Greediness and Equilibrium in Congestion Games

TL;DR

This paper explores the relationship between greedy strategies and Nash equilibria in congestion games, providing conditions under which these concepts coincide, especially in tree-structured strategy sets.

Contribution

It establishes necessary and sufficient conditions for the equivalence of greedy strategies and Nash equilibria in congestion games with tree-form strategy sets.

Findings

Greedy strategies lead to Nash equilibria in tree-structured congestion games.

Equivalence occurs if and only if the strategy set is a tree-form or extension-parallel graph.

Conditions are characterized for monotone symmetric games.

Abstract

Rosenthal (1973) introduced the class of congestion games and proved that they always possess a Nash equilibrium in pure strategies. Fotakis et al. (2005) introduce the notion of a greedy strategy tuple, where players sequentially and irrevocably choose a strategy that is a best response to the choice of strategies by former players. Whereas the former solution concept is driven by strong assumptions on the rationality of the players and the common knowledge thereof, the latter assumes very little rationality on the players' behavior. From Fotakis \cite{fotakis10} it follows that for Tree Representable congestion Games greedy behavior leads to a NE. In this paper we obtain necessary and sufficient conditions for the equivalence of these two solution concepts. Such equivalence enhances the viability of these concepts as realistic outcomes of the environment. The conditions for such equivalence to emerge for monotone symmetric games is that the strategy set has a tree-form, or equivalently is a `extension-parallel graph'.