A PLAY-and-WIN GAME APPROACH FOR DETERMINATION OF STRATEGIES USED IN GAME THEORY

Abstract

In the present study, voluntary people of different age groups consisted of children, youngs, adults and olds were asked to play a simple play-and-win game and the results of the games were analyzed to reveal how they behaved in the games to maximize their winning performances. The games were played in two different forms to represent one-shot Prisoner’s Dilemma (PD) and iterated Prisoner’s Dilemma (IPD). The results showed that age groups in IPD game did not differ from each other in the numbers of games won. On the other hand, gender differences were significant in the children and young groups. Males in children group and females of the youngs group were better in winning a game. In the PD game, the age groups and the genders in these age groups did not differ from each other in the numbers of games won. The evaluation of behaviors of players in general showed that a TIT-FOR-TAT strategy was used by players in combination with pure cooperation to maximize their winnings. We conclude, based on the overall results that cooperation may be the optimal strategy for individual and group success for establishment and maintenance of social dynamics and relationships. 

Keywords

• Prisoner’s Dilemma
• Game Theory
• Cooperation
• Altruism

References

1. 1. Axelrod, R. (1984). The evolution of cooperation. New York.
2. 2. Axelrod, R. & Hamilton, W. D. (1981). The evolution of cooperation. Science 211, 1981, 1390–1396.
3. 3. Balliet, D., Li, N. P., Macfarlan, S. J., & Van Vugt, M. (2011). Sex differences in cooperation: a meta-analytic review of social dilemmas. Psychological Bulletin, 137(6), 881.
4. 4. Bowles, S. & Gintis, H. (2003). Origins of human cooperation. In: Hammerstein P, editor. Genetic and Cultural Evolution of Cooperation, Dahlem Univ. Press, pp. 429–444. 5. Bravetti, A. & Padilla, P. (2018). An optimal strategy to solve the Prisoner’s Dilemma. Scientific Reports, 8(1), 1-6.
5. 6. Brown, J. S. & Vincent, T. L. (2008). Evolution of cooperation with shared costs and benefits. Proc. R. Soc. Lond. B, 275, 1985–1994.
6. 7. Bshary, R. (2010). Cooperation between unrelated individuals–a game theoretic approach. In: Kappeler P, editor. Animal behaviour: evolution and mechanisms, Springer, Berlin, Heidelberg, pp. 213-240.
7. 8. Burnham, T. C. & Johnson, D. D. P. (2005). The Biological and Evolutionary Logic of Human Cooperation. Analyse & Kritik, 27, 113-135.
8. 9. Clutton-Brock, T. (2009). Cooperation between non-kin in animal societies. Nature, 462 (7269), 51-57.

9. 10. Darwin C. (1859). On the Origin of Species. J. Murray, London.
10. 11. Dawes, R. M. (1980). Social dilemmas. Annual Review of Psychology, 31, 169 – 193.
11. 12. Delahaye, J.-P., Mathieu, P. & Beaufils, B. (2000). The iterated dilemma. In, Müller HJ, Dieng R, editors. Computational Conflicts: Conflict Modeling for Distributed Intelligent Systems, Berlin/Heidelberg: Springer, pp. 203–223.
12. 13. Dugatkin, L. A. (2002). Cooperation in animals: an evolutionary overview. Biology and Philosophy, 17(4), 459-476.
13. 14. Eckel, C. C. & Grossmann, P. J. (1996). The relative price of fairness: gender differences in a punishment game. Journal of Economic Behavior & Organization, 30(2), 143-158.
14. 15. Engel, C. (2011). Dictator games: a meta-study. Experimental Economic, 14(4), 583–610.
15. 16. Field, A. J. (2001). Altruistically Included? The University of Michigan Press, Ann Arbor.
16. 17. Fischbacher, U., Gächter, S. & Fehr, E. (2001). Are people conditionally cooperative? Evidence from a public goods experiment. Economics Letters, 71, 397–404.
17. 18. Grujić, J., Fosco C., Araujo, L., Cuesta, J. A. & Sántchez, A. (2010). Social Experiments in the Mesoscale: Humans Playing a Spatial Prisoner’s Dilemma. PLoS ONE, 5(11), e13749.
18. 19. Henrich, N. & Henrich, J. (2007). Why humans cooperate. Oxford: Oxford University Press.
19. 20. Henrich, J., Boyd, R., Bowles, S., Camerer, C., Fehr, E., Gintis, H., McElreath, R., Alvard, M., Barr, A., Ensminger, J., Henrich, N. S., Hill, K., Gil-White, F., Gurven, M., Marlowe, F. W., Patton, J. Q. & Tracer, D. (2005). Economic man in cross-cultural perspective: behavioral experiments in 15 small-scale societies. Behavioral and Brain Science, 28(6), 795–855.
20. 21. LI, J., Hingston, P. & Kendall, G. (2011). Engineering design of strategies for winning iterated prisoner’s dilemma competitions. IEEE Transactions on Computational Intelligence and AI in Games, 3(4), 348–360.
21. 22. LI, J. & Kendall, G. (2013). The effect of memory size on the evolutionary stability of strategies in iterated prisoner’s dilemma. IEEE Transactions on Evolutionary Computation, 18(6), 1–8.
22. 23. Mathieu, P. & Delahaye, J.-P. (2017). New Winning Strategies for the Iterated Prisoner's Dilemma. Journal of Artificial Societies and Social Simulation, 20, 12.
23. 24. Molina, J. A., Giménez-Nadal, J. I., Cuesta, J. A., Gracia-Lazaro, C., Moreno, Y., & Sanchez, A. (2013). Gender differences in cooperation: experimental evidence on high school students. PloS one, 8(12), e83700.
24. 25. Morgan, K. N. (2003). Demonstrating strategies for solving the prisoner's dilemma. In: Ploger BJ, Yasukawa K, editors. Exploring Animal Behavior in Laboratory and Field: An Hypothesis-testing Approach to the Development, Causation, Function and Evolution of Animal Behavior, Academic Press, pp. 359-378.
25. 26. Nowak, M. A. (2006). Five rules for the evolution of cooperation. Science, 314, 1560–1565.
26. 27. O’Riordan, C. (2000). A forgiving strategy for the iterated prisoner’s dilemma. Journal of Artificial Societies and Social Simulation, 3(4), 3.
27. 28. Press, W. H. & Dyson, F. J. (2012). Iterated prisoner’s dilemma contains strategies that dominate any evolutionary opponent. Proceedings of the National Academy of Sciences, 109(26), 10409–10413.
28. 29. Smith, J. M. & Price, G. R. (1973). The logic of animal conflict. Nature, 246(5427), 15-18.
29. 30. Tomasello, M., Melis, A. P., Tennie, C., Wyman, E. & Herrmann, E. (2012). Two key steps in the evolution of human cooperation: The interdependence hypothesis. Current Anthropology, 53(6), 673-692.
30. 31. Trivers, R. L. (1971). The evolution of reciprocal altruism. Q. Rev. Biol., 46, 35–57.
31. 32. Vogelsang, M., Jensen, K., Kirschner, S., Tennie, C. & Tomasello, M. (2014). Preschoolers are sensitive to free riding in a public goods game. Frontiers of Psychology, 5, 1-9.
32. 33. Wilson, D.S. (1975). A general theory of group selection. Proceedings of the National Academy of Sciences, 72, 143–146.