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Large games with a bio-social typology

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  • Khan, M. Ali
  • Rath, Kali P.
  • Sun, Yeneng
  • Yu, Haomiao

Abstract

We present a comprehensive theory of large games in which players have names and determinate social-types and/or biological traits, and identify through four decisive examples, essentially based on a matching-pennies type game, pathologies arising from the use of a Lebesgue interval for playerʼs names. In a sufficiently general context of traits and actions, we address this dissonance by showing a saturated probability space as being a necessary and sufficient name-space for the existence and upper hemi-continuity of pure-strategy Nash equilibria in large games with traits. We illustrate the idealized results by corresponding asymptotic results for an increasing sequence of finite games.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jetheo:v:148:y:2013:i:3:p:1122-1149 DOI: 10.1016/j.jet.2012.11.002
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    Citations

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    Cited by:

    1. Khan, M. Ali & Rath, Kali P. & Yu, Haomiao & Zhang, Yongchao, 2013. "Large distributional games with traits," Economics Letters, Elsevier, vol. 118(3), pages 502-505.
    2. Yu, Haomiao & Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 2015. "Strategic uncertainty and the ex-post Nash property in large games," Theoretical Economics, Econometric Society, vol. 10(1), January.
    3. 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.
    4. Qiao, Lei & Yu, Haomiao, 2014. "On the space of players in idealized limit games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 177-190.
    5. Qiao, Lei & Yu, Haomiao & Zhang, Zhixiang, 2016. "On the closed-graph property of the Nash equilibrium correspondence in a large game: A complete characterization," Games and Economic Behavior, Elsevier, vol. 99(C), pages 89-98.
    6. Fu, Haifeng & Yu, Haomiao, 2015. "Pareto-undominated and socially-maximal equilibria in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 7-15.
    7. Barelli, Paulo & Duggan, John, 2015. "Extremal choice equilibrium with applications to large games, stochastic games, & endogenous institutions," Journal of Economic Theory, Elsevier, vol. 155(C), pages 95-130.
    8. repec:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-016-0528-8 is not listed on IDEAS
    9. Khan, M. Ali & Yu, Haomiao & Zhang, Zhixiang, 2015. "On the centipede game with a social norm," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 16-19.
    10. Khan, Mohammed Ali & Rath, Kali P. & Yu, Haomiao & Zhang, Yongchao, 2017. "On the equivalence of large individualized and distributionalized games," Theoretical Economics, Econometric Society, vol. 12(2), May.
    11. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0539-5 is not listed on IDEAS
    12. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    13. Ennio Bilancini & Leonardo Boncinelli, 2016. "Strict Nash equilibria in non-atomic games with strict single crossing in players (or types) and actions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(1), pages 95-109, April.

    More about this item

    Keywords

    Large games; Social-type; Traits; Idealized limit game; Saturated probability space; Pure-strategy Nash equilibrium; Closed-graph property; Upper hemi-continuity; Asymptotic implementation;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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