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Conditional expectation of Banach valued correspondences and economic applications

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  • He, Wei
  • Sun, Yeneng

Abstract

We present some regularity properties (convexity, weak/weak∗ compactness and preservation of weak/weak∗ upper hemicontinuity) for Bochner/Gel′fand conditional expectation of Banach valued correspondences under the nowhere equivalence condition. These regularity properties for Bochner/Gel′fand integral of Banach valued correspondences are obtained as corollaries. We prove the necessity of the nowhere equivalence condition for any of these properties to hold. Economic applications, including a general class of large games and abstract economies with asymmetric information, are discussed.

Suggested Citation

  • He, Wei & Sun, Yeneng, 2022. "Conditional expectation of Banach valued correspondences and economic applications," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    • Handle: RePEc:eee:mateco:v:101:y:2022:i:c:s0304406822000477
    DOI: 10.1016/j.jmateco.2022.102698
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    1. Podczeck, Konrad, 2008. "On the convexity and compactness of the integral of a Banach space valued correspondence," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 836-852, July.
    2. Jang, Hyo Seok & Lee, Sangjik, 2020. "Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 57-64.
    3. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
    4. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 8(1), pages 15-35, March.
    5. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
    6. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
    7. Sun, Xiang & Zeng, Yishu, 2020. "Perfect and proper equilibria in large games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 288-308.
    8. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346.
    9. Nicholas Yannelis, 2009. "Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 419-432, February.
    10. Xiang Sun & Yongchao Zhang, 2015. "Pure-strategy Nash equilibria in nonatomic games with infinite-dimensional action spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 161-182, January.
    11. Hyo Seok Jang & Sangjik Lee, 2019. "Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences," Papers 1904.07444, arXiv.org, revised Feb 2020.
    12. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
    13. Podczeck, Konrad & Yannelis, Nicholas C., 2008. "Equilibrium theory with asymmetric information and with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 141(1), pages 152-183, July.
    14. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    15. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    16. Wei He & Yeneng Sun, 2018. "Conditional expectation of correspondences and economic applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 265-299, August.
    17. Ostroy, Joseph M & Zame, William R, 1994. "Nonatomic Economies and the Boundaries of Perfect Competition," Econometrica, Econometric Society, vol. 62(3), pages 593-633, May.
    18. Yannelis, Nicholas C. & Zame, William R., 1986. "Equilibria in Banach lattices without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 85-110, April.
    19. Khan, M. Ali & Sagara, Nobusumi, 2016. "Relaxed large economies with infinite-dimensional commodity spaces: The existence of Walrasian equilibria," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 95-107.
    20. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    21. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.
    22. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    23. Sun, Yeneng & Yannelis, Nicholas C., 2008. "Saturation and the integration of Banach valued correspondences," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 861-865, July.
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