Dynamics to equilibrium in Network Games: individual behavior and global response

TL;DR

This paper investigates how individual strategies evolve in network games, revealing that rational updates lead to Nash equilibria while imitation often results in suboptimal states, with implications for understanding social and economic interactions.

Contribution

It introduces numerical simulations to analyze the accessibility of Nash equilibria through different adaptation mechanisms in network games, extending mean-field analysis insights.

Findings

Rational behavior leads to Nash equilibria and better welfare outcomes.

Imitative dynamics often fail to reach equilibria and result in poor states.

Network structure influences the formation and stability of equilibria.

Abstract

Various social contexts ranging from public goods provision to information collection can be depicted as games of strategic interactions, where a player's well-being depends on her own action as well as on the actions taken by her neighbors. Whereas much attention has been devoted to the identification and characterization of Bayes-Nash equilibria of such games, in this work we look at strategic interactions from an evolutionary perspective. Starting from a recent mean-field analysis of the evolutionary dynamics in these games, here we present results of numerical simulations designed to find out whether Nash equilibria are accessible by adaptation of players' strategies, and in general to find the attractors of the evolution. Simulations allow us to go beyond a global characterization of the cooperativeness of the equilibria and probe into the individual behavior. We find that when players imitate each other, the evolution does not reach Nash equilibria and, worse, leads to very unfavorable states in terms of welfare. On the contrary, when players update their behavior rationally, they self-organize into a rich variety of Nash equilibria, where individual behavior and payoffs are shaped by the nature of the game, the structure of the social network and the players' position within the topology. Our results allow us to assess the validity of the mean-field approaches and also show qualitative agreement with theoretical predictions for equilibria in the context of one-shot games under incomplete information.