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The Effect of Stake Size in Experimental Bargaining and Distribution Games: A Survey

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Abstract

We review the literature on bargaining and distribution experiments to investigate whether changes in stake size have significant effects on behaviour in laboratory/field settings. We conclude that experiments in this field do not lead to clear/common results. The joint presence of opposing factors (e.g., increasing relative risk aversion and increasing cost of fairness) might be one reason contributing to this. Moreover, we argue that variables such as subjects’ financial conditions, cognitive abilities, risk attitudes, loss-aversion, justice orientations, and relevant personality characteristics should be controlled in laboratory experiments to understand the effect of stake size on behaviour, more clearly. Finally, quasi-experiments using data from (very) high-stake games/events and meta-analysis studies should complement (individual) controlled experiments.

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Notes

  1. A relatively recent yet influential book by Bardsley et al. (2010) devoted two chapters to these issues.

  2. We do not focus on the effects of a presence (real) versus absence (hypothetical) of financial incentives here (see Hertwig and Ortmann 2001 for a great discussion). Nevertheless, for the sake of giving a more complete picture we will include some studies comparing behavioral patterns in ultimatum, dictator, and trust games with real versus hypothetical stakes.

  3. Bearden (2001) surveyed ultimatum game experiments and he had a section in the survey on the stake size effect. He concluded similarly by saying that the effects found were weaker than he thought and further data is needed for better understanding.

  4. It is worth mentioning that we included also working papers that are not published yet to avoid possible publication biases that may arise in survey studies. We also want to mention that we cover around fifty studies after 1999, which is the publication date of Camerer and Hogarth (1999).

  5. For instance, a proposer who becomes increasingly risk averse as the stake increases may tend to make proportionally more generous offers. On the other hand, if he believes that fairness is a normal good (for the responder) and the cost of behaving fair-mindedly increases as offers become more generous in absolute terms, he may make more generous offers in absolute terms but less generous in relative terms. Hence, the net effect can be indeterminate.

  6. In some of the studies we investigate, the effect of stake-size on individual behaviour is not the main research question. Rather, the authors implement different stake-sizes to test the robustness of their results. When we report such studies, we focus on those parts where they test for stake-size effects.

  7. This hypothesis is empirically supported by studies such as Binswanger (1981), Kachelmeier and Shehata (1992), Bombardini and Trebbi (2005), Andersen et al. (2008), Baltussen et al. (2008) and Post et al. (2008).

  8. This argument (i.e., decision-making has cognitive costs) is supported by recent neuro-scientific research. For further reading, the reader is referred to McGuire and Botvinick (2010).

  9. Their model used Bolton and Ockenfels (2000) inequity averse preferences as a primitive. Note that, Bolton and Ockenfels (2000) and Rabin (1993) both imply that as the stakes increase, rejections of unfair offers will vanish.

  10. This is the subgame perfect Nash equilibrium (SPNE) prediction. Nash equilibrium (NE) concept predicts other outcomes, as well. Nevertheless, SPNE is much more frequently employed in extensive form games (such as the ultimatum game) due to a weakness of NE in capturing sequential rationality.

  11. This article consists of two sections which are the bargaining game and the market game. From the point of the current study, only the bargaining section is explained.

  12. In the dictator game, like in the ultimatum game, first player proposes a division. However, there is no decision to be made for the second player, i.e., the second player cannot accept or reject. In other words, the first player rather dictates the division. Hence the name, dictator game.

  13. Later, Gillis and Hettler (2007) conducted a multiple-round ultimatum game experiment with real versus hypothetical stakes ($10) and found mixed results. In particular, subjects offered—on average—less in the hypothetical stake treatment. However, this effect was not present in the first round of play but became apparent in later rounds.

  14. Another well-known study on ultimatum games where the stake-size is asymmetric information is Nagel and Mitzkewitz (1993). In that study, possible stake sizes were DM1.20, DM2.40, DM3.60, DM4.80, DM6, and DM7.20. The authors reported differences in behaviour across (two versions of the) ultimatum games with different stake sizes.

  15. In the strategy method, subjects declare their decisions for all their possible roles and for all possible situations beforehand. For example, in an ultimatum game, they announce what will be their offer when they are proposer, what will be their answer to all possible offers. After that, roles of players are determined, they are paired up with each other and payoffs are determined according to their strategies.

  16. A recent study by Griffin et al. (2012) also investigated racial differences in ultimatum game behaviour. The authors varied the stake-size between $5 and $100. They concluded that stake-size did not significantly affect responders’ acceptance decisions.

  17. Since the aim of the study is analysing the behaviour of the responders, the possible experimenter demand effects resulting from the mentioned explanation does not pose a problem.

  18. It should be noted that the actual aim of this experiment was not to measure the effects of the amount of money used on the subjects’ behaviour. Accordingly, the change in stakes was implemented only in the last period. Factors such as experience, last period, and boredom effects might have introduced confounds.

  19. The authors used different media (e.g., lab, newspaper, internet) and reached different subject pools (e.g., newspaper readers, business executives, students). They also used different payment methods (e.g., paying everyone their full earnings, randomized payment).

  20. For a comprehensive survey of experiments on bargaining games with joint production, see Karagözoğlu (2012).

  21. “Non-bargaining distribution games” might have been more informative. We are aware of the fact that these games also involve an efficiency component. At the cost of using the label “distribution games” in a way possibly different than the standard one, we use it to differentiate them from bargaining games.

  22. For alternative/opposing arguments, the reader is referred to Bardsley (2008) and List (2007).

  23. There is a lot of important methodological details in Naef and Schupp (2009) study, which we cannot cover here, in this kind of a paper. Hence, the interested reader is referred to the original paper for such details.

  24. For instance, we know that culture plays a role in shaping subjects’ behaviour in social interactions (Henrich et al. 2001; Herrmann et al. 2008), which may make it difficult to generalize these findings. See also Raihani et al. (2013) for a recent study finding behavioural differences across subjects in USA and India in online dictator games with $1, $5, and $10 stakes.

  25. This study and aforementioned Goldreich and Pomorski (2011) study are not experiments conducted in a controlled lab environment. Such experiments are called quasi-experiments in the literature.

  26. In a recent paper very similar to this one, Van den Assem et al. (2012) analysed the cooperative behaviour in the television show, Split or Steal. The stake-size varies between a few dollars and $175,000, averaging over $20,000. The authors found only limited support for the hypothesis that cooperation will decrease as the stakes get larger.

  27. It is worthwhile emphasizing that we are advocating to control only those variables for which there exists some form of theory and/or wide-spread empirical evidence for the link between them and the investigated behaviour.

  28. An important concern here would be anonymity of participants. Nevertheless, this would not be a major issue since (i) participants would be asked to generate participant id’s that conceal their identity and (ii) payment methods that keep participant id’s anonymous to the researcher already exist and are used.

  29. Recently, there has been an increased interest in meta-analysis studies in experimental economics. The reader is referred to Cooper and Dutcher (2011) for ultimatum games, Engel (2011) for dictator games, and Johnson and Mislin (2011) for trust games.

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Acknowledgments

Emin Karagözoglu thanks The Scientific and Technological Research Council of Turkey (TÜBITAK) for the research grant #111K499. The authors would like to thank two anonymous reviewers and an editor for their comments that improved the paper. The authors would also like to thank Gary Bolton and Urs Fischbacher for their comments and Mirza Trokic for proof-reading the manuscript.

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  1. Department of Economics, Bilkent University, 06800, Bilkent, Ankara, Turkey

    Emin Karagözoğlu

  2. Department of Economics, Middle East Technical University, 06800, Çankaya, Ankara, Turkey

    Ümit Barış Urhan

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  1. Emin Karagözoğlu
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Correspondence to Emin Karagözoğlu.

Appendix

Appendix

See Tables 5 and 6.

Table 5 Studies reporting stake-size effects
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Table 6 Studies reporting no stake-size effects
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Karagözoğlu, E., Urhan, Ü.B. The Effect of Stake Size in Experimental Bargaining and Distribution Games: A Survey. Group Decis Negot 26, 285–325 (2017). https://doi.org/10.1007/s10726-016-9490-x

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