Abstract
Weakly-acyclic games—a superclass of potential games—capture distributed environments where simple, globally-asynchronous interactions between strategic agents are guaranteed to converge to an equilibrium. We explore the class of routing games introduced in Fabrikant and Papadimitriou (The Complexity of Game Dynamics: BGP Oscillations, Sink Equilibria, and Beyond, pp. 844–853, 2008) and in Levin et al. (Interdomain Routing and Games, pp. 57–66, 2008), 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.
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Notes
Henceforth, we shall sometimes say that a node selects a route when we mean that the node actually selects an outgoing edge (in its strategy set); the selected edge, followed by the induced route to d of the neighboring node to which that edge points determines what we call the node’s selected route.
Note that at the end of Part I, some node might want to select a path that goes through m; This was not allowed in Part I, but in Part II we allow it.
After each such activation, we make sure we get to a clean strategy, as described above.
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Engelberg, R., Schapira, M. Weakly-Acyclic (Internet) Routing Games. Theory Comput Syst 54, 431–452 (2014). https://doi.org/10.1007/s00224-013-9474-z
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DOI: https://doi.org/10.1007/s00224-013-9474-z