Skip to main content
SpringerLink
Log in

Simultaneous versus sequential all-pay auctions: an experimental study

  • Original Paper
  • Published:
Experimental Economics Aims and scope Submit manuscript

Abstract

While both simultaneous and sequential contests are mechanisms used in practice such as crowdsourcing, job interviews and sports contests, few studies have directly compared their performance. By modeling contests as incomplete information all-pay auctions with linear costs, we analytically and experimentally show that the expected maximum effort is higher in simultaneous contests, in which contestants choose their effort levels independently and simultaneously, than in sequential contests, in which late entrants make their effort choices after observing all prior participants’ choices. Our experimental results also show that efficiency is higher in simultaneous contests than in sequential ones. Sequential contests’ efficiency drops significantly as the number of contestants increases. We also discover that when participants’ ability follows a power distribution, high ability players facing multiple opponents in simultaneous contests tend to under-exert effort, compared to theoretical predictions. We explain this observation using a simple model of overconfidence.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. We assume that each participant’s effort unambiguously determines the quality of the submission, and that the quality is objectively quantifiable. Therefore, we use the words “bid,” “quality,” and “effort” interchangeably throughout the paper. We also use “participant,” “contestant,” and “player” as synonyms.

  2. This assumption enables the existence of an explicit BNE in sequential contests (Segev and Sela 2014).

  3. When there is a tie, the winner is randomly selected.

  4. As a special case of ours (\(c=1\)), Chawla et al. (2012) show that with a uniform distribution, the EME monotonically increases in n.

  5. It is worthwhile to note that with more general distribution functions, the EME in simultaneous all-pay auctions is not necessarily monotonic (Moldovanu and Sela 2006).

  6. Segev and Sela (2014) derive the EME for \(n = 2,\) and 3 under the condition that each participant has a different c,  although they do not provide a generalized explicit solution for n players.

  7. Two simultaneous contest sessions with two players (SIM2) did not have enough subjects. Therefore, we had to run a session with 10 subjects and another with 8 subjects. However, the observed behaviors in these two sessions were not statistically significantly different from other sessions, so we treated them the same as other sessions of the same treatment.

  8. Four decimal points were kept for the display of ability factors, i.e., \(a_{i},\) and for subjects’ input of their effort levels, i.e., \(q_{i}.\)

  9. We chose two tokens as the maximum earning since it was much below the average earning in our auctions in each round (146.67 tokens), so as to avoid hedging biases as suggested by Blanco et al. (2010).

  10. Due to time constraint and fear of experimental subjects’ fatigue, we did not use an incentivized method for measuring risk preference (Charness et al. 2013; Eckel and Grossman 2002; Holt and Laury 2002).

  11. In some literature this measure is simply called “efficiency” (e.g., Noussair and Silver 2006). Here, we call it value efficiency to differentiate it from the first measure.

  12. Seven subjects went bankrupt during the experiment and we decided to pay them a $10 flat fee to compensate them for the time, although such a payment was not pre-announced.

  13. To benchmark our experimental contests’ performance against their BNE predictions, we report two-sided p-values from one-sample signed rank tests. In both simultaneous and sequential contests, the aggregate maximum effort does not appear different from BNE predictions (\(p>0.1,\) two-sided tests).

  14. The comparison remains insignificant for the contests with two players (SIM2 vs. SEQ2: 5.80 vs. 3.12, \(p=0.149,\) two-sided rank-sum tests).

  15. To benchmark the efficiency measures with their theoretical predictions (Table 2), we report results using one-sample signed rank tests. Overall, simultaneous contests’ efficiency levels are lower than expected, i.e., achieving a proportion of efficient allocations lower than 100% (SIM2: 78%, \(p=0.068;\) SIM3: 74%, \(p=0.068,\) two-sided tests). SEQ2 contests’ allocative efficiency levels are very close to their theoretical predictions, i.e., reaching a proportion of efficient allocations at 75% (vs. 77%, \(p=0.26,\) two-sided test). The SEQ3 contests, however, are less efficient than predicted, i.e., achieving a proportion of efficient allocations of 56% (vs. 65%, \(p=0.07,\) two-sided test).

  16. Because z-Tree requires a maximum decimal point for any numerical input, subjects’ efforts were restricted to four decimal points in our experiment. Therefore, we use 0.0001 as the increment of best responses, i.e., when a player tries to match the existing highest effort, she should simply make an effort that equals the existing highest effort plus 0.0001. To account for subjects’ imprecision in entering their efforts, we checked our results using 0.001, 0.01 and 0.1, and found no significant changes to our results.

  17. We also ran probit regressions where the dependent variable was whether overbidding occurred, and the results were qualitatively consistent.

  18. Since the standard errors are clustered at the session level, they could be biased due to the small number of clusters in our data. As a robustness check, we ran regression analyses with a wild cluster bootstrap procedure to correct for the small number of clusters (Cameron et al. 2008) and found that the results remained the same.

  19. Following Muller and Schotter (2010), we used a switching regression model to examine whether the individuals’ effort function was continuous. The switching regression model fit the data significantly better than BNE predictions based on the sum of squared deviations (SSDs) measure (SIM2: 21.37 vs. 549.83, \(p < 0.01;\) SIM3: 25.04 vs. 695.77, \(p < 0.01,\) two-sided signed rank tests). Nevertheless, this switching regression model could not explain why the effort levels of high ability contestants in SIM3 were lower than BNE predictions.

  20. Under the assumption of loss-aversion, Mermer (2013) analytically shows that high ability contestants over-exert effort while low ability contestants under-exert effort.

  21. The power distribution used in our experiment was described by its quantiles in the experimental instructions. See Appendix F in online for details.

  22. Consistently, results from Table 8 show that the BLF model does not fit the data significantly better than BNE.

References

  • Alicke, M. D., Klotz, M. L., Breitenbecher, D. L., Yurak, T. J., & Vredenburg, D. S. (2004). Personal contact, individuation, and the better-than-average effect. Journal of Personality and Social Psychology, 68(5), 804–825.

    Article  Google Scholar 

  • Altmann, S., Falk, A., & Wibral, M. (2012). Promotions and incentives: The case of multistage elimination tournaments. Journal of Labor Economics, 30(1), 149–174.

    Article  Google Scholar 

  • Amegashie, J. A., Cadsby, C. B., & Song, Y. (2007). Competitive Burnout: Theory and Experimental Evidence. Games and Economic Behavior, 59(2), 213–239.

    Article  Google Scholar 

  • Anderson, S. P., Goeree, J. K., & Holt, C. A. (1998). Rent seeking with bounded rationality: An analysis of the all-pay auction. Journal of Political Economy, 106(4), 828–853.

    Article  Google Scholar 

  • Archak, N., & Sundararajan, A. (2009). Attracting the best and the brightest: Asymptotics and optimal prize structure of all-pay contests with heterogeneous participants. Working paper.

  • Barut, Y., Kovenock, D., & Noussair, C. (2002). A comparison of multiple-unit all-pay and winner-pay auctions under incomplete information. International Economic Review, 43(3), 675–708.

    Article  Google Scholar 

  • Baye, M. R., Kovenock, D., & de Vries, C. G. (2005). Comparative analysis of litigation systems: An auction-theoretic approach. The Economic Journal, 115(505), 583–601.

    Article  Google Scholar 

  • Benz, M., & Meier, S. (2008). Do people behave in experiments as in the field? Evidence from donations. Experimental Economics, 11(3), 268–281.

    Article  Google Scholar 

  • Blanco, M., Engelmann, D., Koch, A. K., & Normann, H. T. (2010). Belief elicitation in experiments: Is there a hedging problem? Experimental Economics, 13(4), 412–438.

    Article  Google Scholar 

  • Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2008). Bootstrap-based improvements for inference with clustered errors. The Review of Economics and Statistics, 90(3), 414–427.

    Article  Google Scholar 

  • Carpenter, J., Holmes, J., & Matthews, P. H. (2008). Charity auctions: A field experiment. The Economic Journal, 118(525), 92–113.

    Article  Google Scholar 

  • Charness, G., Gneezy, U., & Imas, A. (2013). Experimental methods: Eliciting risk preferences. Journal of Economic Behavior and Organization, 87, 43–51.

    Article  Google Scholar 

  • Chawla, S., & Hartline, J. D. (2013). Auctions with unique equilibria. In Proceedings of the fourteenth ACM conference on electronic commerce, 2013 (pp. 181–196).

  • Chawla, S., Hartline, J. D., & Sivan, B. (2012). Optimal crowdsourcing contests. In Proceedings of the twenty-third annual ACM–SIAM symposium on discrete Algorithms, 2012 (pp. 856–868).

  • Che, Y.-K., & Gale, I. (2003). Optimal design of research contests. American Economic Review, 93(3), 646–671.

    Article  Google Scholar 

  • Cooper, D., & Fang, H. (2008). Understanding overbidding in second price auctions: An experimental study. The Economic Journal, 118(532), 1572–1595.

    Article  Google Scholar 

  • Dasgupta, P. (1986). The theory of technological competition. In J. E. Stiglitz & F. Mathewson (Eds.), New developments in the analysis of market structures (pp. 519–548). London: Macmillan.

    Chapter  Google Scholar 

  • Davis, D. D., & Reilly, R. J. (1998). Do too many cooks spoil the stew? An experimental analysis of rent-seeking and the role of a strategic buyer. Public Choice, 95(1), 89–115.

    Article  Google Scholar 

  • Dechenaux, E., Kovenock, D., & Sheremeta, R. M. (2015). A survey of experimental research on contests, all-pay auctions and tournaments. Experimental Economics, 18(4), 609–669.

    Article  Google Scholar 

  • Dixit, A. (1987). Strategic behavior in contests. The American Economic Review, 77(5), 891–898.

    Google Scholar 

  • Eckel, C. C., & Grossman, P. J. (2002). Sex differences and statistical stereotyping in attitudes toward financial risk. Evolution and Human Behavior, 23(4), 281–295.

    Article  Google Scholar 

  • Fibich, G., Gavious, A., & Sela, A. (2006). All-pay auctions with risk-averse players. International Journal of Game Theory, 34(4), 583–599.

    Article  Google Scholar 

  • Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10(2), 171–178.

    Article  Google Scholar 

  • Fu, Q. (2006). Endogenous timing of contest with asymmetric information. Public Choice, 129(1), 1–23.

    Article  Google Scholar 

  • Fu, Q., & Lu, J. (2012). The optimal multi-stage contest. Economic Theory, 51(2), 351–382.

    Article  Google Scholar 

  • Gneezy, U., & Smorodinsky, R. (2006). All-pay auction: An experimental study. Journal of Economic Behavior and Organization, 61(2), 255–275.

    Article  Google Scholar 

  • Gradstein, M., & Konrad, K. A. (1999). Orchestrating rent seeking contests. The Economic Journal, 109(458), 536–545.

    Article  Google Scholar 

  • Grosskopf, B., Rentschler, L., & Sarin, R. (2010). Asymmetric information in contests: Theory and experiments. Working paper.

  • Harris, C., & Vickers, J. (1985). Perfect equilibrium in a model of a race. Review of Economic Studies, 52(2), 193–209.

    Article  Google Scholar 

  • Harris, C., & Vickers, J. (1987). Racing with uncertainty. Review of Economic Studies, 54(1), 1–21.

    Article  Google Scholar 

  • Harrison, G. W., & List, J. A. (2004). Field experiments. Journal of Economic Literature, 42(4), 1009–1055.

    Article  Google Scholar 

  • Hillman, A. L., & Riley, J. G. (1989). Politically contestable rents and transfers. Economics and Politics, 1(1), 17–40.

    Article  Google Scholar 

  • Holt, C. A., & Laury, S. K. (2002). Risk aversion and incentive effects. American Economic Review, 92(5), 1644–1655.

    Article  Google Scholar 

  • Irfanoglu, Z., Mago, S., & Sheremeta, R. M. (2015). New Hampshire effect: Behavior in sequential and simultaneous election contests. MPRA paper, October 2015 (pp. 1–36).

  • Jeppesen, L. B., & Lakhani, K. R. (2010). Marginality and problem-solving effectiveness in broadcast search. Organization Science, 21(5), 1016–1033.

    Article  Google Scholar 

  • Klumpp, T., & Polborn, M. K. (2006). Primaries and the new Hampshire effect. Journal of Public Economics, 90(6–7), 1073–1114.

    Article  Google Scholar 

  • Konrad, K. A. (2009). Strategy and dynamics in contests. New York: Oxford University Press.

    Google Scholar 

  • Konrad, K. A., & Leininger, W. (2007). The generalized Stackelberg equilibrium of the all-pay auction with complete information. Review of Economic Design, 11(2), 165–174.

    Article  Google Scholar 

  • Krishna, V., & Morgan, J. (1997). An analysis of the war of attrition and the all-pay auction. Journal of Economic Theory, 72(2), 343–362.

    Article  Google Scholar 

  • Lazear, E. P., & Rosen, S. (1981). Rank-order tournaments as optimum labor contracts. The Journal of Political Economy, 89(5), 841–864.

    Article  Google Scholar 

  • Leininger, W. (1993). More efficient rent-seeking—A Munchhausen solution. Public Choice, 75(1), 43–62.

    Article  Google Scholar 

  • Liu, T. X. (2015). All-pay auctions with endogenous bid timing: An experimental study. Working paper.

  • Liu, T. X., Yang, J., Adamic, L. A., & Chen, Y. (2014). Crowdsourcing with all-pay auctions: A field experiment on Taskcn. Management Science, 60(8), 2020–2037.

    Article  Google Scholar 

  • Mago, S. D., Sheremeta, R. M., & Yates, A. (2013). Best-of-three contest experiments; strategic versus psychological momentum. International Journal of Industrial Organization, 31(3), 287–296.

    Article  Google Scholar 

  • Masiliunas, A., Mengel, F., & Reiss, J. P. (2014). Behavioral variation in Tullock contests. Working paper.

  • Mermer, A. G. (2013). Contests with expectation-based loss-averse players. Working paper.

  • Moldovanu, B., & Sela, A. (2006). Contest architecture. Journal of Economic Theory, 126(1), 70–96.

    Article  Google Scholar 

  • Moore, D. A., & Healy, P. J. (2008). The trouble with overconfidence. Psychological Review, 115(2), 502–517.

    Article  Google Scholar 

  • Morgan, J. (2003). Sequential contests. Public Choice, 116(1), 1–18.

    Article  Google Scholar 

  • Muller, W., & Schotter, A. (2010). Workaholics and dropouts in organizations. Journal of the European Economics Association, 8(4), 717–743.

    Article  Google Scholar 

  • Myerson, R. B. (1981). Optimal auction design. Mathematics of Operations Research, 6(1), 58–73.

    Article  Google Scholar 

  • Nalebuff, B. J., & Stiglitz, J. E. (1983). Prizes and incentives: Towards a general theory of compensation and competition. The Bell Journal of Economics, 14(1), 21–43.

    Article  Google Scholar 

  • Noussair, C., & Silver, J. (2006). Behavior in all-pay auctions with incomplete information. Games and Economic Behavior, 55(1), 189–206.

    Article  Google Scholar 

  • Nyarko, Y., & Schotter, A. (2002). An experimental study of belief learning using elicited beliefs. Econometrica, 70(3), 971–1005.

    Article  Google Scholar 

  • Plott, C., & Smith, V. (1978). An experimental examination of two exchange institutions. Review of Economic Studies, 45(1), 133–153.

    Article  Google Scholar 

  • Potters, J., de Vries, C. G., & van Winden, F. (1998). An experimental examination of rational rent-seeking. European Journal of Political Economy, 14(4), 783–800.

    Article  Google Scholar 

  • Rosen, S. (1986). Prizes and incentives in elimination tournaments. American Economic Review, 76(4), 701–715.

    Google Scholar 

  • Segev, E., & Sela, A. (2014). Multi-stage sequential all-pay auctions. European Economic Review, 70, 371–382.

    Article  Google Scholar 

  • Terwiesch, C., & Xu, Y. (2008). Innovation contests, open innovation, and multiagent problem solving. Management Science, 54(9), 1529–1543.

    Article  Google Scholar 

  • Tullock, G. (1980). Efficient rent seeking. College Station, TX: Texas A&M University Press.

    Google Scholar 

  • Weber, R. J. (1985). Auctions and competitive bidding. In H. Peyton Young (Ed.), Fair allocation, American Mathematical Society proceedings of symposia in applied mathematics (Vol. 33, pp. 143–170). Providence, RI: American Mathematical Society.

  • Zhang, J., & Wang, R. Q. (2009). The role of information revelation in elimination contests. Economic Journal, 119(536), 613–641.

    Article  Google Scholar 

Download references

Acknowledgements

We thank Juan Carrillo and Isabelle Brocas for providing us with access to the Los Angeles Behavioral Economics Laboratory (LABEL). We would also like to thank Yan Chen, Jeffrey Mackie-Mason, Lijia Wei and seminar participants at the 2013 North American ESA Meetings, the 2013 Annual Xiamen University International Workshop on Experimental Economics, and the 2014 Asian-Pacific ESA Meetings for helpful discussions and comments, and Chao Tang for excellent research assistance. We thank the Editor, David Cooper, and two anonymous referees for their constructive comments and suggestions. The financial support from Tsinghua University, the National Natural Science Foundation of China (NSFC) under Grant 71403140 and 71432004, is gratefully acknowledged. Lian Jian thanks the financial support from the APOC Program at the Annenberg School of Communication, University of Southern California.

Author information

Authors and Affiliations

  1. University of Southern California, Los Angeles, CA, USA

    Lian Jian

  2. Tsinghua University, Beijing, China

    Zheng Li & Tracy Xiao Liu

Authors
  1. Lian Jian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tracy Xiao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tracy Xiao Liu.

Electronic supplementary material

Below is the link to the electronic supplementary material.

(PDF 164 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jian, L., Li, Z. & Liu, T.X. Simultaneous versus sequential all-pay auctions: an experimental study. Exp Econ 20, 648–669 (2017). https://doi.org/10.1007/s10683-016-9504-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10683-016-9504-1

Keywords

JEL Classification

Search

Navigation