Cognitive load in the multi-player prisoner's dilemma game: Are there brains in games?

Duffy, Sean and Smith, John (2012): Cognitive load in the multi-player prisoner's dilemma game: Are there brains in games?

Abstract

We find that differences in the ability to devote cognitive resources to a strategic interaction imply differences in strategic behavior. In our experiment, we manipulate the availability of cognitive resources by applying a differential cognitive load. In cognitive load experiments, subjects are directed to perform a task which occupies cognitive resources, in addition to making a choice in another domain. The greater the cognitive resources required for the task implies that fewer such resources will be available for deliberation on the choice. Although much is known about how subjects make decisions under a cognitive load, little is known about how this affects behavior in strategic games. We run an experiment in which subjects play a repeated multi-player prisoner's dilemma game under two cognitive load treatments. In one treatment, subjects are placed under a high cognitive load (given a 7 digit number to recall) and subjects in the other are placed under a low cognitive load (given a 2 digit number). According to two different measures, we find evidence that the low load subjects behave more strategically. First, the behavior of the low load subjects converged to the Subgame Perfect Nash Equilibrium prediction at a faster rate than the high load subjects. Second, we find evidence that low load subjects were better able to condition their behavior on the outcomes of previous periods.

• Item Type: MPRA Paper
• Language: English
• Keywords: bounded rationality; experimental economics; experimental game theory; public goods game; strategic sophistication; rational inattention
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C9 - Design of Experiments > C91 - Laboratory, Individual Behavior

References

Bajo, María T., Brañas-Garza, Pablo, Georgantzís, Nikolaos, Morales, Julia, and Parravano, Melanie (2011): "Cognitive underpinnings of behavior in the Traveler's Dilemma: Treasures and Contradictions revisited," working paper Universidad de Granada.

Ballinger, T. Parker, Hudson, Eric, Karkoviata, Leonie, and Wilcox, Nathaniel T. (2011): "Saving behavior and cognitive abilities," Experimental Economics, 14, 349--374.

Bayer, Ralph and Renou, Ludovic (2011): "Cognitive abilities and behavior in strategic-form games," working paper University of Leicester.

Béal, Sylvain (2010): "Perceptron versus automaton in the finitely repeated prisoner's dilemma," Theory and Decision, 69, 183--204.

Bednar, Jenna, Chen, Yan, Liu, Tracy Xiao, and Page, Scott (2012): "Behavioral Spillovers and Cognitive Load in Multiple Games: An Experimental Study," Games and Economic Behavior, 74(1): 12-31

Benjamin, Daniel, Brown, Sebastian, and Shapiro, Jesse (2012): "Who is 'Behavioral?' Cognitive Ability and Anomalous Preferences," Journal of the European Economic Association, forthcoming.

Ben-Ner, Avner, Kong, Fanmin and Putterman, Louis (2004): "Share and share alike? Gender-pairing, personality, and cognitive ability as determinants of giving," Journal of Economic Psychology, 25, 581--589.

Brañas-Garza, Pablo, Garcia-Muñoz, Teresa and Hernan Gonzalez, Roberto (2012): "Cognitive effort in the Beauty Contest Game," working paper Universidad de Granada.

Brañas-Garza, Pablo, Guillen, Pablo and Lopez del Paso, Rafael (2008): "Math skills and risk attitudes," Economics Letters, 99, 332--336.

Brañas-Garza, Pablo, Paz Espinosa, Maria and Rey-Biel, Pedro (2011): "Travelers' types," Journal of Economic Behavior and Organization, 78, 25--36.

Brandstätter, Hernann and Güth, Werner (2002): "Personality in Dictator and Ultimatum Games," Central European Journal of Operations Research, 10(3), 191--215.

Burks, Stephen V., Carpenter, Jeffrey P., Götte, Lorenz and Rustichini, Aldo (2009): "Cognitive Skills Explain Economic Preferences, Strategic Behavior, and Job Attachment," Proceedings of the National Academy of Sciences, 106(19), 7745--7750.

Burnham, Terence C., Cesarini, David, Johannesson, Magnus, Lichtenstein, Paul and Wallace, Björn (2009): "Higher cognitive ability is associated with lower entries in a p-beauty contest," Journal of Economic Behavior and Organization, 72, 171--175.

Camerer, Colin F., Ho, Teck-Hua, and Chong, Juin Kuan (2004): "A Cognitive Hierarchy Model of Games," Quarterly Journal of Economics, 119(3), 861--898.

Camerer, Colin F., and Hogarth, Robin M. (1999): "The effects of financial incentives in experiments: a review and capital-labor-production framework," Journal of Risk and Uncertainty, 19(1-3), 7--42.

Camerer, Colin F., Johnson, Eric J., Rymon, Talia and Sen, Sankar (1993) "Cognition and Framing in Sequential Bargaining for Gains and Losses." In Frontiers of Game Theory, ed. Ken Binmore, Alan Kirman, and Piero Tani. MIT Press, Cambridge, MA, 27--47.

Cappelletti, Dominique, Güth, Werner, and Ploner, Matteo (2011): "Being of two minds: Ultimatum offers under cognitive constraints," Journal of Economic Psychology, 32(6), 940--950.

Chen, Chia-Ching, Chiu, I-Ming, Smith, John, and Yamada, Tetsuji (2011a): "Too smart to be selfish? Measures of intelligence, social preferences, and consistency," working paper Rutgers University-Camden.

Chen, Chun-Ting, Huang, Chen-Ying and Wang, Joseph Tao-yi (2010): "A Window of Cognition: Eyetracking the Reasoning Process in Spatial Beauty Contest Games," working paper National Taiwan University.

Chen, Shu-Heng, Tai, Chung-Ching, and Yang, Lei-Xieng (2009): "Agent-Based Modeling of Cognitive Double Auction Market Experiments," working paper National Chengchi University.

Chen, Shu-Heng, Yang, Lee-Xieng, and Du, Ye-Rong (2011b): "Intelligence and Level-k Reasoning in Beauty-Contest Experiments: An Integrated Analysis," working paper National Chengchi University.

Cheremukhin, Anton, Popova, Anna and Tutino, Antonella (2012): "Rationalizing Variations in Behavioral Decisions," working paper Federal Reserve of Dallas.

Coricelli, Giorgio and Nagel, Rosemarie (2009): "Neural correlates of depth of strategic reasoning in medial prefrontal cortex," Proceeings of the National Academy of Science, 106 (23), 9163--9168.

Cornelissen, Gert , Dewitte, Siegfried, Warlop, Luk, and Yzerbyt, Vincent (2007): "Whatever people say I am, that's what I am: Social labeling as a social marketing tool," International Journal of Research in Marketing, 24, 278--288.

Cornelissen, Gert, Dewitte, Siegfried, and Warlop, Luk (2011): "Are Social Value Orientations expressed automatically? Decision making in the dictator game," Personality and Social Psychology Bulletin, 37(8), 1080--1090.

Costa-Gomes, Miguel A., Crawford, Vincent P. and Broseta, Bruno (2001): "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, 69(5), 1193--1235.

Costa-Gomes, Miguel A., and Crawford, Vincent P. (2006): "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, 96(5), 1737--1768.

Cowan, Nelson (2001): "The magical number 4 in short-term memory: A reconsideration of mental storage capacity," Behavioral and Brain Sciences, 24(1), 87--185.

Crawford, Vincent P. (2008): "Look-ups as the Windows of the Strategic Soul." In The Foundations of Positive and Normative Economics: A Handbook, ed. Andrew Caplin and Andrew Schotter. Oxford University Press: Oxford, 249--280.

Crawford, Vincent P., Costa-Gomes, Miguel A. and Iriberri, Nagore (2012): "Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications," Journal of Economic Literature, forthcoming.

Devetag, Giovanna and Warglien, Massimo (2003): "Games and phone numbers: Do short-term memory bounds affect strategic behavior?" Journal of Economic Psychology, 24, 189--202.

Dewitte, Siegfried, Pandelaere, Mario, Briers, Barbara, and Warlop, Luk (2005): "Cognitive load has negative after effects on consumer decision making," working paper Katholieke Universiteit Leuven, Belgium.

Dohmen, Thomas, Falk, Armin, Huffman, David, and Sunde, Uwe (2010): "Are Risk Aversion and Impatience Related to Cognitive Ability?" American Economic Review, 100(3), 1238--1260.

Fischbacher, Urs (2007): "z-Tree: Zurich Toolbox for Ready-made Economic Experiments," Experimental Economics, 10(2), 171--178.

Frederick, Shane (2005): "Cognitive Reflection and Decision Making," Journal of Economic Perspectives, 19(4), 25--42.

Georganas, Sotiris, Healy, Paul J., and Weber, Roberto A. (2010): "On the Persistence of Strategic Sophistication," working paper Ohio State University.

Gilbert, Daniel T., Pelham, Brett W., and Krull, Douglas S. (1988): "On Cognitive Busyness: When Person Perceivers Meet Persons Perceived," Journal of Personality and Social Psychology, 54 (5), 733--740.

Gill, David and Prowse, Victoria (2012): "Cognitive ability and learning to play equilibrium: A level-k analysis," working paper Oxford University and Cornell University.

Hauge, Karen Evelyn, Brekke, Kjell Arne, Johansson, Lars-Olof, Johansson-Stenman, Olof, and Svedsäter, Henrik (2009): "Are Social Preferences Skin Deep? Dictators under Cognitive Load," working paper University of Gothenburg.

Hinson, John M., Jameson, Tina L., and Whitney, Paul (2002): "Somatic markers, working memory, and decision making," Cognitive, Affective, and Behavioral Neuroscience, 2 (4), 341--353.

Hinson, John M., Jameson, Tina L., and Whitney, Paul (2003): "Impulsive Decision Making and Working Memory," Journal of Experimental Psychology: Learning, Memory, and Cognition, 29(2), 298--306.

Johnson, Eric J., Camerer, Colin, Sen, Sankar, and Rymon, Talia (2002): "Detecting Failures of Backward Induction Monitoring Information Search in Sequential Bargaining," Journal of Economic Theory, 104, 16--47.

Jones, Garett (2008): "Are smarter groups more cooperative? Evidence from prisoner's dilemma experiments, 1959-2003," Journal of Economic Behavior and Organization, 68, 489--497.

Jones, Matthew T. (2011): "Strategic Complexity and Cooperation: An Experimental Study," working paper Ohio State University.

Komorita, S. S., Sweeney, James, and Kravitz, David A. (1980): "Cooperative Choice in the N-Person Dilemma Situation," Journal of Personality and Social Psychology, 38 (3), 504--516.

Maćkowiak, Bartosz.and Wiederholt, Mirko (2009): "Optimal sticky prices under rational inattention," American Economic Review, 99(3), 769--803.

Miller, George (1956): "The magical number seven, plus or minus two: Some limits on our capacity for processing information," Psychological Review, 63 (2), 343--355.

Millet, Kobe and Dewitte, Siegfried (2007): "Altruistic Behavior as a Costly Signal of General Intelligence," Journal of Research in Personality, 41, 316--326.

Nagel, Rosemarie (1995): "Unraveling in Guessing Games: An Experimental Study," American Economic Review, 85(5), 1313--1326.

Neyman, Abraham (1985): "Bounded complexity justifies the cooperation in the finitely repeated prisoner's dilemma," Economic Letters, 19, 227--229.

Neyman, Abraham (1998): "Finitely repeated games with finite automata," Mathematics of Operations Research, 23, 513--552.

Oechssler, Jörg, Roider, Andreas and Schmitz, Patrick W. (2009): "Cognitive abilities and behavioral biases," Journal of Economic Behavior and Organization, 72, 147--152.

Palacios-Huerta, Ignacio (2003) "Learning to Open Monty Hall's Doors," Experimental Economics, 6(3), 235--251.

Putterman, Louis, Tyran, Jean-Robert and Kamei, Kenju (2011): "Public goods and voting on formal sanction schemes," Journal of Public Economics, 95, 1213--1222.

Reis, Ricardo (2006): "Inattentive consumers," Journal of Monetary Economics, 53, 1761--1800.

Roch, Sylvia G., Lane, John A. S., Samuelson, Charles D., Allison, Scott T. and Dent, Jennifer L. (2000): "Cognitive Load and the Equality Heuristic: A Two-Stage Model of Resource Overconsumption in Small Groups," Organizational Behavior and Human Decision Processes, 83(2), 185--212.

Rydval, Ondrej (2011): "The Causal Effect of Cognitive Abilities on Economic Behavior: Evidence from a Forecasting Task with Varying Cognitive Load," working paper CERGE-EI.

Rydval, Ondrej and Ortmann, Andreas (2004): "How financial incentives and cognitive abilities affect task performance in laboratory settings: an illustration," Economics Letters, 85, 315--320.

Savikhina, Anya and Sheremeta, Roman M. (2012): "Simultaneous Decision-Making in Competitive and Cooperative Environments," Economic Inquiry, forthcoming.

Shiv, Baba and Fedorikhin, Alexander (1999): "Heart and Mind in Conflict: The Interplay of Affect and Cognition in Consumer Decision Making," Journal of Consumer Research, 26(3), 278--292.

Sims, Christopher (2003): "Implications of Rational Inattention," Journal of Monetary Economics, 50(3), 665--690.

Stahl, Dale and Wilson, Paul (1994): "Experimental Evidence on Players' Models of Other Players," Journal of Economic Behavior and Organization, 25, 309--327.

Stahl, Dale, and Wilson, Paul (1995): "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, 10, 218--254.

Swann, William B., Hixon, Gregory, Stein-Seroussi, Alan, and Gilbert, Daniel T. (1990): "The Fleeting Gleam of Praise: Cognitive Processes Underlying Behavioral Reactions to Self-Relevant Feedback," Journal of Personality and Social Psychology, 59 (1), 17--26.

Van den Bos, Kees, Peters, Susanne L., Bobocel, D. Ramona, and Ybema, Jan Fekke (2006): "On preferences and doing the right thing: Satisfaction with advantageous inequity when cognitive processing is limited," Journal of Experimental Social Psychology, 42, 273--289.

Wang, Joseph Tao-yi, Spezio, Michael and Camerer, Colin F. (2010): "Pinocchio's Pupil: Using Eyetracking and Pupil Dilation To Understand Truth Telling and Deception in Sender-Receiver Games," American Economic Review, 100(3), 984--1007.

Ward, Andrew and Mann, Traci (2000): "Don't Mind If I Do: Disinhibited Eating Under Cognitive Load," Journal of Personality and Social Psychology, 78 (4), 753--763.

Wiederholt, Mirko (2010): "Rational Inattention," In The New Palgrave Dictionary of Economics, Online Edition, (Eds.) Steven Durlauf and Lawrence Blume, Palgrave Macmillan.