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Assessing Mental Models via Recording Decision Deliberations of Pairs

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Abstract

In our paper, we aim at assessing the most crucial cognitive step in forward looking decision deliberation, the mental representation of a decision task. Rather than discussing it abstractly, we study mental representation experimentally with pairs of participants deciding together and the discussion preceding their choice being video-/audiotaped. We experimentally implement two tasks: one without social and strategic interaction (the risky choice task) and one with strategic interaction (the outside option game). The videotaped discussions are analyzed assessing which mental models are mentioned by one or both participants in a pair and how decisive such arguments are for the final decision. Pairs of participants are categorized by their mental constellation and their choices in both tasks. This hopefully allows for better explanations, especially of heterogeneity in reasoning styles and choice behavior with and without strategic interaction.

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Notes

  1. Experimental evidence questioning binary-lottery incentives (see Selten et al. 1999), which require only these two assumptions, questions expected utility theory in general. Maintaining expected utility maximization but rejecting binary-lottery incentives is not an option.

  2. The mild time constraint is far from forcing pairs of participants to reason quickly, e.g., in the sense of triggering emotion driven reactions (see Ekman 1994; Loewenstein 2000; Feshbach and Singer 1971; Lee 1993).

  3. E.g., by employing modern techniques as brain scanning (see, e.g., Camerer et al. 2004 or Sanfey et al. 2003), eye tracking (see, e.g., Wang et al. 2010 or Fiedler et al. 2013), or physiological measurements.

  4. This is a more widely shared weakness of “behavioral game theory” (see, for instance, the otherwise impressive survey by Camerer 2003, as well as Cooper and Kagel 2016, for the literature on so-called “social preferences”).

  5. This merely assumes that more money (€15) is better than less money (€5) and that probabilities are calculated properly. Formally: if E(n) is the expected value of n, expected utility \(\frac{E(n)}{30} \cdot u\)(€ 15) + \(\frac{30-E(n)}{30} \cdot u\)(€5) can be simplified via setting u(€ 15) \(=\) 1 and u(€5) \(=\) 0 what implies that expected utility is simply E(n) / 30. Note that questioning binary lottery incentives, e.g. based on the evidence provided by Selten et al. (1999), but maintaining optimality in the sense of expected utility maximization is no option. Actually the risky choice task can be viewed as a best-case scenario for reinforcing such optimality.

  6. Equal payoffs could have been assumed also for constellations after interaction, e.g., when players are dis-coordinated, both might earn the same positive amount. In their experimental test of equilibrium selection theories, Balkenborg and Nagel (2016) employed the outside option game with equal payoffs for the backward rather than the forward induction solution.

  7. If (both U) yielded €4 for pair 1 instead of €6, the game would be symmetric so that isomorphic invariance forbids any selection. But since pair 1 earns €6 rather than only €4 in case of (both U), (payoff) monotonicity selects (both U) as the unique solution (see Harsanyi and Selten 1988).

  8. For the game studied by Balkenborg and Nagel (2016), (ES) would predict differently from (BI).

  9. Balkenborg and Nagel additionally equilibrate other behaviors by allowing for social preferences which, in our approach, would be captured by mental models similar to (ES).

  10. Requiring similar sample size from experimental studies which—via brain scanning or other approaches—directly elicit cognitive correlates or deliberation output in addition to observing choice behavior may be the reason why there are so few attempts to go beyond the revealed preferences approach in experimental economics.

  11. It only requires to prefer more to less money and to calculate the n-expectation properly. See footnote 5.

  12. “Max/min reasoning” stands for all arguments of pairs involving the worst case (ending up with 2!) and/or the best case (ending up with 24!) in justifying their decisions.

  13. Counterfactual in task 1 would be to decide between “stop or continue investing” after “not investing” and in task 2 when, as pair 1, deciding between U and V after having chosen “no interaction”. These decisions are avoided by the protocols used (see the instructions).

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Authors and Affiliations

  1. Institute for Economic Theory and Statistics, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Siegfried K. Berninghaus

  2. Max Planck Institute for Research on Collective Goods, Bonn, Germany

    Werner Güth

  3. LUISS University Guido Carli, Rome, Italy

    Werner Güth

  4. Institute for Applied Economic Research, Tübingen, Germany

    Charlotte Klempt

  5. Eberhard Karls Universität, Tübingen, Germany

    Kerstin Pull

Authors
  1. Siegfried K. Berninghaus
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  2. Werner Güth
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  3. Charlotte Klempt
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  4. Kerstin Pull
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Correspondence to Kerstin Pull.

Appendix

Appendix

1.1 Instructions 1 [The Risky Choice Task]

In this experiment you will have to make either one or two decisions. How successful you will be depends on your choices as well as on chance. Success will be measured by the number n of points which you earn. Your success number n will always be positive and smaller than 30. Actually, your monetary payment will either be €5 or €15. Which of the two you will earn depends on your success number n. You will earn €15 with probability n / 30,  i.e., when taking a ball from an urn with altogether 30 balls of which n are winning balls and the randomly drawn ball is a winning ball, you will earn €15. Similarly, you will earn €5 with probability \((30-n)/30,\) i.e., when the randomly drawn ball is a losing ball, you will earn only €5. Since n is always positive and smaller than 30, both payoffs (€15 and €5) will result with positive probability irrespective of your success number n.

How is n determined by your choices and chance? This is illustrated by the following decision tree:

figure a

You first decide between “invest” and “not investing”. When “not investing” is chosen, your success number n is 15 and you do not have to make another decision.

When you choose “invest,” a chance move can either determine that \(n=24\) or that you have to make another decision, namely between “stop investing” and “continue investing”. If you have to make another decision and choose “stop investing”, your success number n is 12, whereas in case of “continue investing” it is either 2 or 18.

All chance moves are equally likely, i.e., each of them occurs with probability 1/2, and will be realized only after you have decided. Accordingly, you have to choose one of the following three options:

  • \(\Box\) “not investing,” yielding success number \(n=15\)

  • \(\Box\) “invest” and “stop investing,” yielding success number \(n=24\) or \(n=12\), each with probability 1/2

  • \(\Box\) “invest” and “continue investing,” yielding success number \(n=24\) with probability 1/2 or, with probability 1/2, another chance move yielding \(n=2,\) respectively \(n=18\), each with probability 1/2

Please decide (now):

  • \(\Box\)“not investing”

  • \(\Box\) “invest” and “stop investing”

  • \(\Box\) “invest” and “continue investing”

Please decide which choice you expect to be the most frequent one of the other pairs:

I expect the most frequent choice to be

  • \(\Box\) “not investing”

  • \(\Box\) “invest” and “stop investing”

  • \(\Box\) “invest” and “continue investing”

1.2 Instructions 2 [The Outside Option Game]

In this second and last task you will be interacting with another pair of participants. What you will earn depends on your and the other pair’s behavior. How your monetary payoff is derived from the choices by both pairs is illustrated by the decision tree:

figure b

Thus pair 1 has three options, namely

  • \(\Box\) “no interaction”

  • \(\Box\) “interaction” and “U”

  • \(\Box\) “interaction” and “V”

whereas pair 2 only has two options:

  • \(\Box\) “U”

  • \(\Box\) “V”

Since after collecting all decisions it will be randomly determined which pair decides as pair 1, respectively pair 2, you have to tick one of the two boxes for both possibilities. Subsequently, you have to tick one of the three options of pair 1 and one of the two options of pair 2.

Please tick: \(\begin{array}{lr} \text{ as } \text{ pair } \text{1: } &{} \Box \\ \text{ as } \text{ pair } \text{2: }&{} \Box \\ \end{array}\)

Please tick which choice you expect to be the most frequent one of the other pairs:

I expect the most frequent choice of pair 1 to be

  • \(\Box\)“no interaction”

  • \(\Box\)“interaction” and “U”

  • \(\Box\) “interaction” and “V”

I expect the most frequent choice of pair 2 to be:

  • \(\Box\) “U”

  • \(\Box\) “V”

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Berninghaus, S.K., Güth, W., Klempt, C. et al. Assessing Mental Models via Recording Decision Deliberations of Pairs. Homo Oecon 34, 97–115 (2017). https://doi.org/10.1007/s41412-017-0051-6

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  • DOI: https://doi.org/10.1007/s41412-017-0051-6

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