Abstract
Fallback options are relatively common in the business context. If for example a firm fails to acquire a certain target firm—a first-best solution—it may decide to attempt the acquisition of another takeover target—a second best solution. When a decision maker tries to obtain the first-best solution, she may frequently choose different levels of effort to invest into its pursuit. This level of effort is generally influenced by the availability of a fallback option in case she fails to succeed in obtaining her first-best solution. Using a second price auction mechanism, we experimentally test whether subjects react to the existence and attractiveness of this fallback option by changing their bidding behavior. Our results show that subjects only partially adjust to the existence of the fallback option according to the theoretical prediction.
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Notes
Average earnings are somewhat lower than commonly paid at the Max Jung lab. This is owing to the fact that we expected the experiment to require less time, and subjects to succeed in earning somewhat more. Nonetheless, earnings range from 0.1 to 41.1 Euros, with a substantial standard deviation of 6.50 Euros, such that we believe that our incentives have been “salient nonetheless”. This is supported by subjects’ answers on our exit questionnaire, where the average response to the question “Did the payment you were led to expect increase your motivation to give your best?” was 3.12 on a five-point scale ranging from 0 (“Not at all”) to 4 (“Very much”).
Subjects went through a training period to understand the rules of the second price auction. They bid 80 times against rational computer bidders in each group size, with known (first 50 times) and unknown private value ranges (final 30 times).
Scaling the probability with the number of unsuccessful bidders mimics a situation where the unsuccessful bidders in a corporate takeover attempt try to take over the second best target firm. While this accounts for our experimental implementation of the concept of risk, we keep the expected value constant in order to allow us to observe the effect of different risk levels independent of changes in the fallback option’s expected value.
Example: The random choices yield treatment N and group size \(n=3\). The subject has a private value of 780 and bid 800. Out of all 9 subjects in the session, the two randomly chosen bids submitted under treatment N and for group size 3 are, e.g. 400 and 500. Thus, the subject in this example has won the auction in her virtual group, and has a profit of 780–500 = 280 ECU.
In the training periods, subjects earned on average 1.35 Euros which add up to the final payoff. The exact amounts were not known to the subjects before participating in the three auctions in the treatment phase.
Example: assuming the utility function \(u\left( x \right) =\hbox {ln}\left( x \right) \), the certainly equivalents of the fallback options in groups of sizes 3, 6 and 9, are \(e^{\mathrm{ln}\left( {100} \right) /2}=10, e^{\mathrm{ln}\left( {250} \right) /5}=3.02\) and \(e^{\mathrm{ln}\left( {400} \right) /8}=2.11\), respectively.
Observations in which bidders submitted one or zero in at least one of the auctions in a treatment are neglected in the data analysis. Bidders might bid a low value if they believe that they have no chance to win. However, as they did not know whether their values were high or low, we record bids of one or zero as a mistake or a sign of subject confusion. Thus, out of the original 117 observations, we consider 114 in \(N\), 105 in \(L\), and 110 in \(A\). We also run all analyses without removing outliers. The only qualitative difference is that when we do not remove any outliers, BidDev is slightly more negative in treatment \(L\) than in \(A\) in groups of size 9. Throughout the results section, we will flag cases where different outlier treatment yields qualitatively different results.
In cases where statements are based on multiple \(t\) tests, in order to conserve space we report the minimum degrees of freedom of any individual test, and minimum (maximum) \(t\)- and \(F\)-statistic values and maximum (minimum) \(p\) value in case of significant (insignificant) results.
We also find no significant differences in paired \(t\) tests comparing BidDev between groups in treatment \(N(t(105)=1.122, p=0.26)\).
If we do not remove outliers, we find no significant differences for any group size.
If we do not remove outliers, we cannot reject the Null at the 5 % level for any group size (group size 3 \(p=0.8757\); group size 6 \(p=0.0847\); group size 9 \(p=0.8967\)).
A \(t\) test confirms that, over all observations, average BidDev is greater than its predicted value \((t(927)=6.062, p=0.000)\). This result holds for other outlier treatment specifications, but does not hold if all extreme (0 or 1) bids are retained.
A hierarchical regression using subject-specific intercepts and controlling for treatment order yields practically identical results, with no significant coefficients except for those of the treatment dummies. Details are available upon request.
As a robustness check, we ran a random effects panel regression as in Table 3, Model 2, but including interactions between Treatment and each of the two risk aversion measures. We again find that the risk aversion measures carry no significant explanatory power. Details are available upon request.
Analysis available upon request.
If we remove data of all subjects submitting any outlying bids, the \(p\) value increases to 0.059.
Model 4 is the only one where we detect order effects when we include treatment order dummies. We find that order \(N-A-L\) yields significantly lower BidDev than \(L-N-A\), \(L-A-N\) (0.01 level), and \(N-L-A\) (0.05 level). No other treatment orders differ significantly at the 0.05 level.
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Acknowledgments
We are grateful to two anonymous referees, Nobuyuki Hanaki, and Jason Shachat for valuable comments. We furthermore thank audiences at the Experimental Finance 2013 in Tilburg and at the ESA World Meeting 2013 in Zurich for valuable comments. Last but not least, we thank Jakob Eichberger for his excellent research assistance.
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Füllbrunn, S., Kreiner, S. & Palan, S. The value of a fallback option. Cent Eur J Oper Res 23, 375–388 (2015). https://doi.org/10.1007/s10100-015-0389-4
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DOI: https://doi.org/10.1007/s10100-015-0389-4