Client and server games in peer-to-peer networks

We consider a content sharing network of non-cooperative peers. The strategy set of each peer comprises, (i) client strategies, namely feasible request load splits to servers, and (ii) server strategies, namely scheduling disciplines on requests. First, we consider the request load splitting game for given server strategies such as First-In-First-Out or given absolute priority policies. A peer splits its request load to servers to optimize its performance objective. We consider the class of best response load splitting policies residing between the following extremes: a truly selfish, or egotistic one, where a peer optimizes its own delay, and a pseudo-selfish or altruistic one, where a peer also considers incurred delays to others. We derive conditions for Nash equilibrium points (NEPs) and discuss convergence to NEP and properties of the NEP. For both the egotistic cases, the NEP is unique. For the altruistic case, each of the multiple NEPs is an optimum, a global one for the FIFO case and a local one otherwise. Next, we include scheduling in peer strategies. With its scheduling discipline, a peer cannot directly affect its delay, but it can affect the NEP after peers play the load splitting game. The idea is that peer i should offer high priority to (and thus attract traffic from) higher-priority peers that cause large delay to i at other servers. We devise two-stage game models, where, at a first stage, a peer selects a scheduling rule in terms of a convex combination of absolute priorities, and subsequently peers play the load splitting game. In the most sophisticated rule, a peer selects a scheduling discipline that minimizes its delay at equilibrium, after peers play the load splitting game. We also suggest various heuristics for picking the scheduling discipline. Our models and results capture the dual client-server peer role and aim at quantifying the impact of selfish peer interaction on equilibria.