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Published in:
2020 | OriginalPaper | Chapter
Sequential Location Game on Continuous Directional Star Networks
Authors : Xujin Chen, Xiaodong Hu, Mengqi Zhang
Published in: Complexity and Approximation
Publisher: Springer International Publishing
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Abstract
We consider a sequential location game on a continuous directional star network, where a finite number of players (facilities) sequentially choose their locations to serve their consumers who are uniformly and continuously distributed in the network. Each consumer patronizes all the closest locations that have been chosen, bringing them equal shares of payoff. In turn, each location distributes the total payoff it receives evenly to every player choosing it. We study hierarchical Stackelberg equilibria (HSE), a.k.a, subgame perfect equilibria of the game, under which every player chooses a location to maximize its payoff. We establish a universal lower bound for payoff to a player under any HSE outcome. The lower bound is then strengthened with better estimations, and some HSE outcomes are explicitly presented, provided that the number of players and the network parameters satisfy certain relations.