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Article Dans Une Revue Journal of the Operational Research Society Année : 2014

Infrastructure Topology Optimization under Competition through Cross-Entropy

Hélène Le Cadre
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Résumé

In this article, we study a two-level non-cooperative game between providers acting on the same geographic area. Each provider has the opportunity to set up a network of stations so as to capture as many consumers as possible. Its deployment being costly, the provider has to optimize both the number of settled stations as well as their locations. In the first level each provider optimizes independently his infrastructure topology while in the second level they price dynamically the access to their network of stations. The consumers' choices depend on the perception (in term of price, congestion and distances to the nearest stations) that they have of the service proposed by each provider. Each provider market share is then obtained as the solution of a fixed point equation since the congestion level is supposed to depend on the market share of the provider which increases with the number of consumers choosing the same provider. We prove that the two-stage game admits a unique equilibrium in price at any time instant. An algorithm based on the cross-entropy method is proposed to optimize the providers' infrastructure topology and it is tested on numerical examples providing economic interpretations.
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Dates et versions

hal-00740910 , version 1 (11-10-2012)

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Hélène Le Cadre. Infrastructure Topology Optimization under Competition through Cross-Entropy. Journal of the Operational Research Society, 2014, 65, pp.824-841. ⟨10.1057/jors.2012.96⟩. ⟨hal-00740910⟩
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