Asymetric Pavlovian Populations

TL;DR

This paper explores the connection between population protocols and game theory, demonstrating that all semi-linear predicates computable by protocols can be realized through Pavlovian population multi-protocols based on asymmetric games.

Contribution

It shows that restricting to asymmetric games does not limit computational power, as all semi-linear predicates can be computed by Pavlovian protocols derived from such games.

Findings

All semi-linear predicates are computable by Pavlovian population protocols.

Asymmetric game restrictions do not reduce the computational capabilities of population protocols.

Population protocols can be characterized as game-theoretic models, specifically Pavlovian protocols.

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. Predicates on the initial configurations that can be computed by such protocols have been characterized as semi-linear predicates. In an orthogonal way, several distributed systems have been termed in literature as being realizations of games in the sense of game theory. We investigate under which conditions population protocols, or more generally pairwise interaction rules, correspond to games. We show that restricting to asymetric games is not really a restric- tion: all predicates computable by protocols can actually be computed by protocols corresponding to games, i.e. any semi-linear predicate can be computed by a Pavlovian population multi-protocol.