Abstract
We conducted a set of experiments to compare the effect of ambiguity in single-person decisions and games. Our results suggest that ambiguity has a bigger impact in games than in ball and urn problems. We find that ambiguity has the opposite effect in games of strategic substitutes and complements. This confirms a theoretical prediction made by Eichberger and Kelsey (J Econ Theory 106:436–466, 2002). In addition, we note that subjects’ ambiguity attitudes appear to be context dependent: ambiguity loving in single-person decisions and ambiguity averse in games. This is consistent with the findings of Kelsey and le Roux (Theory Decis 79:667–688, 2015).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
We refer to an ex-post Pareto improvement since this efficiency measure does not take into account any ex-ante losses in utility due to ambiguity aversion.
A neo-additive-capacity \(\nu _{i}\) on \(X_{-i}\) is defined by \(\nu _{i}( X_{-i}|\alpha _{i},\delta _{i},\pi _{i}) =1,\) \(\nu _{i}( \varnothing |\alpha _{i},\delta _{i},\pi _{i}) =0\) and \(\nu _{i}( A|\alpha _{i},\delta _{i},\pi _{i}) =( 1-\alpha _{i}) \delta _{i}+( 1-\delta _{i}) \pi _{i}( A) \) for \(\emptyset \subsetneqq A\subsetneqq X_{-i},\) where \(0\leqslant \delta _{i}<1\), \(\pi _{i}\) is an additive probability distribution on \(X_{-i}\).
For a justification of this definition and its relation to other support notions see Eichberger and Kelsey (2014).
This convention is for the sake of convenience only and does not bear any relation to the actual gender of the subjects in our experiments.
It might be worth noting that Eichberger and Kelsey (2014) present a stronger result for more general CEU preferences.
The traditional Ellsberg urn contains Red, Blue and Yellow coloured balls. The number of Red balls in the urn is known, while the remaining Blue and Yellow coloured balls are ambiguous in number.
A probit regression showed that the dummy variable for location (Delhi/Exeter) does not have a significant impact on choosing the ambiguity safe option. Thus, for the purpose of analysing subject behaviour in Treatment I, we have combined the data from sessions where Delhi subjects played against other Delhi subjects (local vs. local) with data from the Exeter vs. Exeter session, without the loss of efficiency.
Subjects knew that their choice would not affect the actual payoff of foreign players, while this was the case when they played the games against local opponents. As a result, when comparing behaviour in the games to test the role of ambiguity, we note that there may be a social preferences confound: subjects might have behaved differently when playing against foreign opponents simply because their choices did not affect the payoff of somebody else.
We were initially testing whether foreign opponents would create more uncertainty. We had expected that difference in backgrounds would create ambiguity on the part of Exeter subjects.
The experimental protocols can be found at the following link: http://saraleroux.weebly.com/experimental-protocols.html.
The experiments were conducted between November 2010–February 2011. The exchange rate during the period was 1 GBP = 80 INR. Our aim was that the average earnings from our experiment which lasted a maximum of 30 minutes should be able to afford subjects (university students) the chance to purchase a meal and a non-alcoholic drink. The purchasing power parity that we were aiming for was a burger meal.
If all rounds count equally towards the final payoff, subjects are likely to try and accumulate a high payoff in the first few rounds and then care less about how they decide in the following rounds. In contrast, if subjects know that they will be paid for a random round, they treat each decision with care.
The computer-simulated urn can be found at the following link: http://saraleroux.weebly.com/experimental-protocols.html.
The number of Y balls in the urn were determined using the MSExcel command “= ROUNDDOWN(RAND()*61,0)”, and the number of Z balls in the urn were simply = (60 minus the number of Y balls).
Note in the case of SC1 and SC2, the equilibrium action under ambiguity coincides with the Nash strategy, for the column player.
A probit regression of \(Certain\_Option\) (choice of the certain option) on the various dummies found that “Quant” was insignificant. It was thus dropped from the final regression. The dummy for \(SS\_2\) was dropped from the probit regression, to avoid the dummy variable trap.
The coefficients from a probit regression do not have the same interpretation as coefficients from an Ordinary Least Squares regression. From the probit results, we can interpret that males are less likely to choose the certain option. If a subject is male, their z-score decreases by 0.41. Moreover, subjects are more likely to choose the certain option in SC1 : the z-score increases by 0.67, in SC2 : the z-score increases by 1.10, and for SS1: the z-score increases by 0.34, when compared to the base which is game SS2.
We consider the sum of the people who chose Y and Z, rather than the number of people who chose Y or Z balls individually, to negate any effect of people choosing Y just because it appeared before Z on the choice set.
The dummy for \(\lambda \_100\) was dropped from the probit regression, to avoid the dummy variable trap. Dummies for Quant and Male were found to be insignificant, and were thus dropped from the final regression.
From the probit results, we can interpret that when \(\lambda =105\): the z-score decreases by 0.03, for \(\lambda =95\): the z-score decreases by 1.27, for \(\lambda =90\): the z-score decreases by 0.96, for \(\lambda =85\) : the z-score decreases by 1.49, when compared to the base which is \( \lambda =100.\)
Of these, 7 were column players and the remaining 2 were row players.
One subject in particular noted that “The urn question is pure luck, because majority of the marked balls are either Y or Z, and choosing either is a gamble.”
References
Binmore, K., Stewart, L., & Voorhoeve, A. (2012). How much ambiguity aversion?: Finding indifferences between Ellsberg’s risky and ambiguous bets. Journal of Risk and Uncertainty, 45(3), 215–238.
Bulow, J., Geanakoplos, J., & Klemperer, P. (1985). Multimarket oligopoly: Strategic substitutes and strategic complements. Journal of Political Economy, 93, 488–511.
Calford, E. (2016) Uncertainty aversion in game theory: Experimental evidence. Working paper UBC.
Charness, G., & Genicot, G. (2009). Informal risk sharing in an infinite-horizon experiment. The Economic Journal, 119(537), 796–825.
Chateauneuf, A., Eichberger, J., & Grant, S. (2007). Choice under uncertainty with the best and worst in mind: NEO-additive capacities. Journal of Economic Theory, 137, 538–567.
Choquet, G. (1953-4). Theory of capacities, Annales Institut Fourier, 5, 131–295.
Di Mauro, C., & Castro, M. F. (2011). Kindness confusion or... ambiguity? Experimental Economics, 14(4), 611–633.
Eichberger, J., & Kelsey, D. (2002). Strategic complements, substitutes and ambiguity: The implications for public goods. Journal of Economic Theory, 106, 436–466.
Eichberger, J., & Kelsey, D. (2014). Optimism and pessimism in games. International Economic Review, 55, 483–505.
Eichberger, J., Kelsey, D., & Schipper, B. (2008). Granny versus game theorist: Ambiguity in experimental games. Theory and Decision, 64, 333–362.
Eliaz, K., & Ortoleva, P. (2011). A variation on Ellsberg, SSRN eLibrary. http://ssrn.com/paper=1761445.
Greiner, B. (2016). Strategic uncertainty aversion in bargaining: Experimental evidence. Working paper, University of New South Wales.
Harsanyi, J. C., & Selten, R. (1988). A general theory of equilibrium selection in games. Cambridge: MIT Press.
Ivanov, A. (2011). Attitudes to ambiguity in one-shot normal form games: An experimental study. Games and Economic Behavior, 71, 366–394.
Keck, S., Diecidue, E., & Budescu, D. V. (2012). Group decisions under ambiguity: Convergence to neutrality. SSRN eLibrary.
Keller, L. R., Sarin, R. K., & Sounderpandian, J. (2007). An examination of ambiguity aversion: Are two heads better than one? Judgment and Decision Making, 2, 390–397.
Kelsey, D., & le Roux, S. (2015). An experimental study on the effect of ambiguity in a coordination game. Theory and Decision, 79, 667–688.
Kelsey, D., & le Roux, S. (2017). Dragon slaying with ambiguity: Theory and experiments. Journal of Public Economic Theory, 19(1), 178–197.
Schmeidler, D. (1989). Subjective probability and expected utility without additivity. Econometrica, 57, 571–587.
Trautmann, S. T., & van de Kuilen, G. (2016). Ambiguity Attitudes. The Wiley Blackwell handbook of judgment and decision making.
Author information
Authors and Affiliations
Corresponding author
Additional information
Financial support from the University of Exeter Business School is gratefully acknowledged. We would like to thank Robin Cubitt, Jürgen Eichberger, Zvi Safra, Dieter Balkenborg, Miguel Fonseca and participants in seminars at Bristol, Exeter and Heidelberg for their comments and suggestions. We thank Tim Miller for programming the Ellsberg urn.
Rights and permissions
About this article
Cite this article
Kelsey, D., le Roux, S. Strategic ambiguity and decision-making: an experimental study. Theory Decis 84, 387–404 (2018). https://doi.org/10.1007/s11238-017-9618-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11238-017-9618-8