Stackelberg competition

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

Equilibrium in hotelling's model of spatial competition

Abstract: We study Hotelling's two-stage model of spatial competition, in which two firms first simultaneously choose locations in the unit interval, then simultaneously choose prices. Under Hotelling's assumptions (uniform distribution of consumers, travel cost proportional to distance, inelastic demand of one unit by each consumer) the price-setting subgames possess equilibria in pure strategies for only a limited set of location pairs. Because of this problem (pointed out independently by Vickrey (1964) and d'Aspremont et al. (1979)), Hotelling's claim that there is an equilibrium of the two-stage game in which the firms locate close to each other is incorrect. A result of Dasgupta and Maskin (1986) guarantees that each price-setting subgame has an equilibrium in mixed strategies. We first study these mixed strategy equilibria. We are unable to provide a complete characterization of them, although we show that for a subset of location pairs all equilibria are of a certain type. We reduce the problem of finding an equilibrium of this type to that of solving three or fewer highly nonlinear equations. At each of a large number of location pairs we have computed approximate solutions to the system of equations. Next, we use our analytical results and computations to study the equilibrium location choices of the firms. There is a unique (up to symmetry) subgame perfect equilibrium in which the location choices of the firms are pure; in it, the firms locate 0.27 from the ends of the market. At this equilibrium, the support of the subgame equilibrium price strategy is the union of two short intervals. Most of the probability weight is in the upper interval, so that this strategy is reminiscent of occasional "sales" by the firms. We also find a subgame perfect equilibrium in which each firm uses a mixed strategy in locations. In fact, in the class of strategy pairs in which the firms use the same mixed strategy over locations, and this strategy is symmetric about 0.5, there is a single equilibrium. In this equilibrium most of the probability weight of the common strategy is between 0.2 and 0.4, and between 0.6 and 0.8. There is a wide range of pure Nash (as opposed to subgame perfect) equilibrium location pairs: the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close.

Stackelburg solution for two-person games with biased information patterns

Abstract: A strategy suggested by Stackelberg for static economic competition is considered and extended to the case of dynamic games with biased information pattern. This strategy is reasonable when one of the players knows only his own cost function but the other player knows both cost functions. As with Nash strategies for nonzero-sum dynamic games open-loop and feedback Stackelberg strategies for dynamic games could lead to different solutions, a phenomenon which does not occur in optimum control problems. Necessary conditions for open-loop Stackelberg strategies are presented. Dynamic programming is used to define feedback Stackelberg strategies for discrete-time games. A simple resource allocation example illustrates the solution concept.

Energy Management for Joint Operation of CHP and PV Prosumers Inside a Grid-Connected Microgrid: A Game Theoretic Approach

Abstract: This paper mainly focuses on the energy management of microgrids (MGs) consisting of combined heat and power (CHP) and photovoltaic (PV) prosumers. A multiparty energy management framework is proposed for joint operation of CHP and PV prosumers with the internal price-based demand response. In particular, an optimization model based on Stackelberg game is designed, where the microgrid operator (MGO) acts as the leader and PV prosumers are the followers. The properties of the game are studied and it is proved that the game possesses a unique Stackelberg equilibrium. The heuristic algorithm based on differential evolution is proposed that can be adopted by the MGO, and nonlinear constrained programing can be adopted by each prosumer to reach the Stackelberg equilibrium. Finally, via a practical example, the effectiveness of the model is verified in terms of determining MGO's prices and optimizing net load characteristic, etc.