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Two-Person Second-Order Games, Part 1: Formulation and Transition Anatomy

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  • P. L. Yu

    (National Chiao Tung University
    University of Kansas)

  • M. Larbani

    (Kainan University
    IIUM University)

Abstract

It is well known that human psychology determines his/her action and behavior. This fact has not been fully incorporated in game theory. This paper intends to incorporate human psychology in formulating games as people play them. In Part 1 of the paper, we formulate a two-person game by the habitual domain theory and the Markov chain theory. Using the habitual domains theory, we present a new model describing the evolution of the states of mind of players over time, the two-person second-order game. We introduce the concept of the focal mind profile as well as the solution concept of the win-win mind profile. In addition, we provide also a method to predict the average number of steps needed for a game to reach a focal or win-win mind profile. Then, in Part 2 of the paper, under some reasonable assumptions, we derive the possibility theorem stating that it is always possible to reach a win-win mind profile when suitable conditions are satisfied.

Suggested Citation

  • P. L. Yu & M. Larbani, 2009. "Two-Person Second-Order Games, Part 1: Formulation and Transition Anatomy," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 619-639, June.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:3:d:10.1007_s10957-008-9487-y
    DOI: 10.1007/s10957-008-9487-y
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Geanakoplos, John & Pearce, David & Stacchetti, Ennio, 1989. "Psychological games and sequential rationality," Games and Economic Behavior, Elsevier, vol. 1(1), pages 60-79, March.
    3. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
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    Cited by:

    1. Po-Lung Yu & Yen-Chu Chen, 2012. "Dynamic multiple criteria decision making in changeable spaces: from habitual domains to innovation dynamics," Annals of Operations Research, Springer, vol. 197(1), pages 201-220, August.
    2. M. Larbani & P. L. Yu, 2011. "n-Person Second-Order Games: A Paradigm Shift in Game Theory," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 447-473, June.
    3. T. Q. Bao & B. S. Mordukhovich & A. Soubeyran, 2015. "Variational Analysis in Psychological Modeling," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 290-315, January.
    4. Moussa Larbani & Po Lung Yu, 2012. "Decision Making and Optimization in Changeable Spaces, a New Paradigm," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 727-761, December.

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