Congestion phenomena caused by matching pennies in evolutionary games

Abstract

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.

Interplay of Elementary Interactions Causing Social Traps in Evolutionary Games

“…By rotating the coordinate axes, we can choose another parametrization for the quantification of pair interactions. Previous studies have justified the usefulness of basis matrices that are defined by the dyadic products of n-dimensional basis vectors which include the all-one vector [45]. The dyadic product of the all-one vector with itself is the all-one matrix, which represents an irrelevant (constant) term that provides the same payoff to the players regardless of their strategy choices.…”

Quantum games of opinion formation based on the Marinatto-Weber quantum game scheme

“…From inequalities (11), it is easy to prove that the quantum GM I can be reduced to the classical GM I if there does exist a term which is equal to 1…”

“…Many models, such as DeGroot model [4], Sznajd model [5], discrete CODA model [6], Hegselmann-Krause model [7], generalized Glauber models [8], Deffuant model [9], have been developed to simulate interaction mechanisms of opinions. In recent years, game theory, which provides a useful framework to build foundational models to mimick the interactions among agents with conflict of interests in many disciplines [10][11][12][13][14][15][16][17][18][19], has also been used in these fields to help understand opinion formation and evolution. With respect to opinion formation, a lot of game models have been proposed or used in previous studies [20][21][22][23][24][25].…”