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Ind. Math. 8(4), 557–567 (2014) 50. A. Mel’nikov, Randomized local search for the discrete competitive facility location problem. Autom. Remote Control 75(4), 700–714 (2014) 51. Q. Meng, Y. L. Cheu, Competitive facility location on decentralized supply chain. Eur. J. Oper. Res.

L. L. Tobin, T. Miller, Existance theory for spatially competitive network facility location models. Ann. Oper. Res. 18, 267–276 (1989) 24. T. Friez, T. Miller, R. Tobin, Competitive network facility location models: a survey. Pap. Reg. Sci. Assoc. 65, 47–57 (1988) 25. D. García, P. Fernández, B. Pelegrín, On price competition in location-price models with spatially separated markets. TOP 12(2), 351–374 (2004) 26. D. García, B. Pelegrín, P. Fernántez, Location strategy for a firm under competitive delivered prices.

The problem is formulated as a two-stage game. si /qi denote the fixed and variable production cost, respectively. In the second stage, the firms simultaneously set delivery price schedules. x2 ; zh /g for all H markets, which constitutes a unique Nash equilibrium in price (stage two). Then, this equilibrium is used to search for the equilibrium in location and technology at the first stage of the game. The study of the equilibrium of the first stage is facilitated by the use of the so-called social cost function.

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