmixed population, but the condition for reciprocators to be advantageous is less restrictive on a graph. For death–birth and imitation updating, in contrast, both conditions are easier to fulfill on a graph. Moreover, for all four update mechanisms, reciprocators can dominate defectors on a graph, which is never possible in a wellmixed population. We also study the effect of an error rate, which increases with the number of links per individual; interacting with more people simultaneously enhances the probability of making mistakes. We provide analytic derivations for all results.