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WeaklyAcyclic (Internet) Routing Games
"... Abstract. Weaklyacyclic games – a superclass of potential games – capture distributed environments where simple, globallyasynchronous interactions between strategic agents are guaranteed to converge to an equilibrium. We explore the class of routing games in [4, 12], which models important aspects ..."
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Abstract. Weaklyacyclic games – a superclass of potential games – capture distributed environments where simple, globallyasynchronous interactions between strategic agents are guaranteed to converge to an equilibrium. We explore the class of routing games in [4, 12], which models important aspects of routing on the Internet. We show that, in interesting contexts, such routing games are weakly acyclic and, moreover, that pure Nash equilibria in such games can be found in a computationally efficient manner. 1
Game Couplings: Learning Dynamics and Applications
"... Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very little is ..."
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Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very little is formally known about their properties and global dynamics. We investigate such distributed systems by introducing a novel gametheoretic construct, that we call gamecoupling. Game coupling intuitively allows us to stitch together the payoff structures of subgames. In order to study efficiency issues, we extend the price of anarchy approach (a major focus of gametheoretical multiagent systems [22]) to this setting, where we now care about the performance of each individual subsystem as well as the global performance. Such concerns give rise to a new notion of equilibrium, as well as a new learning paradigm. We prove matching welfare guarantees for both, both for individual subsystems as well as for the global system, using a generalization of the (λ, µ)smoothness framework [19]. In the second part of the paper, we work on understanding conditions that allow for wellstructured couplings. More generally, we examine when do game couplings preserve or enhance desirable properties of the original games, such as convergence of best response dynamics and low price of anarchy.
1 Game Couplings: Learning Dynamics and Applications
"... Abstract — Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very ..."
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Abstract — Modern engineering systems (such as the Internet) consist of multiple coupled subsystems. Such subsystems are designed with local (possibly conflicting) goals, with little or no knowledge of the implementation details of other subsystems. Despite the ubiquitous nature of such systems very little is formally known about their properties and global dynamics. We investigate such distributed systems by introducing a novel gametheoretic construct, that we call gamecoupling. Game coupling intuitively allows us to stitch together the payoff structures of two or more games into a new game. In order to study efficiency issues, we extend the price of anarchy framework to this setting, where we now care about local and global performance. Such concerns give rise to a new notion of equilibrium, as well as a new learning paradigm. We prove matching welfare guarantees for both, both for individual subsystems as well as for the global system, using a generalization of the (λ, µ)smoothness framework [17]. In the second part of the paper, we establish conditions leading to advantageous couplings that preserve or enhance desirable properties of the original games, such as convergence of best response dynamics and low price of anarchy. I.
Schedulers, Potentials and Weak Potentials in Weakly Acyclic Games
, 2014
"... Abstract. In a number of large, important families of finite games, not only do purestrategy Nash equilibria always exist but they are also reachable from any initial strategy profile by some sequence of myopic singleplayer moves to a better or bestresponse strategy. This weak acyclicity property ..."
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Abstract. In a number of large, important families of finite games, not only do purestrategy Nash equilibria always exist but they are also reachable from any initial strategy profile by some sequence of myopic singleplayer moves to a better or bestresponse strategy. This weak acyclicity property is shared, for example, by all perfectinformation extensiveform games, which are generally not acyclic since even sequences of bestimprovement steps may cycle. Weak acyclicity is equivalent to the existence of a weak potential, which unlike a potential increases along some rather than every sequence as above. It is also equivalent to the existence of an acyclic scheduler, which guarantees convergence to equilibrium by disallowing certain improvement moves. A number of sufficient conditions for acyclicity and weak acyclicity are known.
Proceedings Article BestResponse Dynamics Out of Sync: Complexity and Characterization
"... In many computational and economic models of multiagent interaction, each participant repeatedly “bestresponds ” to the others ’ actions. Game theory research on the prominent “bestresponse dynamics ” model typically relies on the premise that the interaction between agents is somehow synchronize ..."
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In many computational and economic models of multiagent interaction, each participant repeatedly “bestresponds ” to the others ’ actions. Game theory research on the prominent “bestresponse dynamics ” model typically relies on the premise that the interaction between agents is somehow synchronized. However, in many reallife settings, e.g., internet protocols and largescale markets, the interaction between participants is asynchronous. We tackle the following important questions: (1) When are bestresponse dynamics guaranteed to converge to an equilibrium even under asynchrony? (2) What is the (computational and communication) complexity of verifying guaranteed convergence? We show that, in general, verifying guaranteed convergence is intractable. In fact, our main negative result establishes that this task is undecidable. We exhibit, in contrast, positive results for several environments of interest, including complete, computationallytractable, characterizations of convergent systems. We discuss the algorithmic implications of our results, which extend beyond bestresponse dynamics to applications such as asynchronous Boolean circuits.