The price of selfishness in network coding

Abstract

Abstract-A game-theoretic framework is introduced for studying selfish user behavior in shared wireless networks. The investigation treats an -unicast problem in a wireless network that employs a restricted form of network coding called reverse carpooling. Unicast sessions independently choose routes through the network. The cost of a set of unicast routes is the number of wireless transmissions required to establish those connections using those routes. Game theory is employed as a tool for analyzing the impact of cost sharing mechanisms on the global system performance when each unicast independently and selfishly chooses its route to minimize its individual cost. The investigation focuses on the performance of stable solutions, where a stable solution is one in which no single unicast can improve its individual cost by changing its route. The results include bounds on the best-and worst-case stable solutions compared to the best performance that could be found and implemented using a centralized controller. The optimal cost sharing protocol is derived and the worst-case solution is bounded. That worst-case stable performance cannot be improved using cost-sharing protocols that are independent of the network structure.

Distributed Welfare Games

“…Note that when restricting attention to separable welfare functions, the welfare generated at a particular resource depends only on which players are currently using that resource. While separable welfare functions cannot model the global objective for all resource allocation problems, they can model the global objective for several important classes of resource allocation problems including routing over a network (Roughgarden 2005), vehicle target assignment problem (Murphey 1999), content distribution (Goemans et al 2004), graph coloring (Panagopoulou and Spirakis 2008), and network coding (Marden and Effros 2012), among many others. Throughout this paper we frequently restrict our attention to submodular welfare functions.…”

Overcoming limitations of game-theoretic distributed control

“…Examples of cooperative control problems are numerous, e.g., the sensor coverage problem [1], [2], consensus [3], [4], power control in a wireless network [5], and network coding [6], [7]. Regardless of the specific application domain, the central goal is the same: to derive desirable collective behaviors through the design of local control algorithms.…”

The Price of Selfishness in Network Coding

“…Proof: As in the proof of Theorem 4.1, it is straightforward to show that for any , the cost-sharing protocol in (17) guarantees that the resulting game is a potential game with potential function (20) Hence, an equilibrium is always guaranteed to exist.…”