Topic
Stackelberg competition
About: Stackelberg competition is a research topic. Over the lifetime, 6611 publications have been published within this topic receiving 109213 citations.
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TL;DR: In this paper, the authors study a supply chain in which a consumer goods manufacturer sells its product through a retailer and the retailer undertakes promotional expenditures, such as advertising, to increase sales and to compete against other retailers.
Abstract: We study a supply chain in which a consumer goods manufacturer sells its product through a retailer. The retailer undertakes promotional expenditures, such as advertising, to increase sales and to compete against other retailer(s). The manufacturer supports the retailer’s promotional expenditure through a cooperative advertising program by reimbursing a portion (called the subsidy rate) of the retailer’s promotional expenditure. To determine the subsidy rate, we formulate a Stackelberg differential game between the manufacturer and the retailer, and a Nash differential subgame between the retailer and the competing retailer(s). We derive the optimal feedback promotional expenditures of the retailers and the optimal feedback subsidy rate of the manufacturer, and show how they are influenced by market parameters. An important finding is that the manufacturer should support its retailer only when a subsidy threshold is crossed. The impact of competition on this threshold is nonmonotone. Specifically, the manufacturer offers more support when its retailer competes with one other retailer but its support starts decreasing with the presence of additional retailers. In the case where the manufacturer sells through all retailers, we show under certain assumptions that it should support only one dominant retailer. We also describe how we can incorporate retail price competition into the model. [Submitted: September 6, 2010. Revisions received: February 17, 2011; April 26, 2011. Accepted: April 27, 2011.]
45 citations
TL;DR: Numerical results demonstrate that the game model captures the main factors behind cognitive network pricing and network selection, thus representing a promising framework for the design and understanding of CR systems.
Abstract: This paper addresses the joint pricing and network selection problem in cognitive radio networks (CRNs). The problem is formulated as a Stackelberg game, where the primary and secondary operators (POs and SOs) first set the network subscription price to maximize their revenue. Then, users perform the network selection process, deciding whether to pay more for a guaranteed service or to use a cheaper best-effort secondary network, where congestion and low throughput may be experienced. We derive optimal stable price and network selection settings. More specifically, we use the Nash equilibrium concept to characterize the equilibria for the price setting game. On the other hand, a Wardrop equilibrium is reached by users in the network selection game since, in our model, a large number of users must individually determine the network to which they should connect. Furthermore, we study network users' dynamics using a population game model, and we determine its convergence properties under replicator dynamics, which is a simple yet effective selection strategy. Numerical results demonstrate that our game model captures the main factors behind cognitive network pricing and network selection, thus representing a promising framework for the design and understanding of CR systems.
45 citations
TL;DR: In this paper, the optimal location choice in a standard game of horizontal differentiation in which firms are free to locate outside the city boundaries is analyzed, and it turns out that the unique Nash equilibium exhibits a finite distance between the sellers, so that the maximum differentiation principle is not confirmed.
Abstract: In this paper, we try to analyse the optimal location choice in a standard game of horizontal differentiation in which firms are free to locate outside the city boundaries. It turns out that the unique Nash equilibium exhibits a finite distance between the sellers, so that the maximum differentiation principle is not confirmed. Moreover, the two symmetric Stackelberg equilibria exhibit the same degree of differentiation observed when the game is non cooperatively played within the city, except that the leader locates at the center.
45 citations
TL;DR: Study of the optimal pricing decisions in a dual-channel supply chain considering flexible return policies and different government intervention policies revealed that employing the full-refund via the retail channel policy and the government’s price incentive not only maximize the dual-Channel SC profit but also satisfy the government's objective functions.
45 citations
TL;DR: In this article, the authors considered a special type of Stackelberg games, known as inverse Stackeckers games, in which the leader announces his strategy as a mapping from the follower's decision space into his own decision space.
Abstract: Dynamic two-person games are considered, in which the roles of the players are hierarchical. One player behaves as a leader, the other one as a follower. Such games are named after Stackelberg. In the current paper, a special type of such games is considered, known in the literature as inverse Stackelberg games. In such games, the leader announces his strategy as a mapping from the follower’s decision space into his own decision space. Arguments for studying such problems are given. This paper specifically studies dynamic games, i.e. the underlying model is described by an ordinary differential equation. The decisions of both players have a time component. As in the static case, the routine way of analysis, leading to a study of composed functions, is not very fruitful. Other approaches are given, mainly by studying specific examples.
45 citations