On the Price of Stability of Undirected Multicast Games

TL;DR

This paper establishes a constant upper bound on the price of stability for multicast network design games specifically on quasi-bipartite graphs, advancing understanding of cost efficiency in these strategic network formation scenarios.

Contribution

It provides the first constant upper bound on the PoS for multicast games on quasi-bipartite graphs, a significant step beyond previous results for broadcast games.

Findings

Constant upper bound on PoS for quasi-bipartite graphs

Techniques overcoming fundamental analysis difficulties

Progress towards resolving the open problem for general multicast games

Abstract

In multicast network design games, a set of agents choose paths from their source locations to a common sink with the goal of minimizing their individual costs, where the cost of an edge is divided equally among the agents using it. Since the work of Anshelevich et al. (FOCS 2004) that introduced network design games, the main open problem in this field has been the price of stability (PoS) of multicast games. For the special case of broadcast games (every vertex is a terminal, i.e., has an agent), a series of works has culminated in a constant upper bound on the PoS (Bilo` et al., FOCS 2013). However, no significantly sub-logarithmic bound is known for multicast games. In this paper, we make progress toward resolving this question by showing a constant upper bound on the PoS of multicast games for quasi-bipartite graphs. These are graphs where all edges are between two terminals (as in broadcast games) or between a terminal and a nonterminal, but there is no edge between nonterminals. This represents a natural class of intermediate generality between broadcast and multicast games. In addition to the result itself, our techniques overcome some of the fundamental difficulties of analyzing the PoS of general multicast games, and are a promising step toward resolving this major open problem.