Greediness and equilibrium in congestion 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 [4] 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'.

Congestion games viewed from M-convexity

“…The laminarity structure has been recognized as a rooted tree structure [11,13] such that the set of non-root vertices of the rooted tree is the resource set (arc set) A of G and the set of non-root vertices of every path in the tree from the root to a leaf is the arc set of a respective path in G from the source to the sink. The tree structure described in [11,13] is closely related to the Tutte decomposition tree of a 2-connected graph into 3-connected components, cycles, and graphs of parallel arcs (see [26]), where only the latter two kinds of components appear (even for seriesparallel graphs).…”

“…The tree structure described in [11,13] is closely related to the Tutte decomposition tree of a 2-connected graph into 3-connected components, cycles, and graphs of parallel arcs (see [26]), where only the latter two kinds of components appear (even for seriesparallel graphs). Here, for a given extension-parallel (or, more generally, series-parallel) graph G with source s and sink t, we should define a graph G ′ obtained by adding to G a reference arc from s to t and consider the Tutte decomposition tree of G ′ .…”

The Curse of Ties in Congestion Games with Limited Lookahead

“…Subgame-perfect outcomes are introduced as a natural model for farsightedness [17,18], or "full anticipation", and have been studied for various types of congestion games [2,3,4,17]. Another well-studied notion in this context are outcomes of greedy best-response [7,8,12,20], i.e., players enter the game one after another and give a best response to the actions played already, thus playing with "no anticipation". Fotakis et al [7] proved that greedy best-response leads to stable outcomes on all series-parallel graphs (which contain extension-parallel graphs like the one above as a special case).…”