Non-centralized Control for Flow-based Distribution Networks: A Game-theoretical Insight

This paper solves a data-driven control problem for a flow-based distribution network with two objectives: a resource allocation and a fair distribution of costs. These objectives represent both cooperation and competition directions. It is proposed a solution that combines either a centralized or distributed cooperative game approach using the Shapley value to determine a proper partitioning of the system and a fair communication cost distribution. On the other hand, a decentralized noncooperative game approach computing the Nash equilibrium is used to achieve the control objective of the resource allocation under a non-complete information topology. Furthermore, an invariant-set property is presented and the closed-loop system stability is analyzed for the non cooperative game approach. Another contribution regarding the cooperative game approach is an alternative way to compute the Shapley value for the proposed specific characteristic function. Unlike the classical cooperative-games approach, which has a limited application due to the combinatorial explosion issues, the alternative method allows calculating the Shapley value in polynomial time and hence can be applied to large-scale problems.Generalitat de Catalunya FI 2014Ministerio de Ciencia y Educación DPI2016-76493-C3-3-RMinisterio de Ciencia y Educación DPI2008-05818Proyecto europeo FP7-ICT DYMASO

On imitation dynamics in potential population games

Imitation dynamics for population games are studied and their asymptotic properties analyzed. In the considered class of imitation dynamics - that encompass the replicator equation as well as other models previously considered in evolutionary biology - players have no global information about the game structure, and all they know is their own current utility and the one of fellow players contacted through pairwise interactions. For potential population games, global asymptotic stability of the set of Nash equilibria of the sub-game restricted to the support of the initial population configuration is proved. These results strengthen (from local to global asymptotic stability) existing ones and generalize them to a broader class of dynamics. The developed techniques highlight a certain structure of the problem and suggest possible generalizations from the fully mixed population case to imitation dynamics whereby agents interact on complex communication networks.Comment: 7 pages, 3 figures. Accepted at CDC 201

Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution

A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire joint distribution of strategies and types to influence the payoffs of agents. We clarify regularity conditions for the unique existence of a solution trajectory and for the existence of equilibrium. We confirm that equilibrium stationarity in general and equilibrium stability in potential games are extended from the homogeneous setting to the heterogeneous setting. In particular, a wide class of admissible dynamics share the same set of locally stable equilibria in a potential game through local maximization of the potential