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The problem of computing a common point that lies in the intersection of afinite number of closed convex sets, each known to one agent in a network, isstudied. This issue, known as the distributed convex feasibility problem or thedistributed constrained consensus problem, constitutes an important researchgoal mainly due to the large number of possible applications. In this work,this issue is treated from a game theoretic viewpoint. In particular, weformulate the problem as a non-cooperative game for which a potential functionexists and prove that all Nash equilibria of this game correspond to consensusstates. Based upon this analysis, a best-response based distributed algorithmthat solves the constrained consensus problem is developed. Furthermore, onemore approach to solve the convex feasibility problem is studied based upon aprojected gradient type algorithm that seeks the maximum of the consideredpotential function. A condition for the convergence of this scheme is derivedand an exact distributed algorithm is given. Finally, simulation results for asource localization problem are given, that validate the theoretical resultsand demonstrate the applicability and performance of the derived algorithms.

Potential Games for Distributed Constrained Consensus