Endogenous timing in a mixed triopoly with state-owned, labour-managed and capitalist firms

Ohnishi, Kazuhiro (2024): Endogenous timing in a mixed triopoly with state-owned, labour-managed and capitalist firms.

Abstract

Over the past approximately 30 years, many researchers have examined oligopoly models where firms endogenously select the timing of their action decisions. Therefore, this paper studies a mixed triopoly model featuring competition between a labour-managed firm, a capitalist firm and a state-owned firm. The sequence of events is as follows. In stage 0, each firm independently and simultaneously selects either ‘stage 1’ or ‘stage 2’. In this context, stage 1 denotes that a firm produces in stage 1, whereas stage 2 signifies that it produces in stage 2. In stage 1, if a firm opts for stage 1, it determines its output for this stage. In stage 2, if a firm chooses stage 2, it decides on its output for this stage. Upon the conclusion of the game, the market opens, and all firms sell their outputs. The purpose of this paper is to present the equilibrium outcome of triopoly competition where a state-owned firm, a labour-managed firm and a capitalist firm compete in quantities. As a result of the analysis, this paper reveals that there exists an equilibrium wherein both the labour-managed firm and the capitalist firm assume leadership roles. The paper finds that the state-owned firm is precluded from functioning as the Stackelberg leader.

• Item Type: MPRA Paper
• Language: English
• Keywords: Capitalist firm; Cournot game; Endogenous timing; Labour-managed firm; State-owned firm
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D2 - Production and Organizations > D21 - Firm Behavior: Theory; L - Industrial Organization > L3 - Nonprofit Organizations and Public Enterprise > L30 - General

References

Amir, R., 1995. Endogenous timing in two-player games: a counterexample. Games and Economic Behavior 9, 234-237.

Bárcena-Ruiz, J. C., 2007. Endogenous timing in a mixed duopoly: price competition. Journal of Economics 91, 263-272.

Bárcena-Ruiz, J. C., Garzón, M. B., 2003. Mixed duopoly, merger and multiproduct firms. Journal of Economics 80, 27-42.

Bárcena-Ruiz, J. C., Sedano, M., 2011. Endogenous timing in a mixed duopoly: weighted welfare and price competition. Japanese Economic Review 62, 485–503.

Bulow, J., Geanakoplos, J., Klemperer, P., 1985. Multimarket oligopoly: strategic substitutes and complements. Journal of Political Economy 93, 488-511.

Chen, J., Kim, D., Lee, S.-H., 2024. Endogenous timing of R&D decisions with spillovers: output versus research subsidies. Bulletin of Economic Research 76, 631-649.

van Damme, E., Hurkens, S., 1999. Endogenous Stackelberg leadership. Games and Economic Behavior 28, 105-129.

van Damme, E., Hurkens, S., 2004. Endogenous price leadership. Games and Economic Behavior 47, 404-420.

Delbono, F., Rossini, G., 1992. Competition policy vs horizontal merger with public entrepreneurial and labor-managed firms. Journal of Comparative Economics 16, 226-240.

Delbono, F., Scarpa, C., 1995. Upward-sloping reaction functions under quantity competition in mixed oligopolies. Bulletin of Economic Research 47, 341-346.

Deneckere, R., Kovenock, D., 1992. Price leadership. Review of Economic Studies 59, 143-162.

Fjell, K., Heywood, J. S., 2002. Public Stackelberg leadership in a mixed oligopoly with foreign firms. Australian Economic Papers 41, 267-281.

Fjell, K., Pal, D., 1996. A mixed oligopoly in the presence of foreign private firms. Canadian Journal of Economics 29, 737-743.

Furth, D., Kovenock, D., 1993. Price leadership in a duopoly with capacity constraints and product differentiation. Journal of Economics 57, 1-35.

Hamilton, J. H., Slutsky, S. M., 1990. Endogenous timing in duopoly games: Stackelberg or Cournot equilibria. Games and Economic Behavior 2, 29-46.

Haraguchi, J., Matsumura, T., 2020. Endogenous public and private leadership with diverging social and private marginal costs. Manchester School 88, 699-730.

Harris, R. G., Wiens, E, G., 1980. Government enterprise: an instrument for internal regulation of industry. Canadian Journal of Economics 13, 125-132.

Hoffmann, M., Rota-Graziosi, G., 2020. Endogenous timing in the presence of non-monotonicities. Canadian Journal of Economics 53, 359-402.

Lambertini, L., 1996. Choosing roles in a duopoly for endogenously differentiated products. Australian Economic Papers 35, 205-224.

Lambertini, L., 1997. Cournot vs Stackelberg equilibria with entrepreneurial and labour managed firms. Journal of International and Cooperative Economics 5, 31-43.

Lambertini, L., 2000. Extended games played by managerial firms. Japanese Economic Review 51, 274-283.

Lambertini, L., Rossini, G., 1998. Capital commitment and Cournot competition with labour-managed and profit-maximising firms. Australian Economic Papers 37, 14-21.

Lee, S.-H., Xu, L., 2018. Endogenous timing in private and mixed duopolies with emission taxes. Journal of Economics 124, 175–201.

van Leeuwen, B., Offerman, T., van de Ven, J., 2022. Fight or flight: endogenous timing in conflict. Review of Economics and Statistics 104, 217–231.

Lu, Y., 2007. Endogenous timing in a mixed oligopoly consisting of a single public firm and foreign competitors. Economics Bulletin 12, 1-7.

Lu, Y., Poddar, S., 2009. Endogenous timing in a mixed duopoly and private duopoly – ‘capacity-then-quantity’ game: the linear demand case. Australian Economic Papers 48, 138-150.

Matsumura, T., 1999. Quantity-setting oligopoly with endogenous sequencing. International Journal of Industrial Organization 17, 289-296.

Matsumura, T., 2003. Stackelberg mixed duopoly with a foreign competitor. Bulletin of Economic Research 55, 275-287.

Ohnishi, K., 2009. Capacity investment and mixed duopoly with state-owned and labor-managed firms. Annals of Economics and Finance 10, 49-64.

Ohnishi, K., 2010. Wage-rise contract and endogenous timing in international mixed duopoly. Research in Economics 64, 121-127.

Ohnishi, K., 2012. Endogenous timing in a quantity-setting mixed duopoly with state-owned and labor-managed firms. American Journal of Economics 2, 82-86.

Ohnishi, K., 2016. Endogenous timing in a price-setting mixed duopoly with a foreign competitor. International Journal of Management, Accounting and Economics 3, 758-763.

Ohnishi, K., 2018. A three-stage mixed triopoly with capacity choice. In Kazuhiro Ohnishi ed., Firms’ Strategic Decisions: Theoretical and Empirical Findings, Volume 3 (pp. 82-100). Sharjah, UAE: Bentham Science Publishers.

Ohnishi, K., 2020. Capacity choice in an international mixed triopoly. International Economic Journal 34, 371-387.

Ohnishi, K., 2021. A note on Stackelberg mixed triopoly games with state-owned, labour-managed and capitalist firms. International Game Theory Review 23, 2150002.

Pal, D., 1998. Endogenous timing in a mixed oligopoly. Economics Letters 61, 181-185.

Pal, D., White, M. D., 1998. Mixed oligopoly, privatization, and strategic trade policy. Southern Economic Journal 65, 264-281.

Park, Y., Rabanal, J. P., Rud, O. A., Grossman, P. J., 2021. An endogenous-timing conflict game. Journal of Economic Behavior & Organization 186, 592-607.

Poyago-Theotoky, J., 1998. R&D competition in a mixed duopoly under uncertainty and easy imitation. Journal of Comparative Economics 26, 415-428.

Robson, A. J., 1990. Duopoly with endogenous strategic timing: strategic regained. International Economic Review 31, 263-274.

Sadanand, A., Sadanand, V., 1996. Firm scale and the endogenous timing of entry: a choice between commitment and flexibility. Journal of Economic Theory 70, 516-530.

von Stengel, B., 2010. Follower payoffs in symmetric duopoly games. Games and Economic Behavior 69, 512-516.

Tasnádi, A., 2003. Endogenous timing of moves in an asymmetric price-setting duopoly. Portuguese Economic Journal 2, 23-35.

Wang, L. F. S., Wang, J. (2009). Environmental taxes in a differentiated mixed duopoly. Economic Systems, 33, 389-396.

Ware, R., 1986. A model of public enterprise with entry. Canadian Journal Economics 19, 642-655.

White, M. D., 1996. Mixed oligopoly, privatization and subsidization. Economics Letters 53, 189-195.