The Edgeworth Conjecture with Small Coalitions and Approximate Equilibria in Large Economies

Published Online:https://doi.org/10.1287/moor.2022.1263

References

  • [1] Anderson RM (1978) An elementary core equivalence theorem. Econometrica 46(6):1483–1487.CrossrefGoogle Scholar
  • [2] Anderson RM (1982) A market value approach to approximate equilibria. Econometrica 50(1):127–136.CrossrefGoogle Scholar
  • [3] Anderson RM (1992) The core in perfectly competitive economies. Handbook of Game Theory with Economic Applications, vol. 1 (North-Holland, Amsterdam), 413–457.CrossrefGoogle Scholar
  • [4] Anderson RM, Khan MA, Rashid S (1982) Approximate equilibria with bounds independent of preferences. Rev. Econom. Stud. 49(3):473–475.CrossrefGoogle Scholar
  • [5] Arrow KJ, Hahn FH (1971) General Competitive Analysis (Holden, San Francisco).Google Scholar
  • [6] Aumann RJ (1964) Markets with a continuum of traders. Econometrica 32(1–2):39–50.CrossrefGoogle Scholar
  • [7] Barman S (2015) Approximating Nash equilibria and dense bipartite subgraphs via an approximate version of Carathéodory’s theorem. Proc. 47th Annual ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 361–369.Google Scholar
  • [8] Boyd S, Vandenberghe L (2004) Convex Optimization (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [9] Chen X, Dai D, Du Y, Teng SH (2009) Settling the complexity of Arrow-Debreu equilibria in markets with additively separable utilities. Proc. 50th Annual IEEE Sympos. Foundations Comput. Sci. (IEEE Computer Society, Washington, DC), 273–282.Google Scholar
  • [10] Codenotti B, Saberi A, Varadarajan K, Ye Y (2006) Leontief economies encode nonzero sum two-player games. Proc. 17th Annual ACM-SIAM Sympos. Discrete Algorithms (Society for Industrial and Applied Mathematics, Philadelphia), 659–667.Google Scholar
  • [11] Debreu G, Scarf H (1963) A limit theorem on the core of an economy. Internat. Econom. Rev. 4(3):235–246.CrossrefGoogle Scholar
  • [12] Deng X, Du Y (2008) The computation of approximate competitive equilibrium is PPAD-hard. Inform. Processing Lett. 108(6):369–373.CrossrefGoogle Scholar
  • [13] Deng X, Papadimitriou C, Safra S (2002) On the complexity of equilibria. Proc. 34th Annual ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 67–71.Google Scholar
  • [14] Edgeworth FY (1881) Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences, vol. 10 (Kegan Paul, London).Google Scholar
  • [15] Edgeworth FY (1884) The rationale of exchange. J. Statist. Soc. Lond. 47(1):164–166.Google Scholar
  • [16] Garg J, Mehta R, Vazirani VV, Yazdanbod S (2017) Settling the complexity of Leontief and PLC exchange markets under exact and approximate equilibria. Proc. 49th Annual ACM SIGACT Sympos. Theory Comput. (Association for Computing Machinery, New York), 890–901.Google Scholar
  • [17] Grodal B (1972) A second remark on the core of an atomless economy. Econometrica 40(3):581–583.CrossrefGoogle Scholar
  • [18] Grötschel M, Lovász L, Schrijver A (2012) Geometric Algorithms and Combinatorial Optimization, ed. 2 (Springer, Berlin).Google Scholar
  • [19] Hildenbrand W (1974) Core and Equilibria of a Large Economy (Princeton University Press, Princeton, NJ).Google Scholar
  • [20] Hildenbrand W, Schmeidler D, Zamir S (1973) Existence of approximate equilibria and cores. Econometrica 41(6):1159–1166.CrossrefGoogle Scholar
  • [21] Mas-Colell A (1978) A note on the core equivalence theorem: How many blocking coalitions are there? J. Math. Econom. 5(3):207–215.CrossrefGoogle Scholar
  • [22] Mas-Colell A (1979) A refinement of the core equivalence theorem. Econom. Lett. 3(4):307–310.CrossrefGoogle Scholar
  • [23] Mas-Colell A, Whinston MD, Green JR (1995) Microeconomic Theory (Oxford University Press, Oxford, UK).Google Scholar
  • [24] Osborne MJ, Rubinstein A (1994) A Course in Game Theory (MIT Press, Cambridge, MA).Google Scholar
  • [25] Schmeidler D (1972) A remark on the core of an atomless economy. Econometrica 40(3):579–580.CrossrefGoogle Scholar
  • [26] Starr RM (1969) Quasi-equilibria in markets with non-convex preferences. Econometrica 37(1):25–38.CrossrefGoogle Scholar
  • [27] Vazirani VV, Yannakakis M (2010) Market equilibrium under separable, piecewise-linear, concave utilities. Chi-Chih Yao A, ed. Proc. Innovations Comput. Sci. (Association for Computing Machinery, New York), 156–165.Google Scholar
  • [28] Vind K (1972) A third remark on the core of an atomless economy. Econometrica 40(3):585.CrossrefGoogle Scholar
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