Risk attitudes in large stake gambles: evidence from a game show

Abstract

This article estimates the degree of risk aversion of contestants appearing on ‘Vas o No Vas’, the Mexican version of ‘Deal or No Deal’. We consider both dynamic agents, who fully backward induct and myopic agents that only look forward one period. Further, we vary the level of forecasting sophistication by the agents. We find substantial evidence of risk aversion, the degree of which is more modest than what is typically reported in the literature.

Acknowledgements

The authors would like to thank Glen Harrisen and Thierry Post for their valuable comments. Thanks also go to Carlos Reyes for bringing the Mexican Version of Deal or No Deal (Vas o no Vas) game show to our attention in the spring of 2005.

Notes

¹ A variant of this show is now airing in the US under the name ‘Deal or No Deal’.

² See Anderson et al. (2006c) for a survey.

³ The only one who knows the contents of each briefcase is the government official who was in charge of filling the briefcases and he plays no role in the show. This is an important feature of the game because the bank can strategically make offers if it knows the value of the held briefcase and contestants should take it into account for their decisions. Without this kind of complication, it is easier to elicit risk aversion from participants’ decisions in the Mexican show.

⁴ This feature differs from some other contests where the recipient only receives the large novelty check for winning large prizes. Fullenkamp et al. (2003) point out that such a presentation may influence behaviour.

⁵ The show summaries can be viewed at www.esmas.com/vasonovas. The data were collected from the first 62 shows televised in Mexico in 2005 and 2006. As seen in Table 1, during this time, the format of the show changed with respect to the money amounts in the 26 briefcases. The analysis considers this formatting change to be exogenous. The data used in the analysis are available from the authors upon request.

⁶ The predicted log offer for the Christmas show is included in Fig. 1 as an out-of-sample forecast. As expected the show is an outlier.

⁷ The support is divided into two 5%, two 10%, two 20% and one 30% intervals.

⁸ For example, Krahnen et al. (1997) show that it is misleading to estimate the degree of risk aversion by a single-stage procedure.

⁹ A copy of the computer code is available from the authors upon request.

¹⁰ Andersen et al. (2006c) recently suggested using ‘virtual lotteries’ as an alternative approach which eliminates this computational constraint.

¹¹ W_L is computed using the 2002 GDP per capita from the OECD converted into Pesos by using the official exchange rate data from the Central Bank of Mexico for that year. W_H is extracted from Noyola (2000).

¹² The maximum prize is 5 000 000 and thus r  < −12 results in the need to compute (5 000 000  + W)¹³, which creates an overflow error. Therefore, it could be that stopping indicates a constant's r is below −13.5, which is consistent with previous decisions indicting that r is less than −12 or it could be inconsistent with previous decisions indicating r is above −13.

¹³ The CARA utility function is not defined when σ is zero, so maximum likelihood estimation based on normal distribution is not applicable.

¹⁴ With CARA, computational limits do not allow us to evaluate values of σ below −7  × 10⁻⁵.

¹⁵ The Mexican show introduced nonmonetary payoffs after our sample period.

¹⁶ In the case of informative offer, the empirical distribution is specific to the rank of the held briefcase among the active briefcases as well as round.

¹⁷ Instead, De Roos and Sarafidis employ a random utility model including contestant-specific random effects.

¹⁸ Cultural differences across countries could also explain some of the variation. However, such a comparison should be done within a unified analytical framework, which is somehow infeasible due to the differences in show formats.

¹⁹ This framework is exactly equivalent to the static model of Bombardini and Trebbi. They found that the estimated CRRA coefficients from the myopic model are lower than those from the dynamic model. This suggests that Mulino et al. underestimate risk attitudes. On the other hand, as they explain in their paper, the presence of the ‘Chance’ and ‘SuperCase’ supplementary rounds makes contestants more likely to accept low offers. Ignoring these options in the analysis, as they do, would lead to overestimating the risk aversion coefficient. Therefore, it is not clear which of these effects dominates.

²⁰ Both the new version of Post et al. and Andersen et al. (2006a) used the expo-power utility function which generalizes CARA and CRRA. While Andersen et al. (2006a) rejected the standard utility functions, Post et al. found mixed results for different countries and suggested cross-country comparison to examine the role of culture and social environment. Andersen et al. (2006c) found the CRRA coefficient ranging from 0.016 to 0.38, indicating that US players are moderately risk averse or risk neutral. But, using Hyperbolic Absolute Risk Aversion function, they again rejected the validity of the CRRA assumption.

²¹ In fact, based upon laboratory experiments, Isaac and James (2000) conclude that the same individual exhibits different risk preferences in different decision problems.

²² For comparison, the relatively high stakes in the experiments of Holt and Laury (2002) involved a maximum prize of US$346.50. The ability to offer such large prizes on game shows is derived from the television network's ability to sell advertising space to large viewing audience, which may impact behaviour. Laboratory experiments by Dufwenberg and Muren (forthcoming) show that an audience can impact behaviour in two-person games. Of course, none of the models of risk aversion specify a minimum magnitude threshold below which risks are viewed differently.

²³ The ability to offer large prizes on game shows is in part derived form the television network's ability to sell advertising space to large viewing audience. In an unrelated context laboratory experiments by Dufwenberg and Muren (2006) show that as audience can impact behaviour in two person games.