The Give and Take game: Analysis of a resource sharing game

Pedro Mariano ; Luís Correia

International Journal of Applied Mathematics and Computer Science, Tome 25 (2015), p. 753-767 / Harvested from The Polish Digital Mathematics Library

Résumé

We analyse Give and Take, a multi-stage resource sharing game to be played between two players. The payoff is dependent on the possession of an indivisible and durable resource, and in each stage players may either do nothing or, depending on their roles, give the resource or take it. Despite these simple rules, we show that this game has interesting complex dynamics. Unique to Give and Take is the existence of multiple Pareto optimal profiles that can also be Nash equilibria, and a built-in punishment action. This game allows us to study cooperation in sharing an indivisible and durable resource. Since there are multiple strategies to cooperate, Give and Take provides a base to investigate coordination under implicit or explicit agreements. We discuss its position in face of other games and real world situations that are better modelled by it. The paper presents an in-depth analysis of the game for the range of admissible parameter values. We show that, when taking is costly for both players, cooperation emerges as players prefer to give the resource.

Détail

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:275940

Bibliographie

[000] Akiyama, E. and Kaneko, K. (2000). Dynamical systems game theory and dynamics of games, Physica D 147(3-4): 221-258. | Zbl 1038.91510

[001] Anderlini, L. (1999). Communication, computability, and common interest games, Games and Economic Behavior 27(1): 1-37. | Zbl 0926.91001

[002] Axelrod, R. (1984). The Evolution of Cooperation, Basic Books New York, New York, NY. | Zbl 1225.92037

[003] Binmore, K. (1996). A note on backward induction, Games and Economic Behavior 17(1): 135-137.

[004] Blackwell, C. and McKee, M. (2003). Only for my own neighborhood? Preferences and voluntary provision of local and global public goods, Journal of Economic Behavior & Organization 52(1): 115-131.

[005] Boyd, R., Gintis, H., Bowles, S. and Richerson, P.J. (2003). The evolution of altruistic punishment, Proceedings of the National Academy of Sciences 100(6): 3531-3535.

[006] Brembs, B. (1996). Chaos, cheating and cooperation: Potential solutions to the prisoner's dilemma, Oikos 76(1): 14-24.

[007] Camerer, C. (2003). Behavioral Game Theory, Princeton University Press, Princeton, NJ. | Zbl 1019.91001

[008] Cason, T.N. and Mui, V.-L. (1998). Social influence in the sequential dictator game, Journal of Mathematical Psychology 42(2-3): 248-265. | Zbl 0936.91004

[009] Chen, X. and Deng, X. (2006). Settling the complexity of two-player Nash equilibrium, 47th Annual IEEE Symposium on Foundations of Computer Science, FOCS'06, Berkeley, CA, USA, pp. 261-272.

[010] Dong, H. and Dai, Z. (2011). A multi intersections signal coordinate control method based on game theory, 2011 International Conference on Electronics, Communications and Control (ICECC), Ningbo, China, pp. 1232-1235.

[011] Doniec, A., Mandiau, R., Piechowiak, S. and Espié, S. (2008). A behavioral multi-agent model for road traffic simulation, Engineering Applications of Artificial Intelligence 21(8): 1443-1454.

[012] Fehr, E. and Gächter, S. (2002). Altruistic punishment in humans, Nature 415(6868): 137-140.

[013] Fehr, E. and Gintis, H. (2007). Human motivation and social cooperation: Experimental and analytical foundations, Annual Review of Sociology 33: 43-64.

[014] Fehr, E. and Leibbrandt, A. (2011). A field study on cooperativeness and impatience in the tragedy of the commons, Journal of Public Economics 95(9-10): 1144-1155.

[015] Gintis, H. (2000). Game Theory Evolving-A Problem-centered Introduction to Modeling Strategic Interaction, 1st Edn., Princeton University Press, Princeton, NJ. | Zbl 1159.91300

[016] Helbing, D., Schönhof, M., Stark, H.-U. and Holyst, J.A. (2005). How individuals learn to take turns: Emergence of alternating cooperation in a congestion game and the prisoner's dilemma, Advances in Complex Systems 8(1): 87-116. | Zbl 1112.91012

[017] Hofbauer, J. and Sigmund, K. (1998). Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge. | Zbl 0914.90287

[018] Jones, P.J.S. (2006). Collective action problems posed by no-take zones, Marine Policy 30(2): 143-156.

[019] Koller, D., Megiddo, N. and von Stengel, B. (1996). Efficient computation of equilibria for extensive two-person games, Games and Economic Behavior 14(2): 247-259, http://www.sciencedirect.com/science/article/pii/S0899825696900512. | Zbl 0859.90127

[020] Lau, S.-H. and Mui, V.-L. (2012). Using turn taking to achieve intertemporal cooperation and symmetry in infinitely repeated 2×2 games, Theory and Decision 72(2): 167-188, DOI: 10.1007/s11238-011-9249-4. | Zbl 1243.91012

[021] López-Pérez, R. (2008). Aversion to norm-breaking: A model, Games and Economic Behavior 64(1): 237-267. | Zbl 1154.91354

[022] Mariano, P. and Correia, L. (2002a). The effect of agreements in a game with multiple strategies for cooperation, in R. Standish, M.A. Bedau and H.A. Abbass (Eds.), Artificial Life VIII: Proceedings of the Eighth International Conference on Artificial Life, MIT Press, Cambridge, MA, pp. 375-378.

[023] Mariano, P. and Correia, L. (2002b). A game to study coordination and cooperation, 5th Workshop on Deception, Fraud and Trust in Agent Societies, Bologna, Italy, pp. 101-112.

[024] Mariano, P. and Correia, L. (2003). A resource sharing model to study social behaviours, Progress in Artificial Intelligence-11th Portuguese Conference on Artificial Intelligence, EPIA 2003, Beja, Portugal, pp. 84-88. | Zbl 1205.91023

[025] McCarter, M.W., Budescu, D.V. and Scheffran, J. (2011). The give-or-take-some dilemma: An empirical investigation of a hybrid social dilemma, Organizational Behavior and Human Decision Processes 116(1): 83-95.

[026] McKelvey, R.D. and Palfrey, T.R. (1992). An experimental study of the centipede game, Econometrica 60(4): 803-836. | Zbl 0764.90093

[027] Nicolò, A. and Yu, Y. (2008). Strategic divide and choose, Games and Economic Behavior 64(1): 268-289. | Zbl 1152.91408

[028] Nowak, M., Bonhoeffer, S. and May, R. (1994). Spatial games and the maintenance of cooperation, Proceedings of the National Academy of Sciences 91(11): 4877-4881. | Zbl 0799.92010

[029] Ottone, S. (2008). Are people Samaritans or Avengers?, Economics Bulletin 3(10): 1-3.

[030] Papadimitriou, C.H. (1994). On the complexity of the parity argument and other inefficient proofs of existence, Journal of Computer and System Sciences 48(3): 498-532. http://www.sciencedirect.com/science/article/pii/S0022000005800637. | Zbl 0806.68048

[031] Rosenthal, R.W. (1981). Games of perfect information, predatory pricing and the chain-store paradox, Journal of Economic Theory 25(1): 92-100, http://ideas.repec.org/a/eee/jetheo/v25y1981i1p92-100.html. | Zbl 0467.90084

[032] Rowland, M. (2005). A framework for resolving the transboundary water allocation conflict conundrum, Ground Water 43(5): 700-705.

[033] Shapley, L.S. (1953). Stochastic games, Proceedings of the National Academy of Sciences 39(10): 1095-1100, http://www.pnas.org/content/39/10/1095.short. | Zbl 0051.35805

[034] Shoham, Y. and Leyton-Brown, K. (2009). Multiagent Systems: Algorithmic, Game-theoretic and Logical Foundations, Cambridge University Press, Cambridge. | Zbl 1163.91006

[035] Sigmund, K., Hauert, C. and Nowak, M.A. (2001). Reward and punishment in minigames, Proceedings of the National Academy of Sciences 98(19): 10757-10762.

[036] Sutter, M. and Strassmair, C. (2009). Communication, cooperation and collusion in team tournaments-an experimental study, Games and Economic Behavior 66(1): 506-525. | Zbl 1161.91340

[037] van Dijk, F., Sonnemans, J. and van Winden, F. (2002). Social ties in a public good experiment, Journal of Public Economics 85(2): 275-299.

[038] Velez, M.A., Stranlund, J.K. and Murphy, J.J. (2009). What motivates common pool resource users? Experimental evidence from the field, Journal of Economic Behavior & Organization 70(3): 485-497.

[039] Wallace, J.S., Acreman, M.C. and Sullivan, C.A. (2003). The sharing of water between society and ecosystems: from conflict to catchment-based co-management, Philosophical Transactions of the Royal Society of London, Series B: Biological Sciences 358(1440): 2011-2026.

[040] Ward, H. (1998). A game theoretic analysis of the politics of taking it in turns, British Journal of Political Science 28(2): 355-387.