Estimating the Experience-Weighted Attractions for the Migration-Emission Game
Author(s)
Michinori Uwasu*
Affiliation(s)
Center for Environmental Innovation Design for Sustainability, Osaka University, Osaka, Japan.
Center for Environmental Innovation Design for Sustainability, Osaka University, Osaka, Japan.
ABSTRACT
Players are unlikely to immediately play equilibrium strategies in complicated games or in games in which they do not have much experience playing. In these cases, players will need to learn to play equilibrium strategies. In laboratory experiments, subjects show systematic patterns of learning during a game. In psychological and economic models of learning, players tend to play a strategy more if it has been successful in the past (reinforcement learning) or that would have given higher payoffs given the strategies of other players (belief learning). This paper uses experimental data from the four sessions of a pilot experiment of a three-stage emission game to estimate parameters of experience-weighted-attraction (EWA) learning, which is a hybrid of reinforcement and belief learning models. In this estimation, we transform the strategy space for the three-stage game extensive form game to a normal form game. This paper also considers asymmetric information across players in estimating EWA parameters. In three of the four sessions, estimated parameters are consistent with reinforcement learning, which means that players tend to choose to strategies looking at past strategies that are more successful than the others. In the other session, estimated parameters are consistent with belief learning, which means that players consider forgone payoffs to update their beliefs that determine the probability of strategy choice.
Players are unlikely to immediately play equilibrium strategies in complicated games or in games in which they do not have much experience playing. In these cases, players will need to learn to play equilibrium strategies. In laboratory experiments, subjects show systematic patterns of learning during a game. In psychological and economic models of learning, players tend to play a strategy more if it has been successful in the past (reinforcement learning) or that would have given higher payoffs given the strategies of other players (belief learning). This paper uses experimental data from the four sessions of a pilot experiment of a three-stage emission game to estimate parameters of experience-weighted-attraction (EWA) learning, which is a hybrid of reinforcement and belief learning models. In this estimation, we transform the strategy space for the three-stage game extensive form game to a normal form game. This paper also considers asymmetric information across players in estimating EWA parameters. In three of the four sessions, estimated parameters are consistent with reinforcement learning, which means that players tend to choose to strategies looking at past strategies that are more successful than the others. In the other session, estimated parameters are consistent with belief learning, which means that players consider forgone payoffs to update their beliefs that determine the probability of strategy choice.
Cite this paper
M. Uwasu, "Estimating the Experience-Weighted Attractions for the Migration-Emission Game," Theoretical Economics Letters, Vol. 2 No. 5, 2012, pp. 494-501. doi: 10.4236/tel.2012.25092.
M. Uwasu, "Estimating the Experience-Weighted Attractions for the Migration-Emission Game," Theoretical Economics Letters, Vol. 2 No. 5, 2012, pp. 494-501. doi: 10.4236/tel.2012.25092.
References
[1] A. E. Roth and E. Ido, “Learning in Extensive Form Games: Experimental Data and Simple Dynamic Modelsin the Intermediate Term,” Games and Economic Behavior, Vol. 8, No. 1, 1995, pp. 164-212. doi:10.1016/S0899-8256(05)80020-X [2] T. H. Ho and K. Weigelt, “Task Complexity, Equilibrium Selection, and Learning: An Experimental Study,” Management Science, Vol. 42, No. 5, 1996, pp. 659-679. doi:10.1287/mnsc.42.5.659 [3] C. Camerer and T. H. Ho, “Experienced-Weighted Attraction Learning in Normal Form Games,” Econometrica, Vol. 67, No. 4, 1999, pp. 827-874. doi:10.1111/1468-0262.00054 [4] M. Uwasu, “Essays on Environmental Cooperation,” Dissertation Thesis, University of Minnesota, Minnesota, 2008. [5] C. Camerer, “Behavioral Game Theory: Experiments in Strategic Interaction,” Princeton University Press, Princeton, 2003. [6] R. M. Isaac, K. McCue and C. Plott, “Public Goods Provision in an Experimental Environment,” Journal of Public Economics, Vol. 26, No. 1, 1985, pp. 51-74. doi:10.1016/0047-2727(85)90038-6 [7] J. Brown-Kruse and D. Hummels, “Gender Effects in Laboratory Public Goods Contribution: Do Individuals Put Their Money Where Their Mouth Is?” Journal of Economic Behavior and Organization, Vol. 22, No. 3, 1993, pp. 255-267. doi:10.1016/0167-2681(93)90001-6
[1] A. E. Roth and E. Ido, “Learning in Extensive Form Games: Experimental Data and Simple Dynamic Modelsin the Intermediate Term,” Games and Economic Behavior, Vol. 8, No. 1, 1995, pp. 164-212. doi:10.1016/S0899-8256(05)80020-X [2] T. H. Ho and K. Weigelt, “Task Complexity, Equilibrium Selection, and Learning: An Experimental Study,” Management Science, Vol. 42, No. 5, 1996, pp. 659-679. doi:10.1287/mnsc.42.5.659 [3] C. Camerer and T. H. Ho, “Experienced-Weighted Attraction Learning in Normal Form Games,” Econometrica, Vol. 67, No. 4, 1999, pp. 827-874. doi:10.1111/1468-0262.00054 [4] M. Uwasu, “Essays on Environmental Cooperation,” Dissertation Thesis, University of Minnesota, Minnesota, 2008. [5] C. Camerer, “Behavioral Game Theory: Experiments in Strategic Interaction,” Princeton University Press, Princeton, 2003. [6] R. M. Isaac, K. McCue and C. Plott, “Public Goods Provision in an Experimental Environment,” Journal of Public Economics, Vol. 26, No. 1, 1985, pp. 51-74. doi:10.1016/0047-2727(85)90038-6 [7] J. Brown-Kruse and D. Hummels, “Gender Effects in Laboratory Public Goods Contribution: Do Individuals Put Their Money Where Their Mouth Is?” Journal of Economic Behavior and Organization, Vol. 22, No. 3, 1993, pp. 255-267. doi:10.1016/0167-2681(93)90001-6