6533b831fe1ef96bd12998fa

RESEARCH PRODUCT

Adaptation, coordination, and local interactions via distributed approachability

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This paper investigates the relation between cooperation, competition, and local interactions in large distributed multi-agent\ud systems. The main contribution is the game-theoretic problem formulation and solution approach based on the new framework\ud of distributed approachability, and the study of the convergence properties of the resulting game model. Approachability\ud theory is the theory of two-player repeated games with vector payoffs, and distributed approachability is here presented for\ud the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local\ud information and interaction structure. The game model turns into a nonlinear differential inclusion, which after a proper design\ud of the control and disturbance policies, presents a consensus term and an exogenous adversarial input. Local interactions enter\ud in the model through a graph topology and the corresponding graph-Laplacian matrix. Given the above model, we turn the\ud original questions on cooperation, competition, and local interactions, into convergence properties of the differential inclusion.\ud In particular, we prove convergence and exponential convergence conditions around zero under general Markovian strategies.\ud We illustrate our results in the case of decentralized organizations with multiple decision-makers.