5 research outputs found
Attainability in Repeated Games with Vector Payoffs
We introduce the concept of attainable sets of payoffs in two-player repeated
games with vector payoffs. A set of payoff vectors is called {\em attainable}
if player 1 can ensure that there is a finite horizon such that after time
the distance between the set and the cumulative payoff is arbitrarily
small, regardless of what strategy player 2 is using. This paper focuses on the
case where the attainable set consists of one payoff vector. In this case the
vector is called an attainable vector. We study properties of the set of
attainable vectors, and characterize when a specific vector is attainable and
when every vector is attainable.Comment: 28 pages, 2 figures, conference version at NetGCoop 201
Adaptation, coordination, and local interactions via distributed approachability
This paper investigates the relation between cooperation, competition, and local interactions in large distributed multi-agent
systems. The main contribution is the game-theoretic problem formulation and solution approach based on the new framework
of distributed approachability, and the study of the convergence properties of the resulting game model. Approachability
theory is the theory of two-player repeated games with vector payoffs, and distributed approachability is here presented for
the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local
information and interaction structure. The game model turns into a nonlinear differential inclusion, which after a proper design
of the control and disturbance policies, presents a consensus term and an exogenous adversarial input. Local interactions enter
in the model through a graph topology and the corresponding graph-Laplacian matrix. Given the above model, we turn the
original questions on cooperation, competition, and local interactions, into convergence properties of the differential inclusion.
In particular, we prove convergence and exponential convergence conditions around zero under general Markovian strategies.
We illustrate our results in the case of decentralized organizations with multiple decision-makers
Attainability in Repeated Games with Vector Payoffs ∗
We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called attainable if player 1 can ensure that there is a finite horizon T such that after time T the distance between the set and the cumulative payoff is arbitrarily small, regardless of what strategy player 2 is using. This paper focuses on the case where the attainable set consists of one payoff vector. In this case the vector is called an attainable vector. We study properties of the set of attainable vectors, and characterize when a specific vector is attainable and when every vector is attainable