Abstract
We conduct an experiment on a minimum effort coordination game in a (quasi-)continuous time-frame, where effort choices can be switched freely during a 60-s period. The cooperation levels of the continuous time treatments are not significantly different from the discrete time treatments. Providing subjects with the information on the effort choices of all group members increases the average effort level in continuous time only. The minimum effort level in continuous time with full information feedback is also substantially higher than that with limited information feedback, but the difference is statistically insignificant. With limited information feedback, subjects rarely coordinate to increase their efforts simultaneously to change the group minimum within a period. Our findings imply that continuous time games are not behaviorally equivalent to infinitely repeated discrete time games.
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Notes
No experiment is in continuous time in the strictest sense, as there are always software delays. For brevity, quasi-continuous time will be referred to as continuous time for the rest of this paper.
Other factors found to affect the coordination outcome in discrete time are the communication protocol (Blume and Ortmann 2007), deviation cost (Goeree and Holt 2005), group size (Van Huyck et al. 1997), and precedent behavior (Devetag 2005). Devetag and Ortmann (2007) provide a comprehensive survey.
To avoid confusion or biasing of decision making, the word “effort” is replaced with “value” in the instructions.
See Online Appendix for the experimental instructions for the ConFull treatment.
The experiment has ten 60-s periods instead of one 10-m period. This is to avoid the persistent effect of mistakes in the first few minutes, especially because the coordination level can be highly sensitive to the effort level at the beginning of a period. We do not offer unpaid periods for practice, so that subjects cannot signal their intention to choose high effort levels (in the paid period) without incurring any costs in the practice period.
We let subjects pick their initial effort levels because the initial effort levels cannot be randomly assigned by our program without affecting the results. If some subjects choose to match the group minimum as closely as possible in a period, the minimum effort in the period will be the same as the initial minimum effort randomly picked by our program.
The visual response time, measured by how long it takes to click a mouse immediately when a dot appears on a screen, is 0.2 s for an average person (Sanders and Sanders 2013), while some trained athletes can reach nearly 0.11 s (Lipps et al. 2011). Although the refresh interval in our experiment is slightly longer than the average response time, we believe that the delay should not affect decision making. Even if subjects do not experience the experiment setting as a continuous time frame, thinking about the strategy and moving the mouse to the right position as required in our experiment will take more time than an immediate visual response.
The continuous time treatments have more questions because these treatments are more complicated.
The group minimum effort of each group is shown in Fig. A.1 in Online Appendix. In each treatment, there are groups cooperating at effort level 7 and groups stuck at effort level 1.
We also conducted panel data regressions which yield results similar to those discussed in this section. We include the regression results in Online Appendix.
The within-period group minimum effort of each group is shown in Fig. A.1.
Each row represents a group in the ConMin or ConFull treatment. The height of the line indicates the minimum effort level. The top of the row indicates level 7, and the bottom of the row indicates level 1.
Each row represents a subject in the representative group. The height of the line indicates the subject’s effort level. The top of the row indicates level 7, and the bottom of the row indicates level 1.
At the start of each period, subjects cannot observe the others’ efforts or the group minimum before they click the “OK” button to submit their period starting efforts.
An upward switch indicates a positive change and a downward switch indicates a negative change. The within and start period coordination outcomes are compared by the percentage of upward switches. We do not count non-switches either at the start of a period or within a period as the non-switches do not change the coordination outcome. Although there is an asymmetry in start and within period switches in that, within period, anytime a subject does not change their effort for 0.3 s there is a non-switch, the asymmetry is irrelevant to our analysis.
In the ConFull treatment, one group does not have any switches within period, and another group does not have any switches at the start of period. The former is excluded from Mann–Whitney test of the within-period comparison and the latter is excluded from the start-of-period comparison.
Although the intuition is that the percentages of total individual effort switches should be the same in the two treatments if the percentages of within-period and start-of-period individual effort switches are the same, our test results indicate that the ConFull treatment has a higher percentage of individual effort switches. When the start-of-period switches are summed with the within-period switches, the rank of percentage of upward total switches is changed.
There are two groups in each continuous time treatment that do not have any within-period upward group minimum switches. The ratio cannot be calculated for these four groups and they are excluded from the two-tailed Mann–Whitney test.
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Acknowledgements
We received useful comments from audiences at the 2015 Economic Science Association World Meeting in Sydney, the 2015 Australian Conference of Economists in Brisbane, and the 10th Annual Australia New Zealand Workshop on Experimental Economics in Hobart. Specific comments from Paul Frijters, Elias Lafi Khalil, Ryan Oprea, Andreas Ortmann, Anmol Ratan, Vera te Velde and Tom Wilkening are much appreciated. We also thank an anonymous referee for valuable feedback. Funding from the School of Economics at the University of Queensland is gratefully acknowledged. Kenan Kalayci acknowledges financial support from Australian Research Council Grant DE160101242. Many thanks to Maria Bigoni for sharing the z-tree code used in Bigoni et al. (2015).
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Leng, A., Friesen, L., Kalayci, K. et al. A minimum effort coordination game experiment in continuous time. Exp Econ 21, 549–572 (2018). https://doi.org/10.1007/s10683-017-9550-3
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DOI: https://doi.org/10.1007/s10683-017-9550-3