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Game Theory
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Erik G. Larsson, Eduard Jorswiec
Reconsidering the invader game in Figure 19.8, we apply the backward induction argument: Assume that the history is h = c. Then the defender has a dominating strategy which maximizes the payoff namely quit. Taking this knowledge into account, the invader will always challenge since this gives a payoff 2 instead of 1. The corresponding subgame is illustrated in Figure 19.9. The only subgame-perfect equilibrium is therefore (challenge, quit).
A review of game theory models of lane changing
Published in Transportmetrica A: Transport Science, 2020
Over several decades of exploration and discovery, game theory, especially the conventional two-player, non-cooperative game, has been experimentally tested and verified in a variety of cases (Von Neumann and Morgenstern 1944; Nisan et al. 2007; Camerer 2011). During this period, there have been many strategy solutions with different assumptions. Classic Nash Equilibrium is one of the widely-used methods to find the solution that maximizes individual benefits, which is fit for games with complete information. As people deepen their understanding of GT, some refined solutions were also proposed to solve particular problems. A Bayesian Nash Equilibrium can be applied to games with imperfect information (Harsanyi 1967). A ‘Subgame Perfect Equilibrium’ is usually deployed in sequential games with perfect information (Fudenberg and Levine 1983). A Perfect Bayesian Equilibrium solves for the best solutions in sequential games with imperfect information (Fudenberg and Tirole 1991). These progressive refinements extend conventional theory to adapt to both incomplete information and dynamic scenarios.
Optimal pricing for cloud service providers in a competitive setting
Published in International Journal of Production Research, 2019
Guofang Nan, Zan Zhang, Minqiang Li
We solve for the subgame perfect equilibrium of the two-period game using backward induction. That is, we first solve the game in the second period and then in the first period. The second-period upgrade price and market price of the incumbent’s new product are first determined, and simultaneously the price of the entrant’s SaaS is obtained. Then these prices are substituted into the first-period profit function of the incumbent to derive the equilibrium value of the first-period price. For ease of exposition, we define the following notations. The demand of the incumbent in period is () and the demand of the entrant in period 2 is . , where and are demands for the incumbent’s upgrade from its old customers and new customers, respectively. , where represents the number of customers that switch to the entrant from the incumbent and represents the number of new customers subscribing to the entrant’s SaaS. The profit of the entrant is denoted by . The profit of the incumbent in period is denoted by , and represents the incumbent’s total profit over the two periods.
Impact of pricing leadership on blockchain data acquisition efforts in a circular supply chain
Published in International Journal of Production Research, 2022
Junbin Wang, Yangyan Shi, Changping Zhao, V. G. Venkatesh, Weiwei Chen
First, we analyze the case where the supplier owns pricing leadership and acts as a Stackelberg game leader. In this case, given the advent of blockchain, the supplier and retailer determine the quantities of data-acquisition nodes in the upstream and downstream supply chains, respectively. After the supplier sets a wholesale price for the product, the retailer chooses its retail price for the consumers. Subsequently, the magnitude of return from product recycling was also confirmed for the supplier. This is a three-stage game, and we use backward induction to seek the subgame perfect equilibrium.