Lensberg, Terje and Schenk-Hoppé, Klaus R. (2020): Cold play: Learning across bimatrix games.
Preview |
PDF
MPRA_paper_104438.pdf Download (554kB) | Preview |
Abstract
We study one-shot play in the set of all bimatrix games by a large population of agents. The agents never see the same game twice, but they can learn `across games' by developing solution concepts that tell them how to play new games. Each agent's individual solution concept is represented by a computer program, and natural selection is applied to derive a stochastically stable solution concept. Our aim is to develop a theory predicting how experienced agents would play in one-shot games. To use the theory, visit https://gplab.nhh.no/gamesolver.php.
Item Type: | MPRA Paper |
---|---|
Original Title: | Cold play: Learning across bimatrix games |
Language: | English |
Keywords: | One-shot games, solution concepts, genetic programming, evolutionary stability. |
Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C90 - General |
Item ID: | 104438 |
Depositing User: | Klaus R. Schenk-Hoppé |
Date Deposited: | 05 Dec 2020 13:32 |
Last Modified: | 05 Dec 2020 13:32 |
References: | Arifovic, J. (1994). Genetic algorithm learning and the cobweb model, Journal of Economic Dynamics and Control 18(1): 3–28. Arifovic, J. (1995). Genetic algorithms and inflationary economies, Journal of Monetary Economics 36(1): 219–243. Arifovic, J. (1996). The behavior of the exchange rate in the genetic algorithm and experimental economies, Journal of Political Economy 104(3): 510–541. Basu, K. (1994). The Traveler’s dilemma: Paradoxes of rationality in game theory, American Economic Review: Papers and Proceedings 84(2): 391–395. Bernheim, B. D. (1984). Rationalizable strategic behavior, Econometrica 52(4): 1007–1028. Brown, G. W. (1951). Iterative solution of games by fictitious play, Activity Analysis of Production and Allocation 13(1): 374–376. Capra, C. M., Goeree, J. K., Gomez, R. & Holt, C. A. (1999). Anomalous behavior in a traveler’s dilemma?, American Economic Review 89(3): 678–690. Carlson, H. & van Damme, E. (1993). Equilibrium selection in stag hunt games, in K. Binmore, A. Kirman & P. Tani (eds), Frontiers of Game Theory, Addison-Wesley, Reading, MA, pp. 237–254. Chen, S.-H., Duffy, J. & Yeh, C.-H. (2005). Equilibrium selection via adaptation: Using genetic programming to model learning in a coordination game, Advances in Dynamic Games, Springer, pp. 571–598. Cooper, D. J. & Kagel, J. H. (2003). Lessons learned: Generalizing learning across games, American Economic Review 93(2): 202–207. Cooper, D. J. & Kagel, J. H. (2008). Learning and transfer in signaling games, Economic Theory 34(3): 415–439. Costa-Gomes, M., Crawford, V. P. & Broseta, B. (2001). Cognition and behavior in normal-form games: An experimental study, Econometrica 69(5): 1193–1235. Crawford, V. P., Costa-Gomes, M. A. & Iriberri, N. (2013). Structural models of nonequilibrium strategic thinking: Theory, evidence, and applications, Journal of Economic Literature 51(1): 5–62. Fudenberg, D. & Liang, A. (2019). Predicting and Understanding Initial Play, American Economic Review 109(12): 4112–4141. Gale, J., Binmore, K. G. & Samuelson, L. (1995). Learning to be imperfect: The ultimatum game, Games and Economic Behavior 8(1): 56–90. Germano, F. (2007). Stochastic evolution of rules for playing finite normal form games, Theory and Decision 62(4): 311–333. Gilboa, I. & Schmeidler, D. (1995). Case-based decision theory, Quarterly Journal of Economics 110: 605–639. Gilboa, I., Schmeidler, D. & Wakker, P. P. (2002). Utility in case-based decision theory, Journal of Economic Theory 105(2): 483–502. Grimm, V. & Mengel, F. (2012). An experiment on learning in a multiple games environment, Journal of Economic Theory 147(6): 2220–2259. Güth, W. R., Schmittberger, R. & Schwarze, B. (1982). An experimental analysis of ultimatum bargaining, Journal of Economic Behaviour & Organization 3(4): 367–388. Güth, W. R. & Tietz, R. (1990). Ultimatum bargaining behavior: A survey and comparison of experimental results, Journal of Economic Psychology 11(3): 417–449. Harsanyi, J. & Selten, R. (1988). A General Theory of Equilibrium Selection in Games, MIT Press. Haruvy, E. & Stahl, D. O. (2012). Between-game rule learning in dissimilar symmetric normal-form games, Games and Economic Behavior 74(1): 208–221. Jehiel, P. (2005). Analogy-based expectation equilibrium, Journal of Economic Theory 123(2): 81–104. Kohlberg, E. & Mertens, J.-F. (1986). On the strategic stability of equilibria, Econometrica 54(5): 1003–1037. Koza, J. R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press. Koza, J. R. (ed.) (1992-2003). Genetic Programming Series, Kluwer Academic Publishers. Lensberg, T., Schenk-Hoppé, K. R. & Ladley, D. (2015). Costs and benefits of financial regulation: Short-selling bans and transaction taxes, Journal of Banking & Finance 51: 103–118. LiCalzi, M. (1995). Fictitious play by cases, Games and Economic Behavior 11(1): 64–89. Marks, R. E. (2002). Playing games with genetic algorithms, in S. H. Chen (ed.), Evolutionary Computation in Economics and Finance. Studies in Fuzziness and Soft Computing, Vol. 100, Physica, Heidelberg, pp. 31–44. McKelvey, R. D. & Palfrey, T. R. (1992). An experimental study of the centipede game, Econometrica 60(4): 803–836. Mengel, F. (2012). Learning across games, Games and Economic Behavior 74(2): 601–619. Mookherjee, D. & Sopher, B. (1994). Learning behavior in an experimental matching pennies game, Games and Economic Behavior 7(1): 62–91. Nagel, R. (1995). Unraveling in guessing games: An experimental study, American Economic Review 85(5): 1313–1326. Nordin, P. (1997). Evolutionary Program Induction of Binary Machine Code and its Applications, Krehl Verlag, Münster. Pace, M. (2009). How a genetic algorithm learns to play traveler’s dilemma by choosing dominated strategies to achieve greater payoffs, 2009 IEEE Symposium on Computational Intelligence and Games, IEEE, pp. 194–200. Pearce, D. G. (1984). Rationalizable strategic behavior and the problem of perfection, Econometrica 52(4): 1029–1050. Rosenthal, R. W. (1981). Games of perfect information, predatory pricing and the chain-store paradox, Journal of Economic Theory 25(1): 92–100. Roth, A. E. & Erev, I. (1995). Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term, Games and Economic Behavior 8(1): 164–212. Samuelson, L. (2001). Analogies, adaptation, and anomalies, Journal of Economic Theory 97(2): 320–366. Selten, R. (1967). Die Strategiemethode zur Erforschung des eingeschränkt rationalen Verhaltens im Rahmen eines Oligopolexperiments, in H. Sauermann (ed.), Beiträge zur experimentellen Wirtschaftsforschung, Mohr, Tübingen, pp. 136–168. Selten, R., Abbink, K., Buchta, J. & Sadrieh, A. (2003). How to play (3×3)-games. A strategy method experiment, Games and Economic Behavior 45(1): 19–37. Sgroi, D. & Zizzo, D. J. (2009). Learning to play 3×3 games: Neural networks as bounded- rational players, Journal of Economic Behavior & Organization 69(1): 27–38. Spiliopoulos, L. (2011). Neural networks as a unifying learning model for random normal form games, Adaptive Behavior 19(6): 383–408. Spiliopoulos, L. (2015). Transfer of conflict and cooperation from experienced games to new games: A connectionist model of learning, Frontiers in Neuroscience 9(102): 1–18. Stahl, D. O. (1996). Boundedly rational rule learning in a guessing game, Games and Economic Behavior 16(2): 303–330. Stahl, D. O. (1999). Evidence based rules and learning in symmetric normal-form games, International Journal of Game Theory 28(1): 111–130. Stahl, D. O. (2000). Rule learning in symmetric normal-form games: Theory and evidence, Games and Economic Behavior 32(1): 105–138. Stahl, D. O. (2001). Population rule learning in symmetric normal-form games: Theory and evidence, Journal of Economic Behavior & Organization 45(1): 19–35. Stahl, D. O. & Wilson, P. W. (1994). Experimental evidence on players’ models of other players, Journal of Economic Behavior & Organization 25(3): 309–327. Steiner, J. & Stewart, C. (2008). Contagion through learning, Theoretical Economics 3(4): 431–458. Taylor, P. D. & Jonker, L. B. (1978). Evolutionary stable strategies and game dynamics, Mathematical biosciences 40(1-2): 145–156. Van der Heijden, E. C., Nelissen, J. H., Potters, J. J. & Verbon, H. A. (1998). The poverty game and the pension game: The role of reciprocity, Journal of Economic Psychology 19(1): 5–41. Young, H. P. (1994). The evolution of conventions, Econometrica 61(1): 57–84. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/104438 |
Available Versions of this Item
-
Cold play: Learning across bimatrix games. (deposited 18 Mar 2020 07:55)
- Cold play: Learning across bimatrix games. (deposited 05 Dec 2020 13:32) [Currently Displayed]