Equilibria, information and frustration in heterogeneous network games with conflicting preferences

Abstract

Interactions between people are the basis on which the structure of our society arises as a complex system and, at the same time, are the starting point of any physical description of it. In the last few years, much theoretical research has addressed this issue by combining the physics of complex networks with a description of interactions in terms of evolutionary game theory. We here take this research a step further by introducing a most salient societal factor such as the individuals' preferences, a characteristic that is key to understand much of the social phenomenology these days. We consider a heterogeneous, agent-based model in which agents interact strategically with their neighbors but their preferences and payoffs for the possible actions differ. We study how such a heterogeneous network behaves under evolutionary dynamics and different strategic interactions, namely coordination games and best shot games. With this model we study the emergence of the equilibria predicted analytically in random graphs under best response dynamics, and we extend this test to unexplored contexts like proportional imitation and scale free networks. We show that some theoretically predicted equilibria do not arise in simulations with incomplete Information, and we demonstrate the importance of the graph topology and the payoff function parameters for some games. Finally, we discuss our results with available experimental evidence on coordination games, showing that our model agrees better with the experiment that standard economic theories, and draw hints as to how to maximize social efficiency in situations of conflicting preferences.

An experimental study of network effects on coordination in asymmetric games

“…These situations are often formalized by asymmetric coordination games, such as the ‘battle of the sexes’. Computational models 9,10 and other theoretical studies 11,12 show that network structure is an important predictor of behavior in iterated asymmetric games. Although these models convincingly show that there are network effects on equilibrium behavior, no empirical studies have been conducted to corroborate these findings.…”

“…In this study we empirically test behavioral predictions from previous computational 9,10 and theoretical studies 11,12 ; specifically, we consider the influence of network structure on equilibrium behavior in iterated asymmetric ‘battle of the sexes’ games. We focus on the computational model described in Broere et al .…”

Investigating Peer and Sorting Effects within an Adaptive Multiplex Network Model

“…Hence, the strategies are dynamic and not fixed. Furthermore, our work contributes to the literature of coordination on social networks, either static [20][21][22][23][24][25] and dynamic [26][27][28][29][30][31][32][33] structures 4 .…”

How the weak and strong links affect the evolution of prisoner's dilemma game

“…Since social interactions are traditionally described by networks, evolutionary games on networks and structured populations have received ample attention in the recent past [14][15][16]. In general, the study of game evolution in complex networks mainly focuses on the influence of network topology, the choice mechanism of individuals' strategies and external environment disturbance [17][18][19]. The evolutionary version of the prisoner's dilemma (PD) game was first proposed in small-world networks in [20], after that the game model based on the mutual interactions (such as the stag hunt game, the boxed pigs' game and the snowdrift game) or the group interactions (such as the public goods game) have received extensive attentions [21][22][23][24][25].…”

“…It is easy to see that equation(19) has the trivial solutions r = 0 the general solution of formula(19) can be obtained as follows: supports the coexistence of cooperators and defectors.…”