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Solving a Location Problem of a Stackelberg Firm Competing with Cournot-Nash Firms

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Abstract

We study a discrete facility location problem on a network, where the locating firm acts as the leader and other competitors as the followers in a Stackelberg-Cournot-Nash game. To maximize expected profits the locating firm must solve a mixed-integer problem with equilibrium constraints. Finding an optimal solution is hard for large problems, and full-enumeration approaches have been proposed in the literature for similar problem instances. We present a heuristic solution procedure based on simulated annealing. Computational results are reported.

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Notes

  1. This discussion assumes \(p=1\) (or that the number of “movable” sites is 1) but the same concept applies if \(p>1\) if we assume that two candidate solutions are adjacent if they have \(p-1\) facilities in common and that the remaining facility is adjacent in the sense that it would be for \(p=1\).

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Authors and Affiliations

  1. 3Gtms, Shelton, CT, USA

    Paul G. Berglund

  2. Department of Industrial and Systems Engineering, University at Buffalo, SUNY, Buffalo, NY, USA

    Changhyun Kwon

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  1. Paul G. Berglund
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  2. Changhyun Kwon
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Correspondence to Changhyun Kwon.

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Berglund, P.G., Kwon, C. Solving a Location Problem of a Stackelberg Firm Competing with Cournot-Nash Firms. Netw Spat Econ 14, 117–132 (2014). https://doi.org/10.1007/s11067-013-9217-3

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