Stackelberg competition

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

Computing optimal strategies to commit to in stochastic games

Abstract: Significant progress has been made recently in the following two lines of research in the intersection of AI and game theory: (1) the computation of optimal strategies to commit to (Stackelberg strategies), and (2) the computation of correlated equilibria of stochastic games. In this paper, we unite these two lines of research by studying the computation of Stackelberg strategies in stochastic games. We provide theoretical results on the value of being able to commit and the value of being able to correlate, as well as complexity results about computing Stackelberg strategies in stochastic games. We then modify the QPACE algorithm (MacDermed et al. 2011) to compute Stackelberg strategies, and provide experimental results.

Stackelberg strategies in linear-quadratic stochastic differential games

Abstract: This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution.

The effectiveness of stackelberg strategies and tolls for network congestion games

Abstract: It is well known that in a network with arbitrary (convex) latency functions that are a function of edge traffic, the worst-case ratio, over all inputs, of the system delay caused due to selfish behavior versus the system delay of the optimal centralized solution may be unbounded even if the system consists of only two parallel links. This ratio is called the price of anarchy (PoA). In this article, we investigate ways by which one can reduce the performance degradation due to selfish behavior. We investigate two primary methods (a) Stackelberg routing strategies, where a central authority, for example, network manager, controls a fixed fraction of the flow, and can route this flow in any desired way so as to influence the flow of selfish users; and (b) network tolls, where tolls are imposed on the edges to modify the latencies of the edges, and thereby influence the induced Nash equilibrium. We obtain results demonstrating the effectiveness of both Stackelberg strategies and tolls in controlling the price of anarchy.For Stackelberg strategies, we obtain the first results for nonatomic routing in graphs more general than parallel-link graphs, and strengthen existing results for parallel-link graphs. (i) In series-parallel graphs, we show that Stackelberg routing reduces the PoA to a constant (depending on the fraction of flow controlled). (ii) For general graphs, we obtain latency-class specific bounds on the PoA with Stackelberg routing, which give a continuous trade-off between the fraction of flow controlled and the price of anarchy. (iii) In parallel-link graphs, we show that for any given class L of latency functions, Stackelberg routing reduces the PoA to at most α + (1-α)cρ(L), where α is the fraction of flow controlled and ρ(L) is the PoA of class L (when α = 0).For network tolls, motivated by the known strong results for nonatomic games, we consider the more general setting of atomic splittable routing games. We show that tolls inducing an optimal flow always exist, even for general asymmetric games with heterogeneous users, and can be computed efficiently by solving a convex program. This resolves a basic open question about the effectiveness of tolls for atomic splittable games. Furthermore, we give a complete characterization of flows that can be induced via tolls.

Demand uncertainty and manufacturer returns policies for style-good retailing competition

Abstract: This paper investigates the role of the returns policy in the co-ordination of supply chain: A manufacturer provides a return policy for unsold goods to two competing retailers who face uncertain demand. The problem is described with a game theory structure: The manufacturer, as the Stackelberg leader, first commits a returns price to the retailers under a given wholesale price. Upon receiving this information, two competing retailers, as followers, make decisions for their retail price and order size, in which the process of pricing and ordering is played as Nash equilibrium. Anticipated the retailers’ responses, the manufacturer designs his returns policy. Adopting the classic newsboy problem model framework and using numerical study methods, the study finds that the provision of a returns policy is dependent on the market conditions faced by the retailers. The paper also analyses the impact of demand variability on the decisions of optimal retail price and order quantity and profit reallocation between the manufacturer and the retailers. Finally, it investigates how the competing factor influences the decision-making of supply chain members in response to uncertain demand and profit variability.

Three-Stage Stackelberg Game for Defending Against Full-Duplex Active Eavesdropping Attacks in Cooperative Communication

Abstract: In this paper, we study how to defend against full-duplex active eavesdropping attacks in the cooperative communication system. Unlike passive eavesdropping attackers, a full-duplex active eavesdropper acts as both a jammer and a classical eavesdropper in full-duplex mode, and seeks to maximize eavesdropping. Furthermore, in a real-world network, the relays may be selfish and have their own objectives due to competing/limited resources. This may lead to the failure of cooperative communication if there is no incentive to stimulate relays to participate in forwarding the transmitter's messages. Therefore, in this paper, we propose a three-stage Stackelberg game approach to model the behaviors of attacker, and the competitions among the transmitter, relays and attacker. Through finding the Stackelberg equilibrium of our scheme, the legitimate users can achieve cooperative communication to improve the secrecy capacity and to defend against full-duplex active eavesdropping attacks. Findings from the evaluations demonstrate that with an increasing number of channels, our scheme can significantly reduce the intercept probability; therefore, the security performance is improved. It is shown that our scheme can greatly improve the utilities of both the transmitter and multiple relays over the results of the Nash equilibrium scheme and rand power control scheme, which means that the relays are more willing to participate in the cooperative communication, and the transmitter can achieve better secure transmission in our scheme. We also demonstrate that our scheme outperforms other existing schemes, i.e., power control with smart jamming game in a single-channel model/multiple-channel model.