Abstract
We experimentally investigate the disposition of decision makers to use case-based reasoning as suggested by Hume (An enquiry concerning human understanding, 1748) and formalized by case-based decision theory (Gilboa and Schmeidler in Q J Econ 110:605–639, 1995). Our subjects face a monopoly decision problem about which they have very limited information. Information is presented in a manner which makes similarity judgements according to the feature matching model of Tversky (Psychol Rev 84:327–352, 1977) plausible. We provide subjects a “history” of cases. In the \(2\times 2\) between-subject design, we vary whether information about the current market is given and whether immediate feedback about obtained profits is provided. The results provide support for the predictions of case-based decision theory, particularly when no immediate feedback is provided.
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Notes
For a formal relation between expected utility theory and CBDT see Matsui (2000).
For a version of case-based decision theory that allows the agent to use such information, see Gilboa and Schmeidler (1997).
CBDT usually does not make any distinction between an action that resulted in zero utility and one that simply was not chosen, since zero utility is typically taken as the default aspiration level.
In such a scenario a case-based DM is assumed to randomly choose an action from the set of available actions that have not yet been chosen.
In particular, several of the properties of the geometric models are consistently violated by experimental subjects. First, it has been shown that the identity property does not hold, i.e. subjects do not always perceive an object as identical to itself (see Podgorny and Garner 1979). Second, actual similarity evaluations are not always symmetric (see Holyoak and Gordon 1983; and Ortony et al. 1985). For instance, a subject reporting that domestic cats are very similar to tigers does not necessarily indicate that the same subject will report that tigers are very similar to domestic cats. Lastly, the triangle inequality often does not hold, nor does transitivity (Tversky and Gati 1982). Finding objects \(A\) and \(B\) very similar and objects \(B\) and \(C\) very similar does not necessarily indicate that the subject will find objects \(A\) and \(C\) very similar.
If one only knows if attributes are equal or not, one can represent it as the “city block” distance in a model where the new attribute \(a_{ij}\) is an indicator of the old attribute \(b_{i}\) and takes the value \(v_{i}\). This is standard encoding of qualitative variables as indicator ones in econometrics.
We chose to work in a framework where a DM never encounters the same problem twice. CBDT can, however, be modified to study choices in repeated decision problems (see, e.g., Gilboa and Schmeidler 2001).
See Appendix 1 for a full set of the instructions.
We used a square, a triangle and a circle. To distinguish shapes easier, we colored them. Squares were always green, triangles blue and circles orange. Since the experimental interface included geometric forms and colors, we asked participants after the experiment how they interpreted those. In particular, participants were asked: “If it were the case that the three symbols you saw during the experiment [symbols again given here] stood for high, medium and low, which symbol would you think stood for which level?” We found no correlation between any symbol and level.
The market conditions displayed in the hypothetical scenarios are the same as those given in the marketing report so that similarity comparisons could be made between them.
To ensure comparability across treatments, the subjects faced the same payoffs function in the same order.
An example of a payoff function is \(\pi (.)=50q-0.009(3C_{1}C_{2}-C_{3}C_{4})q^{2}-1150\ln (q-48)\), where \(q\) is the quantity chosen and \(C_{i}\) indicates market condition \(i\).
Sessions varied in size from 4 to 18 participants.
The relatively coarse and simplified version of the feature based similarity function that we employ makes the same predictions as a more generalized similarity function used by Gilboa et al. (2006) in all but one market.
Note that subjects did not even know the range of payoffs. Any judgement regarding the satisfaction through the evaluation of obtained payoffs is highly subjective.
For the non-parametric tests used in this paper see Siegel and Castellan (1998).
For a first analysis we assume that the aspiration level of a case-based decision maker is zero. This aspiration level can be easily adapted as we discuss in section 6.2.
Such a calculation would lead to a MSD of 0.75. In general, the calculation of MSDs favors probabilistic models over point predictions (see Selten 1998 for an axiomatization of quadratic scoring rules).
Choices predicted by CBDT are different from those predicted by MAX in all but seven markets. Note that if only the rank of profit were available instead of the exact profit, then the results should not change according to the MAX heuristic. Since the focus of this paper is not the MAX heuristic, we do not vary the design to investigate its robustness.
As suggested by Karl Schlag, an alternative rule of thumb could be to prioritize similarity, i.e., choose the production value whose scenario has the most features in common with the current report (as long as its profit is positive). If there are more than one of those production values, choose the one with the highest profit from this set. If the production value whose scenario has the highest number of features in common with the current report has a negative profit associated with it, choose the one that has the next highest number of features in common. Again, if there are more of those, choose the one that has the highest profit associated with it. In our experimental setup predicted choices of such a heuristic coincide with predicted choices of CBDT in all but three markets. We therefore do not separately analyze its predictive power.
The specific test statistic is \(z=(p_{1}-p_{2})/S_{p_{c}}\), where \(p_{i}\) is the proportion in subsample \(i\), and \(S_{p_{c}}=\sqrt{p_{c}(1-p_{c})(\frac{1 }{N_{1}}+\frac{1}{N_{2}})} \) is an estimate of the standard error of the difference in proportions, \(p_{1}-p_{2}\). \(p_{c}\) is an estimate of the population proportion under the null hypothesis of equal proportions, \( p_{c}=(p_{1}N_{1}+p_{2}N_{2})/(N_{1}+N_{2})\), where \(N_{i}\) is the total number of subjects in subsample \(i\) (see Glasnapp and Poggio 1985).
Each subject is characterized by one number that corresponds to how many of her observed choices coincide with theoretically predicted choices.
These percentages are 100 % minus the percentage that is found at the intersection of the solid line with the vertical line at 1/4.
Given that our paper aims at explaining individual behavior, we do not simulate a probabilistic reinforcement learning model (e.g., Roth and Erev 1995) which would either lead to comparing choices with a probability vector or analyzing population means.
Given that there is not much variance in individual MSDs, we determine overall performance by calculating the average MSD for each treatment. Interestingly, when no current information is given, the model that fits “best” gives a weight of 0.1 to the obtained payoff independent of whether immediate feedback is given or not. Behavior seems quite “backward” looking. When current information is given, 0.2 returns the lowest average MSD when immediate feedback is given. However, when feedback is delayed the lowest average MSD is obtained with a weight of 0.9.
References
Fischbacher, U. (2007). z-Tree—Zurich toolbox for readymade economic experiments: Experimenter’s manual. Experimental Economics, 10(2), 171–178.
Gayer, G., Gilboa, I., & Lieberman, O. (2007). Rule-based and case-based reasoning in housing prices. The BE Journals in Theoretical Economics, 7(1), 1–37.
Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103, 650–669.
Gilboa, I., & Schmeidler, D. (1995). Case-Based Decision Theory. Quarterly Journal of Economics, 110, 605–639.
Gilboa, I., & Schmeidler, D. (1997). Act similarity in case based decision theory. Economic Theory, 9, 47–61.
Gilboa, I., & Schmeidler, D. (2001). A theory of case-based decisions. Cambridge: Cambridge university press.
Gilboa, I., Liebermann, O., & Schmeidler, D. (2006). Empirical Similarity. The Review of Economics and Statistics, 88, 433–444.
Glasnapp, D., & Poggio, J. (1985). Essentials of statistical analysis for the behavioral sciences. Columbus: Merrill.
Goldstone, R. L., & Son, J. (2005). Similarity. In K. Holyoak & R. Morrison (Eds.), Cambridge handbook of thinking and reasoning (pp. 13–36). Cambridge: Cambridge University Press.
Guerdjikova, A. (2002). Case-based decision theory—an application for the financial markets. New York: Mimeo.
Guerdjikova, A. (2003). On the definition and existence of an equilibrium in a financial market with case-based decision makers. New York: Mimeo.
Holyoak, K. J., & Gordon, P. C. (1983). Social reference points. Journal of Personality and Social Psychology, 44, 881–887.
Hume, D. (1748). An enquiry concerning human understanding. Peterborough, ON: Broadview Press. Retrieved from http://eserver.org/18th/hume-enquiry.html.
Jahnke, H., Chwolka, A., & Simons, D. (2005). Coordinating service-sensitive demand and capacity by adaptive decision making: An application of case-based decision theory. Decision Sciences, 36, 1–32.
Matsui, A. (2000). Expected utility and case based reasoning. Mathematical Social Sciences, 39, 1–12.
Ortony, A., Vondruska, R., Foss, M., & Jones, L. (1985). Salience, similes, and the asymmetry of similarity. Journal of Memory and Language, 24, 569–594.
Ossadnik, W., Wilmsmann, D., & Niemann, B. (2013). Experimental evidence on case-based decision theory. Theory and Decision, 75(2), 211–232.
Podgorny, P., & Garner, W. R. (1979). Reaction time as a measure of inter- and intraobject visual similarity: Letters of the alphabet. Perception & Psychophysics, 26, 37–52.
Polya, G. (1954). Mathematics and plausible reasoning, vol. 1: induction and analogy in mathematics. Princeton, NJ: Princeton University Press.
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, 164–212.
Rubinstein, A. (1988). Similarity in decision making under risk (is there a utility resolution to the allais paradox ?). Journal of Economic Theory, 46, 145–153.
Sarin, R., & Vahid, F. (1999). Payoff assessments without probabilities: A simple dynamic model of choice. Games and Economic Behavior, 28, 294–309.
Sarin, R., & Vahid, F. (2004). Strategy similarity and coordination. The Economic Journal, 114, 506–527.
Selten, R. (1998). Axiomatic characterization of the quadratic scoring rule. Experimental Economics, 1, 43–62.
Siegel, S., & Castellan, N. J, Jr. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.). New York: McGraw-Hill Book Company.
Simon, H. A. (1955). A behavioral model of rational choice. Quarterly Journal of Economics, 69, 99–118.
Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327–352.
Tversky, A., & Gati, I. (1982). Similarity, separability, and the triangle inequality. Psychological Review, 89, 123–154.
Acknowledgments
We thank Gerd Gigerenzer and the audiences at the Max Planck Institute for Human Development, the Department of Economics at Texas A&M, the ESA meetings in Atlanta, Rome and Tucson and the Second Santa Barbara Workshop in Experimental Economics for helpful suggestions and discussions. Financial support from the Department of Economics and the Melbern G. Glasscock Center for Humanities Research at Texas A&M and the NSF is gratefully acknowledged.
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Appendices
Appendix 1: Instructions
This is an experiment in the economics of decision making. Texas A&M University has provided funds for this research. If you follow the instructions and make good decisions, you can earn an appreciable amount of money. At the end of today’s session, you will be paid your earnings in private and in cash.
It is important that you remain silent and do not look at other people’s work. If you have any questions, or need assistance of any kind, please raise your hand and an experimenter will come to you. If you talk, laugh, exclaim out loud, etc. you will be asked to leave and you will not be paid. We expect and appreciate your cooperation.
During this session you will be acting as a firm who is selling a good. You will be selling your good to 30 independent markets. You can think of these as 30 geographically separated islands. In each of the 30 markets (islands) you are the only seller of the good. This means that nothing any other seller or firm does can affect you or your market. Each period represents a new market and you will have to make a decision about how many units you want to produce for that market. It is costly to produce this good and if you produce units that do not get sold in that market, you will not be able to keep those units for use in other markets. At the end of each period you will earn profits on the units of your good that you do sell in that market.
At the beginning of each period you will receive a marketing report that contains information regarding some market conditions for the current market. You can think of this as information about the market that has been gathered for you by the marketing department of your firm. Gathering this data is costly to your firm, as such your marketing department is not able to gather all information in every market. Therefore, the information that your marketing department does collect can vary from market to market. However, nothing you or anyone else does can change what information is gathered in any market.
After gathering the data the marketing department sends it to you. Unfortunately there is an error that occurs during that transmission. Instead of receiving the actual data all you receive is a list of the market conditions that were collected and a table of symbols representing the actual data. Fortunately the error is consistent. This means that identical symbols for a given market condition represent the same actual data. For instance, if the marketing department gathers data that says median income is $35,000 and a blue triangle gets transmitted, then whenever the marketing department reports $35,000 for median income it will be transmitted as a blue triangle in the marketing report. However, a blue triangle can also appear for other market conditions, where it does not necessarily stand for $35,000. For example, if the marketing department gathers data on a high inflation rate and this information gets transmitted as a blue triangle, then all marketing reports with a high inflation rate will have a blue triangle in the table for inflation rate.
After you have received the current marketing report you will be asked to choose a production Value of 50, 100, 150, or 200 units. Your profits each period depend on your production value and may also depend upon some of the market conditions. After you have made your production choice, you will be informed of your profits for that market. You will then proceed to the next market where you will be given the new market’s current marketing report. You will then be asked to choose a production value for that market. The session will continue in this manner until you have made production choices for 30 markets.
In order to help you with your decisions, for each market the experimenter has included four different scenarios. In each of these scenarios the experimenter was given a marketing report similar to the marketing reports that you will be given. The experimenter then chose a production value in such a manner that each of the four production choices was chosen once. The Profits reported in these scenarios are the profits that would have been earned in that market given the reported market conditions and the chosen production value. The profits reported in these scenarios will not be included in your total profits. Your total profits consist only of those profits that you earn during the session, i.e. when you are making the production decision. Your total profits will be calculated by simply adding up the profits you earn in each of your markets.
Figure 1 gives an example of the decision screen. At the top right of the screen you will see labeled the current market. At the bottom right of the screen you will see your total profits, which will include all profits you have earned so far. On the left side of the screen you will also see a table with the four scenarios for the current market. In the first column from the left you will see labels for the market conditions, the production values, and profits. So in this market, your marketing department has gathered information on: the tourist population, the wind, the humidity, the UV factor, and the temperature. Looking at the symbols in the table you can see that there is a blue triangle for tourist population in scenario 1 and scenario 2. This means that the Tourist Population was the same in both of these scenarios. You can also see that there is a blue triangle for Humidity in scenario 3. While this is the same symbol that was present in scenarios 1 and 2 for the tourist population, it does not necessarily represent the same thing that it did for tourist population. Below the scenarios you will see the production values and profits for those scenarios. Again, the production values were chosen so that each value was chosen exactly once. The profits that you see are the profits that would have been earned had the given production value been chosen with the given scenario. On the right side of the screen you will see the Marketing Report for the current market, in the left hand column are the symbols representing the data from the report and in the right hand column are the labels for the different market conditions that are reported. On the bottom of the screen you will see the menu of choices for your production value.
In order to select a production value simply use your mouse to click in the circle to the left of the value you wish to choose. After clicking in one of the circles you must click the confirm button before your choice will be submitted. If you wish to change your choice you may do so at any time before clicking the confirm button. You may change your choice of production value as many times as you wish. However, once you have clicked the confirm button you will NOT be able to change your production value for the current market. After you have clicked confirm a results screen will appear and inform you of your profits for the current market. Once you have finished viewing these results click continue to move on. After you have clicked continue, you will proceed to the next market where you will be given the new market’s marketing reports and asked to make a production choice for that market.
After you have made production choices for 30 markets the session will be over. A screen will appear informing you of your total profits and total earnings. Your total earnings are the amount you will be paid in cash. Your total earnings are calculated by dividing your total profits by 6000. In other words for every $6000 in Profits that you made you will earn $1.00 in cash. For instance, if you earn a total profit of $96,000 then your total earnings will be $16. If you did not choose to receive a hang tag for parking then you will receive a $5.00 show-up fee in addition to your total earnings. In that case your total payment will be calculated by adding the $5.00 show-up fee to your total earnings. So in the above example your total payment would be $16.00 + $5.00 or $21.00 in cash. However, if you did choose to take a hang tag for parking your total payment will be the same as your total earnings. Once the session is over and everyone has viewed their total earnings you will be called up, one at a time, to be paid privately and in cash. The session will not be finished until everyone has made decisions for all 30 of their markets. After you have finished please wait patiently for all remaining markets to finish.
Appendix 2: Individual data
Appendix 3: More screenshots
Screenshot for immediate with current treatment
Screenshot for delayed without current treatment
Screenshot for immediate without current treatment
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Grosskopf, B., Sarin, R. & Watson, E. An experiment on case-based decision making. Theory Decis 79, 639–666 (2015). https://doi.org/10.1007/s11238-015-9492-1
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DOI: https://doi.org/10.1007/s11238-015-9492-1