Games on graphs

Allen, Benjamin; Nowak, Martin A.

doi:10.4171/emss/3

Cited by 152 publications

(202 citation statements)

References 118 publications

Supporting

Mentioning

194

Contrasting

Order By: Relevance

“…In evolutionary games n × n payoff matrices are used to define the interactions among (equivalent) players following one of their n strategies against their coplayers defined by a connectivity network [1][2][3]. The systematic analysis of the games [4] and the classification of the resultant behavior are prevented by the large number of parameters (n 2 ) characterizing the interaction itself, particularly if n > 3.…”

Section: Introductionmentioning

confidence: 99%

Four classes of interactions for evolutionary games

et al. 2015

Self Cite

View full text Add to dashboard Cite

The symmetric four-strategy games are decomposed into a linear combination of 16 basis games represented by orthogonal matrices. Among these basis games four classes can be distinguished as it is already found for the three-strategy games. The games with self-dependent (cross-dependent) payoffs are characterized by matrices consisting of uniform rows (columns). Six of 16 basis games describe coordination-type interactions among the strategy pairs and three basis games span the parameter space of the cyclic components that are analogous to the rock-paper-scissors games. In the absence of cyclic components the game is a potential game and the potential matrix is evaluated. The main features of the four classes of games are discussed separately and we illustrate some characteristic strategy distributions on a square lattice in the low noise limit if logit rule controls the strategy evolution. Analysis of the general properties indicates similar types of interactions at larger number of strategies for the symmetric matrix games.

show abstract

Section: Introductionmentioning

confidence: 99%

Four classes of interactions for evolutionary games

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…In multiagent evolutionary games [1][2][3][4] the players are located on the sites of a lattice or graph, play two-player games with their nearest neighbors, and are allowed to change their strategies by following a dynamical rule based on their payoffs. It is already clarified that the resulting stationary state depends on the number of strategies, the payoff matrix, the dynamical rule, and the connectivity structures defining the interacting pairs.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary games with coordination and self-dependent interactions

Király

Szabó

2017

Phys. Rev. E

View full text Add to dashboard Cite

Multistrategy evolutionary games are studied on a square lattice when the pair interactions are composed of coordinations between strategy pairs and an additional term with self-dependent payoff. We describe a method for determining the strength of each elementary coordination component in n-strategy potential games. Using analytical and numerical methods, the presence and absence of Ising-type order-disorder phase transitions are studied when a single pair coordination is extended by some types of self-dependent elementary games. We also introduce noise-dependent three-strategy equivalents of the n-strategy elementary coordination games.

show abstract

“…Throughout this paper we study evolutionary games on an N = L × L-site square lattice with periodic boundary conditions [6,13,36]. There is one player located at each site, all of whom repeatedly play the same two-player game with their four nearest neighbors and may choose one of n available pure strategies to play in all four games.…”

Section: The Model and Its General Featuresmentioning

confidence: 99%

Entropy Affects the Competition of Ordered Phases

Király

Szabó

2018

Entropy

View full text Add to dashboard Cite

Abstract:The effect of entropy at low noises is investigated in five-strategy logit-rule-driven spatial evolutionary potential games exhibiting two-fold or three-fold degenerate ground states. The non-zero elements of the payoff matrix define two subsystems which are equivalent to an Ising or a three-state Potts model depending on whether the players are constrained to use only the first two or the last three strategies. Due to the equivalence of these models to spin systems, we can use the concepts and methods of statistical physics when studying the phase transitions. We argue that the greater entropy content of the Ising phase plays an important role in its stabilization when the magnitude of the Potts component is equal to or slightly greater than the strength of the Ising component. If the noise is increased in these systems, then the presence of the higher entropy state can cause a kind of social dilemma in which the players' average income is reduced in the stable Ising phase following a first-order phase transition.

show abstract

Games on graphs

Cited by 152 publications

References 118 publications

Four classes of interactions for evolutionary games

Four classes of interactions for evolutionary games

Evolutionary games with coordination and self-dependent interactions

Entropy Affects the Competition of Ordered Phases

Contact Info

Product

Resources

About