33 research outputs found
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
On the communication discussion of two distributed population-game approaches for optimization purposes
© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Population games have become a powerful tool for solving resource-allocation problems in a distributed manner, and for the design of non-centralized optimization-based controllers. The aim of this paper is to illustrate the advantages of two recently introduced population-game approaches in comparison to other classical optimization methods. More specically, the discussion is mainly devoted to the communication requirements. Finally, an illustrative example shows with more detail the advantages highlighted throughout the comparative discussion, i.e., fewer communications links are required for resource allocation problems, and there is not need of additional computation stages to solve the problem in a distributed manner.Peer ReviewedPostprint (author's final draft
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