The fashion game: Network extension of Matching Pennies

In spatial evolutionary games the payoff matrices are used to describe pair interactions among neighboring players located on a lattice. Now we introduce a way how the payoff matrices can be built up as a sum of payoff components reflecting basic symmetries. For the two-strategy games this decomposition reproduces interactions characteristic to the Ising model. For the three-strategy symmetric games the Fourier components can be classified into four types representing games with self-dependent and cross-dependent payoffs, variants of three-strategy coordinations, and the rock-scissors-paper (RSP) game. In the absence of the RSP component the game is a potential game. The resultant potential matrix has been evaluated. The general features of these systems are analyzed when the game is expressed by the linear combinations of these components.

show abstract

“…Here it is worth mentioning that, among the nonsymmetric 2 × 2 games, the matching pennies component can induce similar effects [37][38][39].…”

Section: Fourier Decomposition Of 3 × 3 Gamesmentioning

confidence: 95%

Fourier decomposition of payoff matrix for symmetric three-strategy games

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Such situations were reported previously by van Valen [67,68] who suggested the concept of Red Queen mechanism to explain biological evolution via a constant arm race between co-evolving species. The interactions between buyers and sellers [69], property owners and criminals [70], or conformists and rebels [71] exhibit similar features. For very recent investigations of the Red Queen mechanism at the level of population dynamics we suggest reading the papers by Sardanyés and Solé [72] and Juul et al [73].…”

Section: Decomposition Of Two-strategy Bi-matrix Gamesmentioning

confidence: 99%

Evolutionary potential games on lattices

2016

View full text Add to dashboard Cite

Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide scale of biological objects, human individuals, or even their associations. In these systems the interactions are characterized by matrices that can be decomposed into elementary matrices (games) and classified into four types. The concept of decomposition helps the identification of potential games and also the evaluation of the potential that plays a crucial role in the determination of the preferred Nash equilibrium, and defines the Boltzmann distribution towards which these systems evolve for suitable types of dynamical rules. This survey draws parallel between the potential games and the kinetic Ising type models which are investigated for a wide scale of connectivity structures. We discuss briefly the applicability of the tools and concepts of statistical physics and thermodynamics. Additionally the general features of ordering phenomena, phase transitions and slow relaxations are outlined and applied to evolutionary games. The discussion extends to games with three or more strategies. Finally we discuss what happens when the system is weakly driven out of the "equilibrium state" by adding non-potential components representing games of cyclic dominance.

show abstract

“…The relevance of a conceptually similar circular transition in biological systems was first described by van Valen [25,26], who named this effect the Red Queen mechanism. Similar endless races can be observed in social systems between buyers and sellers [27], property owners and criminals [28], males and females [29,30], or conformists and rebels [31]. The consideration of an evolutionary multiagent system on network with this type of interaction prescribes two kinds of players distributed on bipartite graphs or lattices [32].…”

Section: Introductionmentioning

confidence: 82%

“…In the light of these results the utilization of congestion phenomenon emerges directly. The relevance of this question is stressed by recent experiments investigating human behavior in real-life situations involving the matchingpennies component in the payoffs [31,52,53].…”

Section: Exploitation Of Congestionmentioning

confidence: 99%

Congestion phenomena caused by matching pennies in evolutionary games

Szabó

Szolnoki

2015

Phys. Rev. E

View full text Add to dashboard Cite

Evolutionary social dilemma games are extended by an additional matching-pennies game that modifies the collected payoffs. In a spatial version players are distributed on a square lattice and interact with their neighbors. First, we show that the matching-pennies game can be considered as the microscopic force of the Red Queen effect that breaks the detailed balance and induces eddies in the microscopic probability currents if the strategy update is analogous to the Glauber dynamics for the kinetic Ising models. The resulting loops in probability current breaks symmetry between the chessboardlike arrangements of strategies via a bottleneck effect occurring along the four-edge loops in the microscopic states. The impact of this congestion is analogous to the application of a staggered magnetic field in the Ising model; that is, the order-disorder critical transition is wiped out by noise. It is illustrated that the congestion induced symmetry breaking can be beneficial for the whole community within a certain region of parameters.

show abstract

The fashion game: Network extension of Matching Pennies

Cited by 15 publications

References 19 publications

Fourier decomposition of payoff matrix for symmetric three-strategy games

Fourier decomposition of payoff matrix for symmetric three-strategy games

Evolutionary potential games on lattices

Congestion phenomena caused by matching pennies in evolutionary games

Contact Info

Product

Resources

About