Modeling choice and estimating utility in simple experimental games

Breitmoser, Yves (2012): Modeling choice and estimating utility in simple experimental games.

Abstract

Current experimental research seeks to estimate shape and parameterization of utility functions. The underlying experimental games tend to be "simple" in that best responses are salient and individual choices consistent, but the analyses arrive at diverging results. I analyze how precision of estimation and robustness of results depend on the choice models used in the analysis. Analyzing dictator and public goods games, I find that regression models overfit drastically when choices exhibit high precision (dictator games), that structural models with simple error structure (normal or extreme value) do not fit the curvature, and that random behavior and random taste models do not identify social motives robustly. The choice process is captured well through the random utility model for ordered alternatives ("ordered GEV", Small, 1987).

• Item Type: MPRA Paper
• Language: English
• Keywords: choice models; utility function; estimation; cross validation; dictator game; public goods game
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C50 - General; D - Microeconomics > D6 - Welfare Economics > D64 - Altruism ; Philanthropy; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Amemiya, T. (1978). On a two-step estimation of a multivariate logit model. Journal of Econometrics, 8(1):13–21.

Anderson, S. and De Palma, A. (1992). Multiproduct firms: a nested logit approach. The Journal of Industrial Economics, pages 261–276.

Anderson, S., Goeree, J., and Holt, C. (1998). A theoretical analysis of altruism and decision error in public goods games. Journal of Public Economics, 70(2):297–323.

Anderson, S., Goeree, J., and Holt, C. (2001). Minimum-effort coordination games: Stochastic potential and logit equilibrium. Games and Economic Behavior, 34(2):177–199.

Anderson, S., Goeree, J., and Holt, C. (2002). The logit equilibrium: A perspective on intuitive behavioral anomalies. Southern Economic Journal, 69(1):21–47.

Andreoni, J. (1995a). Cooperation in public-goods experiments: Kindness or confusion? American Economic Review, 85(4):891–904.

Andreoni, J. (1995b). Warm-glow versus cold-prickle: The effects of positive and negative framing on cooperation in experiments. The Quarterly Journal of Economics, 110(1):1–21.

Andreoni, J. and Miller, J. (2002). Giving according to GARP: An experimental test of the consistency of preferences for altruism. Econometrica, 70(2):737–753.

Andreoni, J. and Scholz, J. (1998). An econometric analysis of charitable giving with interdependent preferences. Economic Inquiry, 36(3):410–428.

Arcidiacono, P. and Jones, J. (2003). Finite mixture distributions, sequential likelihood and the em algorithm. Econometrica, 71(3):933–946.

Auger, A., Hansen, N., Perez Zerpa, J., Ros, R., and Schoenauer, M. (2009). Experimental comparisons of derivative free optimization algorithms. Experimental Algorithms, pages 3–15.

Auten, G., Sieg, H., and Clotfelter, C. (2002). Charitable giving, income, and taxes: an analysis of panel data. American Economic Review, 92(1):371–382.

Bakija, J. and Heim, B. (2011). How does charitable giving respond to incentives and income? new estimates from panel data. National Tax Journal, 64(2):615–50.

Bardsley, N. and Moffatt, P. (2007). The experimetrics of public goods: Inferring motivations from contributions. Theory and Decision, 62(2):161–193.

Battalio, R., Samuelson, L., and Huyck, J. (2001). Optimization incentives and coordination failure in laboratory stag hunt games. Econometrica, 69(3):749–764.

Biernacki, C., Celeux, G., and Govaert, G. (1999). An improvement of the nec criterion for assessing the number of clusters in a mixture model. Pattern Recognition Letters, 20(3):267–272.

Biernacki, C., Celeux, G., and Govaert, G. (2000). Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(7):719–725.

Blanco, M., Engelmann, D., and Normann, H. T. (2011). A within-subject analysis of other-regarding preferences. Games and Economic Behavior, 72(2):321–338.

Breitmoser, Y. (2012). Strategic reasoning in p-beauty contests. Games and Economic Behavior (in press).

Bruhin, A., Fehr-Duda, H., and Epper, T. (2010). Risk and rationality: Uncovering heterogeneity in probability distortion. Econometrica, 78(4):1375–1412.

Burman, P. (1989). A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods. Biometrika, 76(3):503.

Camerer, C. (2003). Behavioral game theory: Experiments in strategic interaction. Princeton, NJ: Princeton University Press.

Cappelen, A., Hole, A., Sørensen, E., and Tungodden, B. (2007). The pluralism of fairness ideals: An experimental approach. American Economic Review, 97(3):818–827.

Cappelen, A., Hole, A., Sørensen, E., and Tungodden, B. (2010a). Modeling individual choices in experiments: Random utility versus random behavior. Working paper.

Cappelen, A., Moene, K., Sørensen, E., and Tungodden, B. (2011). Needs vs entitlements: an international fairness experiment. Journal of the European Economic Association.

Cappelen, A., Sørensen, E., and Tungodden, B. (2010b). Responsibility for what? Fairness and individual responsibility. European Economic Review, 54(3):429–441.

Card, D., DellaVigna, S., and Malmendier, U. (2011). The role of theory in field experiments. The Journal of Economic Perspectives, 25(3):39–62.

Choi, S., Gale, D., and Kariv, S. (2008). Sequential equilibrium in monotone games: A theory-based analysis of experimental data. Journal of Economic Theory, 143(1):302–330.

Conte, A., Hey, J., and Moffatt, P. (2011). Mixture models of choice under risk. Journal of Econometrics, 162(1):79–88.

Conte, A. and Moffatt, P. (2009). The pluralism of fairness ideals: a comment. Working paper.

Conte, A. and Moffatt, P. (2010). The econometric modelling of social preferences. Jena Economic Research Papers No. 2010-042.

Costa-Gomes, M., Crawford, V., and Iriberri, N. (2009). Comparing models of strategic thinking in Van Huyck, Battalio, and Beil’s coordination games. Journal of the European Economic Association, 7(2-3):365–376.

Cox, J., Friedman, D., and Gjerstad, S. (2007). A tractable model of reciprocity and fairness. Games and Economic Behavior, 59(1):17–45.

Crawford, V. and Iriberri, N. (2007a). Fatal attraction: Salience, naivete, and sophistication in experimental "hide-and-seek" games. American Economic Review, 97(5):1731–1750.

Crawford, V. and Iriberri, N. (2007b). Level-k auctions: Can a nonequilibrium model of strategic thinking explain the winner’s curse and overbidding in private-value auctions? Econometrica, 75(6):1721–1770.

Fischbacher, U., Gächter, S., and Fehr, E. (2001). Are people conditionally cooperative? Evidence from a public goods experiment. Economics Letters, 71(3):397–404.

Fisman, R., Kariv, S., and Markovits, D. (2007). Individual preferences for giving. American Economic Review, 97(5):1858–1876.

Forsythe, R., Horowitz, J., Savin, N., and Sefton, M. (1994). Fairness in simple bargaining experiments. Games and Economic Behavior, 6(3):347–369.

Goeree, J. and Holt, C. (2004). A model of noisy introspection. Games and Economic Behavior, 46(2):365–382.

Goeree, J., Holt, C., and Laury, S. (2002). Private costs and public benefits: Unraveling the effects of altruism and noisy behavior. Journal of Public Economics, 83(2):255–276.

Hansen, N. and Kern, S. (2004). Evaluating the cma evolution strategy on multimodal test functions. Parallel Problem Solving from NaturePPSN VIII, 3242(x):282–291.

Hansen, N., Müller, S., and Koumoutsakos, P. (2003). Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (cmaes). Evolutionary Computation, 11(1):1–18.

Harrison, G. and Rutström, E. (2009). Expected utility theory and prospect theory: One wedding and a decent funeral. Experimental Economics, 12(2):133–158.

Hey, J. (2005). Why we should not be silent about noise. Experimental Economics, 8(4):325–345.

Hey, J., Lotito, G., and Maffioletti, A. (2010). The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity. Journal of risk and uncertainty, 41(2):81–111.

Hoffman, E., McCabe, K., Shachat, K., and Smith, V. (1994). Preferences, property rights, and anonymity in bargaining games. Games and Economic Behavior, 7(3):346–380.

Keane, M. (2010a). A structural perspective on the experimentalist school. Journal of Economic Perspectives, 24(2):47–58.

Keane, M. and Wolpin, K. (2007). Exploring the usefulness of a nonrandom holdout sample for model validation: Welfare effects on female behavior. International Economic Review, 48(4):1351–1378.

Keane, M. P. (2010b). Structural vs. atheoretic approaches to econometrics. Journal of Econometrics, 156(1):3–20.

Keser, C. and van Winden, F. (2000). Conditional cooperation and voluntary contributions to public goods. Scandinavian Journal of Economics, 102(1):23–39.

Kübler, D. and Weizsäcker, G. (2004). Limited depth of reasoning and failure of cascade formation in the laboratory. Review of Economic Studies, 71(2):425–441.

Kübler, D. and Weizsäcker, G. (2005). Are longer cascades more stable? Journal of the European Economic Association, 3(2-3):330–339.

Lee, B. (1999). Calling patterns and usage of residential toll service under self selecting tariffs. Journal of Regulatory economics, 16(1):45–82.

Levine, D. (1998). Modeling altruism and spitefulness in experiments. Review of Economic Dynamics, 1(3):593–622.

Loomes, G. (2005). Modelling the stochastic component of behaviour in experiments: Some issues for the interpretation of data. Experimental Economics, 8(4):301–323.

Luce, R. (1959). Individual choice behavior. Wiley New York.

McFadden, D. (1973). Conditional logit analysis of qualitative choice models. Frontiers of Econometrics, ed. P. Zarembka. New York: Academic Press, pages 105–142.

McFadden, D. (1976). Quantal choice analysis: A survey. Annals of Economic and Social Measurement, 5(4):363–390.

McFadden, D. (1978). Modelling the choice of residential location. In Karlqvist, A., Lundqvist, L., Snickars, F., and Weibull, J., editors, Spatial interaction theory and planning models, pages 75–96. North Holland, Amsterdam.

McFadden, D. (1981). Econometric models of probabilistic choice. In Manski, C. and McFadden, D., editors, Structural analysis of discrete data with econometric applications, pages 198–274. MIT Press, Cambridge.

McKelvey, R. and Palfrey, T. (1995). Quantal response equilibria for normal form games. Games and Economic Behavior, 10(1):6–38.

McLachlan, G. and Peel, D. (2000). Finite Mixture Models. Wiley series in probability and statistics.

Moré, J. and Wild, S. (2009). Benchmarking derivative-free optimization algorithms. SIAM Journal on Optimization, 20(1):172–191.

Myatt, D. and Wallace, C. (2008). An evolutionary analysis of the volunteer’s dilemma. Games and Economic Behavior, 62(1):67–76.

Nevo, A. and Whinston, M. (2010). Taking the dogma out of econometrics: Structural modeling and credible inference. The Journal of Economic Perspectives, 24(2):69–81.

Offerman, T., Schram, A., and Sonnemans, J. (1998). Quantal response models in step-level public good games. European Journal of Political Economy, 14(1):89–100.

Payne, A. (1998). Does the government crowd-out private donations? new evidence from a sample of non-profit firms. Journal of Public Economics, 69(3):323–345.

Powell, M. (2008). Developments of newuoa for minimization without derivatives. IMA journal of numerical analysis, 28(4):649.

Rabin, M. (1993). Incorporating fairness into game theory and economics. American Economic Review, 83(5):1281–1302.

Rosenthal, R. (1989). A bounded-rationality approach to the study of noncooperative games. International Journal of Game Theory, 18(3):273–292.

Rust, J. (2010). Comments on: "structural vs. atheoretic approaches to econometrics" by Michael Keane. Journal of Econometrics, 156(1):21–24.

Samuelson, L. (1985). On the independence from irrelevant alternatives in proba- bilistic choice models. Journal of Economic Theory, 35(2):376–389.

Schokkaert, E. (2006). The empirical analysis of transfer motives. Handbook on the Economics of Giving, Reciprocity and Altruism, 1:127–181.

Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2):461–464.

Small, K. (1987). A discrete choice model for ordered alternatives. Econometrica, 55(2):409–424.

Small, K. (1994). Approximate generalized extreme value models of discrete choice. Journal of Econometrics, 62(2):351–382.

Smyth, P. (2000). Model selection for probabilistic clustering using cross-validated likelihood. Statistics and Computing, 10(1):63–72.

Stahl, D. and Wilson, P. (1995). On players’ models of other players: Theory and experimental evidence. Games and Economic Behavior, 10(1):218–254.

Train, K. (2003). Discrete choice methods with simulation. Cambridge Univ Pr.

Train, K., McFadden, D., and Ben-Akiva, M. (1987). The demand for local telephone service: A fully discrete model of residential calling patterns and service choices. Rand Journal of Economics, pages 109–123.

Turocy, T. (2005). A dynamic homotopy interpretation of the logistic quantal response equilibrium correspondence. Games and Economic Behavior, 51(2):243–263.

Tversky, A. (1972). Elimination by aspects: A theory of choice. Psychological Review, 79(4):281–299.

Vovsha, P. (1997). Application of cross-nested logit model to mode choice in Tel Aviv, Israel, metropolitan area. Transportation Research Record, 1607(-1):6–15.

Vuong, Q. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57(2):307–333.

Wakker, P. (2010). Prospect theory: For risk and ambiguity. Cambridge Univ Pr.

Whitten, G. and Palmer, H. (1996). Heightening comparativists’ concern for model choice: Voting behavior in great britain and the netherlands. American Journal of Political Science, 40(1):231–260.

Wilcox, N. (2008). Stochastic models for binary discrete choice under risk: A critical primer and econometric comparison. Risk aversion in experiments, 12:197–292.

Wilcox, N. (2011). Stochastically more risk averse: A contextual theory of stochastic discrete choice under risk. Journal of Econometrics, 162(1):89–104.

Willinger, M. and Ziegelmeyer, A. (2001). Strength of the social dilemma in a public goods experiment: An exploration of the error hypothesis. Experimental Economics, 4(2):131–144.

Yi, K. (2003). A quantal response equilibrium model of order-statistic games. Journal of Economic Behavior and Organization, 51(3):413–425.

Zhang, P. (1993). Model selection via multifold cross validation. Annals of Statistics, 21(1):299–313.