  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).
