04Mar 2018

A NEW APPROACH TOWARDS TRANSFORMATION OF BOTH CARDINAL AND ORDINAL 2 2 GAMES.

  • School of management, China University of mining and technology, Xuzhou, Jiangsu province, 221116, China.
  • Department of management sciences, COMSATS institute of information technology, Islamabad, Pakistan.
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Game theory literature largely lacks a generally accepted method, capable of transforming both cardinal and ordinal games or games where one player is cardinal and the other one is ordinal. We devised a new method to overcome this problem. We used propositional logic to represent our general argument. Afterwards developed basic inferences, conclusion is derived according to modus ponens, based on these inferences we derived biconditional statement and truth table. By adding and subtracting same figure to/from opposite expected outcomes (according to change in preference of one or both players) games having ordinal and/or cardinal payoffs can be transformed. We used the Notorious ?Prisoners Dilemma? as an example and transformed it under our new method. Our method will not only expand the available knowledge in game theory by including both ordinal and cardinal transformations but it can also be helpful for the potential development of new taxonomies and topologies.

  1. Robinson and D. Goforth, The Topology of the 2?2 Games: A New Periodic Table, New York: Routledge, 2005.
  2. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, 3rd ed., Princeton, N J.: Princeton University Press, 1953.
  3. J. Brams and M. D. Davis, The verification problem in arms control: A game theoretic analysis, in Interaction and Communication in Global Politics, London: Sage Press, 1983.
  4. J. Brams and D. M. Kilgour, Notes on Arms Control Verification: A Game- Theoretic Analysis, in modeling and Analysis of Arms Control Problems, Berlin: Springer-Verlag, 1986.
  5. Rapoport, ?Exploiter, leader, hero, and martyr: The four archetypes of the 2 x 2 game,? Behavioral Science, vol. 12, pp. 81-84, 1967.
  6. H. Snyder, ?Prisoner\'s dilemma and chicken models in international politics,? International Studies Quarterly, 1971.
  7. C. Zagare, ?Non-myopic equilibria and the Middle East Crisis of 1967,? Conflict Management and Peace Science, vol. 5, pp. 139-162, 1981.
  8. C. Zagare, The pathology of unilateral deterrence\', in Dynamic Models of International Conflict, Lynne Rienner, Boulder, CO, 1985.
  9. Rapoport and M. Guyer, ?A taxonomy of 2?2 games,? General Systems Yearbook of the Society for General Systems Research, vol. 11, p. 203?214, 1966.
  10. M. Kilgour and N. M. Fraser, ?A taxonomy of all ordinal 2?2 games,? Theory and Decision, vol. 24, pp. 99-117, 1988.
  11. C. Fishburn and M. D. Kilgour, ?Binary 2?2 games,? Theory and Decision, vol. 29, pp. 165-182, 1990.
  12. Bruns, ?Navigating the Topology of 2?2 Games: An Introductory Note on Payoff Families, Normalization, and Natural Order,? 2010a. [Online]. Available: https://arxiv.org/ftp/arxiv/papers/1010/1010.4727.pdf. [Accessed 12 December 2017].
  13. Bruns, ?Transmuting Social Dilemmas into Win-Win Games: Payoff Families in the Topology of 2?2 Ordinal Games,? 2010b. [Online]. Available: http://www.bryanbruns.com/Bruns,%20Bryan%202010%20Transmuting%20social%20dilemmas%20into%20winwin%20Games100722.pdf. [Accessed 01 November 2017].
  14. Bruns, ?Escaping Prisoner?s Dilemmas: From Discord to Harmony in the Landscape of 2?2 Games,? 2012. [Online]. Available: https://arxiv.org/ftp/arxiv/papers/1206/1206.1880.pdf. [Accessed 22 August 2017].
  15. Bruns, ?An Atlas of 2?2 Games: Mapping Elementary Models of Cooperation and Conflict,? 2013. [Online]. Available: http://bryanbruns.com/2x2atlas.pdf. [Accessed 15 December 2017].
  16. Bruns, ?Names for Games: A Binomial Nomenclature for 2?2 Ordinal Games,? 2014. [Online]. Available: http://www.bryanbruns.com/Names_for_Games140331.pdf. [Accessed 12 July 2017].
  17. Bruns, ?Names for Games: Locating 2?2 Games,? Games, pp. ISSN 2073-4336, 2015.
  18. Echenique and A. Galichon, ?Ordinal and cardinal solution concepts for two-sided matching,? Games and Economic Behavior, vol. 101, p. 63?77, 2017.
  19. Calvo and H. Peters, ?Bargaining with ordinal and cardinal players,? Games and Economic Behavior, vol. 52, p. 20?33, 2005.
  20. Kim, ?Ordinal versus cardinal voting rules: A mechanism design approach,? Games and Economic Behavior, vol. 104, p. 350?371, 2017.
  21. F. Saen, ?Suppliers selection in the presence of both cardinal and ordinal data,? European Journal of Operational Research, vol. 183, p. 741?747, 2007.
  22. J. Daniel, How to Prove It: A Structured Approach, 2nd ed., New York: Cambridge University Press, 2006.
  23. J. Hurley , A Concise Introduction to Logic, 11th ed., Boston,USA: Wadsworth publishing, 2011.
  24. Papineau , Philosophical Devices: Proofs, Probabilities, Possibilities, and sets, 1st ed., Oxford, United Kingdom: Oxford University Press, 2012.
  25. Bruns, ?http://www.bryanbruns.com,? [Online]. Available: http://www.bryanbruns.com/2x2table.pdf. [Accessed 29 December 2017].
  26. Mikhael, ?\"Cardinal Payoff,\" Dictionary of Game Theory Terms,? Game Theory .net, 15 August 2005. [Online]. Available: http://www.gametheory.net/Dictionary/CardinalPayoffs.html. [Accessed 13 March 2018].

[M. Jawad sajid, Qingren Cao, Li Xinchun and M. Fahad sajid. (2018); A NEW APPROACH TOWARDS TRANSFORMATION OF BOTH CARDINAL AND ORDINAL 2 2 GAMES. Int. J. of Adv. Res. 6 (Mar). 389-395] (ISSN 2320-5407). www.journalijar.com

MUHAMMAD JAWAD SAJID
SCHOOL OF MANAGEMENT, CHINA UNIVERSITY OF MINING AND TECHNOLOGY, XUZHOU, JIANGSU PROVINCE, 221116, CHINA.

DOI:

Article DOI: 10.21474/IJAR01/6691      
DOI URL: http://dx.doi.org/10.21474/IJAR01/6691

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