Stackelberg competition

About: Stackelberg competition is a research topic. Over the lifetime, 6611 publications have been published within this topic receiving 109213 citations.

WLC41-4: Stackelberg Game for Distributed Resource Allocation over Multiuser Cooperative Communication Networks

Abstract: In this paper, we propose a Stackelberg game theoretic framework for distributive resource allocation over multiuser cooperative communication networks to improve the system performance and stimulate cooperation. Two questions of who should relay and how much power for relaying are answered, by employing a two-level game to jointly consider the benefits of source nodes as buyers and relay nodes as sellers in cooperative communication. From the derived results, the proposed game not only helps the source smartly find relays at relatively better locations but also helps the competing relays ask reasonable prices to maximize their own utilities. From the simulation results, the relays in good locations or good channel conditions can play more important roles in increasing source node's utility, so the source would like to buy power from these preferred relays. On the other hand, because of competition from other relays and selections from the source, the relays have to set proper prices to attract the source's buying so as to optimize their utility values.

Off-Line Computation of Stackelberg Solutions with the Genetic Algorithm

Abstract: The paper studies off-line computation of the Stackelberg solution in a repeated game framework, utilizing the Genetic Algorithm. Simulations are conducted with a numerical linear quadratic example and a Fish War game example. Furthermore, it is shown that an evolutionary mutation probability is preferable to a fixed one as usually assumed.

The price of optimum in Stackelberg games on arbitrary single commodity networks and latency functions

Abstract: Let M be a single s-t network of parallel links with load dependent latency functions shared by an infinite number of selfish users. This may yield a Nash equilibrium with unbounded Coordination Ratio [12, 26]. A Leader can decrease the coordination ratio by assigning flow αr on M, and then all Followers assign selfishly the (1 - α)r remaining flow. This is a Stackelberg Scheduling Instance (M,r,α), 0 ≤ α ≤ 1. It was shown [23] that it is weakly NP-hard to compute the optimal Leader's strategy.For any such network M we efficiently compute the minimum portion βM of flow r needed by a Leader to induce M's optimum cost, as well as his optimal strategy.Unfortunately, Stackelberg routing in more general nets can be arbitrarily hard. Roughgarden presented a modification of Braess's Paradox graph, such that no strategy controlling αr flow can induce ≤ 1α times the optimum cost. However, we show that our main result also applies to any s-t net G. We take care of the Braess's graph explicitly, as a convincing example.

An Existence Result for Hierarchical Stackelberg v/s Stackelberg Games

Abstract: In Stackelberg v/s Stackelberg games a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium problems are plagued by the nonuniqueness of follower equilibria and nonconvexity of leader problems whereby the problem of providing sufficient conditions for existence of global or even local equilibria remains largely open. Indeed available existence statements are restrictive and model specific. In this paper, we present what is possibly the first general existence result for equilibria for this class of games. Importantly, we impose no single-valuedness assumption on the equilibrium of the follower-level game. Specifically, under the assumption that the objectives of the leaders admit a quasi-potential function, a concept we introduce in this paper, the global and local minimizers of a suitably defined optimization problem are shown to be the global and local equilibria of the game. In effect existence of equilibria can be guaranteed by the solvability of an optimization problem, which holds under mild and verifiable conditions. We motivate quasi- potential games through an application in communication networks.