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Why did he do that? Using counterfactuals to study the effect of intentions in extensive form games

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Abstract

We investigate the role of intentions in two-player two-stage games. For this purpose we systematically vary the set of opportunity sets the first mover can choose from and study how the second mover reacts not only to opportunities of gains but also of losses created by the choice of the first mover. We find that the possibility of gains for the second mover (generosity) and the risk of losses for the first mover (vulnerability) are important drivers for second mover behavior. On the other hand, efficiency concerns and an aversion against violating trust seem to be far less important motivations. We also find that second movers compare the actual choice of the first mover and the alternative choices that would have been available to him to allocations that involve equal material payoffs.

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Notes

  1. Another example for a model where decisions are shaped by distributional properties of the available allocations is the quasi-maximin model by Charness and Rabin (2002), which adds to material self-interest surplus maximization and the Rawlsian maximin motive as drivers for behavior.

  2. This is the baseline experiment in Fisman et al. (2007). In addition to this the authors also investigate two alternative treatments: one has linear budget sets as the baseline but differs from the latter in that each dictator decision has now consequences for two other persons (i.e., budget sets are three-dimensional in this treatment); the other has two-dimensional budget sets as the baseline but differs from the latter in having allocations in the choice set that differ only in the material payoff of the recipient, or only in the material payoff of the dictator (i.e., budgets are step-shaped in this treatment).

  3. As will become clear later, the treatments in Cox et al. (2016) are all located in area 11 of Fig. 2 while we expose subjects to decision situations in each of the cells in the figure.

  4. Our design can be seen as a (generalization of a) hybrid between an investment game (à la Berg et al. 1995) where both players have rich choice sets (provided the FM has made a “trusting choice”) and a mini trust game (à la McCabe et al. 2003) where both players have only a binary choice to make (provided the FM has made the ’trusting choice’): In our design the FM has a binary choice to make (it can be interpreted as a choice between transferring a given amount s to the SM and not transferring anything), while the SM has a richer choice set (in our design a choice between seven allocations provided the FM has transferred s). Some of the games investigated by Charness and Rabin (2002) constitute special cases of our design. They found in these cases that the SM often reciprocated to the kindness of the FM (as revealed by his choice). Our design systematically varies the set of choices offered to the FM to investigate other potential factors driving the behavior of the SM.

  5. While there are potential effects of using the strategy method instead of the direct-response method (such as a reduction in incentives or a “hot” versus “cold” effect that might affect the participants’ choices—see Zizzo 2010, for a discussion), the experimental literature reports no case in which a treatment effect was observed with the strategy method and not with the direct-response method (see Brandts and Charness 2011).

  6. The randomization also limits concerns for an indirect experimenter demand effect whereby participants observing systematic variations of the location of a point relative to the same line would infer that their behavior is expected to change as a consequence of the relative position of the point.

  7. See online appendix for further details.

  8. Cox et al. (2016) design comprises five treatments implemented between subjects. In all these treatments the SM decides how to divide 60 experimental currency units between herself and the FM in case the FM sends her his endowment of 15. The treatments differ in what happens in case the FM decides not to send the endowment to the SM, and whether the FM can make such a decision at all. Thus, in the language of the current paper, the Cox et al. (2016) design keeps the location of the line constant and varies the location of the point and whether a point is available at all. In terms of Fig. 2, the Cox et al. design only investigates constellations in area 11 while we expose subjects to decision situations in each of the cells in the figure.

  9. Since \(\theta =0\) for purely selfishly acting individuals, the behavior of subjects in this subsample is not informative about how intentions influence social preferences.

  10. The experiment was conducted by pen and paper and a small number of answers (\(N=17\)) were missing in the questionnaires. This leaves a dataset of 3463 observations.

  11. Note that the shaded areas in Fig. 2 cover situations where the choice of the line allows for a deal, while area 111 contains all situations where the choice of the line reveals trust.

  12. This is called the “Luce model” (see Wilcox 2008).

  13. If the line crosses the 45 degree line and if the crossing point is one of the seven feasible allocations on the line, then this allocation is the LUA; if the line crosses the 45 degree line but the crossing point is not a feasible allocation then the feasible allocation on the line that is closest to the 45 degree line is the LUA; and if the line does not cross the 45 degree line then the feasible allocation on the line that is closest to the 45 degree line is the LUA.

  14. We thank a reviewer for pointing out this connection to us.

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Authors and Affiliations

  1. School of Economics and Finance, Queensland University of Technology, 2 George Street, Brisbane, Australia

    Yola Engler & Lionel Page

  2. Department of Economics, University of Innsbruck, Universitaetsstrasse 15, Innsbruck, Australia

    Rudolf Kerschbamer

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  1. Yola Engler
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  2. Rudolf Kerschbamer
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  3. Lionel Page
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Correspondence to Lionel Page.

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Engler, Y., Kerschbamer, R. & Page, L. Why did he do that? Using counterfactuals to study the effect of intentions in extensive form games. Exp Econ 21, 1–26 (2018). https://doi.org/10.1007/s10683-017-9522-7

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