Competitive Equilibria and Benefit Distributions of Population Production Economies with External Increasing Returns

doi:10.1007/s40305-021-00340-1

Abstract

Abstract: Inspired by the work of population games, we establish the model of population production economies with external increasing returns and introduce the notion of competitive equilibria. We first prove the existence of competitive equilibria under some regular assumptions. Furthermore, we assume that there exists the cooperative behavior of different populations. By proving the existence of transferable utility (TU) core, we analyze the benefit distributions of population production economies with external increasing returns.

Key words: Population production economy, Competitive equilibrium, TU core, Benefit distribution

CLC Number:

Zhe Yang, Xian Zhang. Competitive Equilibria and Benefit Distributions of Population Production Economies with External Increasing Returns[J]. Journal of the Operations Research Society of China, 2021, 9(4): 723-740.

TrendMD

References

[1] Nash, J.:Noncooperative games. Dissertation, Princeton University, Dept. Mathematics, Princeton (1950)
[2] Sandholm, W.H.:Population Games and Evolutionary Dynamics. MIT Press, Cambridge (2010)
[3] Sandholm, W.H.:Local stability under evolutionary game dynamics. Theor. Econ. 5, 27-50(2011)
[4] Yang, G.H., Yang, H.:Stability of weakly Pareto-Nash equilibria and Pareto-Nash equlibria for multiobjective population games. Set Valued Var. Anal. 25, 427-439(2017)
[5] Yang, Z., Zhang, H.Q.:Essential stability of cooperative equilibria for population games. Optim. Lett. 13(7), 1573-1582(2019)
[6] Yang, Z., Zhang, H.Q.:NTU core, TU core and strong equilibria of coalitional population games with infinitely many pure strategies. Theor. Decis. 87, 155-170(2019)
[7] Lahkar, R., Sandholm, W.H.:The projection dynamic and the geometry of population games. Games Econ. Behav. 64, 565-590(2008)
[8] Reluga, T.C., Galvani, A.P.:A general approach for population games with application to vaccination. Math. Biosci. 230, 67-78(2011)
[9] Arrow, K.J., Debreu, G.:Existence of an equilibrium for a competitive economy. Econometrica 22, 265-290(1954)
[10] Aumann, R.J.:Markets with a continum of traders. Econometrica 32, 39-50(1964)
[11] Aumann,R.J.:Existenceofcompetitiveequilibriainmarketswithacontinumoftraders.Econometrica 34, 1-17(1966)
[12] Bewley, T.F.:Existence of equilibria with infinitely many commodities. J. Econ. Theory 4, 514-540(1970)
[13] Greenberg, J.:Quasi-equilibrium in abstract economies without ordered preferences. J. Math. Econ. 4, 163-165(1977)
[14] Hildenbrand, W.:Existence of equilibria for economies with production and a measure space of consumers. Econometrica 38, 608-623(1970)
[15] Kajii, A.:How to discard non-satiation and free-disposal with paper money. J. Math. Econ. 25, 75-84(1996)
[16] Zhao, J.:The hybrid equilibria and core selection in exchange economies with externalities. J. Math. Econ. 26, 387-407(1996)
[17] Florenzano, M.:General Equilibrium Analysis:Existence and Optimality Properties of Equilibria. Springer, Dordrecht (2003)
[18] Liu, J.Q.:Existence of competitive equilibrium in coalition production economies with a continuum of agents. Int. J. Game Theory 46, 941-955(2017)
[19] Romer, P.:Increasing returns and long-run growth. J. Polit. Econ. 94, 1002-1037(1986)
[20] Romer, P.:Crazy explanations for the productivity slow down. NBER Macroecon. Ann. 2, 163-202(1987)
[21] Suzuki, T.:Intertemporal general equilibrium model with external increasing returns. J. Econ. Theory 69, 117-133(1996)
[22] Villar, A.:General Equilibrium with Increasing Returns. Springer, Berlin (1996)
[23] Villar, A.:Equilibrium and Efficiency in Production Economies. Springer, Berlin (2000)
[24] Aumann, R.J.:The core of a cooperative game without sidepayments. Trans. Am. Math. Soc. 98, 339-552(1961)
[25] Scarf, H.:On the existence of a cooperative solution for a general class of n-person games. J. Econ. Theory 3, 169-181(1971)
[26] Kajii, A.:A generalization of Scarf's theorem:an α-core existence theorem without transitivity or completeness. J. Econ. Theory 56, 194-205(1992)
[27] Zhao, J.:The existence of TU α-core in normal form games. Int. J. Game Theory 28, 25-34(1999)
[28] Askoura, Y., Sbihi, M., Tikobaini, H.:The ex ante α-core for normal form games with uncertainty. J. Math. Econ. 49, 157-162(2013)
[29] Askoura, Y.:An interim core for normal form games and exchange economies with incomplete information. J. Math. Econ. 58, 38-45(2015)
[30] Noguchi, M.:Cooperative equilibria of finite games with incomplete information. J. Math. Econ. 55, 4-10(2014)
[31] Noguchi, M.:Alpha cores of games with nonatomic asymmetric information. J. Math. Econ. 75, 1-12(2018)
[32] Askoura, Y.:The weak core of a game in normal form with a continuum of players. J. Math. Econ. 58, 38-45(2011)
[33] Askoura, Y.:On the core of normal form games with a continuum of players. Math. Soc. Sci. 89, 32-42(2017)
[34] Yang, Z.:Some infinite-player generalizations of Scarf's theorem:finite-coalition α-cores and weak α-cores. J. Math. Econ. 73, 81-85(2017)
[35] Yang, Z.:Some generalizations of Kajii's theorem to games with infinitely many players. J. Math. Econ. 76, 131-135(2018)
[36] Yang, Z.:The weak α-core of exchange economies with a continuum of players and pseudo-utilities. J. Math. Econ. 91, 43-50(2020)
[37] Yang, Z., Yuan, X.Z.:Some generalizations of Zhao's theorem:hybrid solutions and weak hybrid solutions for games with nonordered preferences. J. Math. Econ. 84, 94-100(2019)
[38] Shafer, W., Sonnenschein, H.:Equilibrium in abstract economies without ordered preferences. J. Math. Econ. 2, 345-348(1975)
[39] Bondareva, O.:The theory of the core in an n-person game. Vestn. Leningr. Univ. 13, 141-142(1962)