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Pure-strategy Nash equilibria in large games: characterization and existence

Author

Listed:
  • Haifeng Fu

    () (Xi’an Jiaotong-Liverpool University)

  • Ying Xu

    (National University of Singapore)

  • Luyi Zhang

    (National University of Singapore)

Abstract

Abstract In this paper, we first characterize pure-strategy Nash equilibria in large games restricted with countable actions or countable payoffs. Then, we provide a counterexample to show that there is no such characterization when the agent space is an arbitrary atomless probability space (in particular, Lebesgue unit interval) and both actions and payoffs are uncountable. Nevertheless, if the agent space is a saturated probability space, the characterization result is still valid. Next, we show that the characterizing distributions for the equilibria exist in a quite general framework. This leads to the existence of pure-strategy Nash equilibria in three different settings of large games. Finally, we notice that our characterization result can also be used to characterize saturated probability spaces.

Suggested Citation

  • Haifeng Fu & Ying Xu & Luyi Zhang, 2016. "Pure-strategy Nash equilibria in large games: characterization and existence," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 685-697, August.
  • Handle: RePEc:spr:jogath:v:45:y:2016:i:3:d:10.1007_s00182-015-0477-7
    DOI: 10.1007/s00182-015-0477-7
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    References listed on IDEAS

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    1. 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.
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    8. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive 585, The Johns Hopkins University,Department of Economics.
    9. Yu, Haomiao & Zhang, Zhixiang, 2007. "Pure strategy equilibria in games with countable actions," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 192-200, February.
    10. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
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