Johanne Cohen

On the convergence of population protocols when population goes to infinity

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.

Distributed Learning of Wardrop Equilibria

We consider the problem of learning equilibria in a well known game theoretic traffic model due to Wardrop. We consider a distributed learning algorithm that we prove to converge to equilibria. The proof of convergence is based on a differential equation governing the global macroscopic evolution of the system, inferred from the local microscopic evolutions of agents. We prove that the differential equation converges with the help of Lyapunov techniques.

Shuffling biological sequences with motif constraints

We study the following problem: given a biological sequence S, a multiset M of motifs and an integer k, generate uniformly random sequences which contain the given motifs and have exactly the same frequencies of occurrence of k-lets (i.e. factors of length k) of S. We notably prove that the problem of deciding whether a sequence respects the given motif constraints is NP-complete. Nevertheless, we give a random generation algorithm which turns out to be experimentally efficient.

Transit prices negotiation: combined repeated game and distributed algorithmic approach

We present both a game theoretic and a distributed algorithmic approach for the transit price negotiation problem in the interdomain routing framework. The analysis of the centralized transit price negotiation problem shows that the only one non cooperative equilibrium is when the lowest cost provider takes all the market. The perspective of the game being repeated makes cooperation possible while maintaining higher prices. We consider then the system under a realistic distributed framework and simulate its behaviour under a simple price adjustment strategy and analyse whether it matches the theoretical results.

Pricing composite cloud services: The cooperative perspective

We are interested in analyzing situations of competition among the providers in emerging service oriented networks where added value services may be obtained by composing services offered by cloud providers. Those activities are not regulated and may give rise to coalition formation. The comparison between different potential coalitions and their characterization in terms of stability and dominance can be considered using cooperative game concepts. Indeed, a fair revenue sharing mechanism such as the Shapley value can ensure the stability of the formed coalition. However, when the core is empty the grand coalition is no more stable, though other concepts from the bargaining theory may apply. We will investigate potential revenue sharing mechanisms that make alliances sustainable.