Population Protocols that Correspond to Symmetric Games

TL;DR

This paper explores the connection between population protocols and symmetric games, showing that some protocols can be realized as symmetric games and that any protocol can be simulated by a symmetric one, highlighting the relationship between distributed computing and game theory.

Contribution

It establishes conditions under which population protocols correspond to symmetric games and demonstrates that all protocols can be simulated by symmetric protocols.

Findings

Some basic protocols can be realized using symmetric games.

Not all rules in population protocols can be considered as symmetric games.

Any population protocol can be simulated by a symmetric protocol.

Abstract

Population protocols have been introduced by Angluin et {al.} as a model of networks consisting of very limited mobile agents that interact in pairs but with no control over their own movement. A collection of anonymous agents, modeled by finite automata, interact pairwise according to some rules that update their states. The model has been considered as a computational model in several papers. Input values are initially distributed among the agents, and the agents must eventually converge to the the correct output. Predicates on the initial configurations that can be computed by such protocols have been characterized under various hypotheses. In an orthogonal way, several distributed systems have been termed in literature as being realizations of games in the sense of game theory. In this paper, we investigate under which conditions population protocols, or more generally pairwise interaction rules, can be considered as the result of a symmetric game. We prove that not all rules can be considered as symmetric games.% We prove that some basic protocols can be realized using symmetric games. As a side effect of our study, we also prove that any population protocol can be simulated by a symmetric one (but not necessarily a game).