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International audience; We define a general model capturing the behavior of a population of anonymous agents that interact in pairs. This model captures some of the main features of opportunistic networks, in which nodes (such as the ones of a mobile ad hoc networks) meet sporadically. For its reminiscence to Population Protocol, we call our model \emph{Large-Population Protocol}, or LPP. We are interested in the design of LPPs enforcing, for every $\nu\in[0,1]$, a proportion $\nu$ of the agents to be in a specific subset of marked states, when the size of the population grows to infinity; In which case, we say that the protocol \emph{computes} $\nu$. We prove that, for every $\nu\in[0,1]$, $\nu$ is computable by a LPP if and only if $\nu$ is algebraic. Our positive result is constructive. That is, we show how to construct, for every algebraic number $\nu\in[0,1]$, a protocol which computes $\nu$.

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement. A population protocol corresponds to a collection of anonymous agents, modeled by finite automata, that interact with one another to carry out computations, by updating their states, using some rules. Their computational power has been investigated under several hypotheses but always when restricted to finite size populations. In particular, predicates stably computable in the original model have been characterized as those definable in Presburger arithmetic. We study mathematically the convergence of population protocols when the size of the population goes to infinity. We do so by giving general results, that we illustrate through the example of a particular population protocol for which we even obtain an asymptotic development. This example shows in particular that these protocols seem to have a rather different computational power when a huge population hypothesis is considered., Submitted to Applied Mathematics and Computation. 2009

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement: A collection of anonymous agents, modeled by finite automata, interact in pairs according to some rules. Predicates on the initial configurations that can be computed by such protocols have been characterized under several hypotheses. We discuss here whether and when the rules of interactions between agents can be seen as a game from game theory. We do so by discussing several basic protocols.