Best Response Algorithms for Selfish Routing

Keywords and Synonyms

Atomic selfish flows    

Problem Definition

A setting is assumed in which n selfish users compete for routing their loads in a network. The network is an ${ s - t }$ directed graph with a single source vertex s and a single destination vertex t. The users are ordered sequentially. It is assumed that each user plays after the user before her in the ordering, and the desired end result is a Pure Nash Equilibrium (PNE for short). It is assumed that, when a user plays (i. e. when she selects an ${ s-t }$ path to route her load), the play is a best response (i. e. minimum delay), given the paths and loads of users currently in the net. The problem then is to find the class of directed graphs for which such an ordering exists so that the implied sequence of best responses leads indeed to a Pure Nash Equilibrium.

The Model

A network congestion game is a tuple ${ \left((w_i)_{i \in N}, G, (d_e)_{e \in E} \right) }$ where ${ N = \{1, \dots, n\} }$is the set...