Overcoming coordination failure using a mechanism based on gradualism and endogeneity

We examine three tools that can enhance coordination success in a repeated multiple-choice coordination game. Gradualism means that the game starts as an easy coordination problem and moves gradually to a more difficult one. The Endogenous Ascending mechanism implies that a gradual increase in the upper bound of coordination occurs only if coordination with the Pareto superior equilibrium in a stage game is attained. The Endogenous Descending mechanism requires that when the game’s participants fail to coordinate, the level of the next coordination game be adjusted such that the game becomes simpler. We show that gradualism may not always work, but in such instances, its effect can be reinforced by endogeneity. Our laboratory experiment provides evidence that a mechanism that combines three tools, herein termed the "Gradualism with Endogenous Ascending and Descending (GEAD)" mechanism, works well. We discuss how the GEAD mechanism can be applied to real-life situations that suffer from coordination failure.

1. For a pre-2007 survey on experimental coordination games, see Devetag and Oltmann (2007).

2. Previous studies using laboratory experiments about coordination problems explored a direct or an indirect way to overcome coordination failure. Financial incentives (Brandts and Cooper 2006a; Guillen et al. 2006; Hamman et al. 2007), communication among players (Cooper et al. 1989, 1992), the observability of others’ choices (Brandts and Cooper 2006b), and leadership (Cooper 2006; Brandts and Cooper 2007; Brandts et al. 2007, 2014) are effective at reducing coordination failure.

3. 900–1000 yen is equivalent to a student’s hourly wage. Thus, the stake was substantial.

4. To conduct non-parametric analysis in this section, we use one observation per group. More concretely, when we are comparing group efforts from the 6th to the 20th period, each group provides us one observation (the average group effort over the 15 periods), not fifteen.

5. No possible comparison of the four treatments is statistically significant by the rank sum test after the Bonferroni adjustment. We think this is because the number of observations is too limited.

6. In the groups achieving full coordination in the first period, the ratio of Pareto coordination success is not statistically different between three conditions; it was 50 % (3 groups out of 6) in the G condition, almost 66 % (8 groups out of 12) in the GEA condition, and almost 58 % in the GEAD condition (7 groups out of 12). Thus, we may combine all the groups achieving full coordination in the first period into one.

7. If we use the word "recovery" more strictly, it means a "restoration to a former and better condition." Thus, we choose every case that a group could achieve the Nash equilibrium at period t and could not at period t + 1 (t ≥ 1), and we compare the frequencies of recovery and non-recovery cases in period t + 2. The results are essentially the same. The GEAD treatment may show a "recovery power": 30 of 32 cases are recovery cases in the GEAD treatment, and the corresponding numbers are 5 of 17 in the GEA treatment and 0 of 23 in the G treatment.

8. If we count the number of ordinary Nash equilibria (including the payoff dominant equilibria of each period) after coordination failure, the result is essentially the same: the recovery rates in the GEAD, GEA, G, and CON treatments are 94 % (31 of 33), 19 % (17 of 90), 15 % (24 of 165), and 15 % (20 of 131) respectively.

9. We may need a huge sample to provide definitive evidence about the recovery effect. There are three reasons. First, the "one observation per group" principle, which is indispensable for the analysis, does not provide enough independent data. Second, we should keep the strategy space (i.e., number of choices available) after coordination failure constant in order for the choices to be comparable. Third, as the coordination failure is much less likely to occur in GEAD, there are fewer cases we can use to test the "recovery effect."

10. There is one difference between our result and that of Ye et al. (2014), who found that gradualism alone works better compared with the constant condition in their binary choice minimum effort coordination game. This contrasts with our finding about the comparison between the G and CON treatments, wherein their performances are not statistically different. It is difficult to detect a compelling reason for the two different experimental results; it could be attributed to the fact that the binary coordination game is theoretically different from the multiple coordination game. Rather, it is possible that their result may not really contradict ours: If we had increased the upper bound more gradually in our experimental design, say, in increments of 2.5, the G treatment would have shown a better outcome than the CON treatment.

This paper owes much to the thoughtful and helpful comments of Professor David Cooper and two anonymous reviewers of Experimental Economics. We gratefully acknowledge financial support from the MEXT KAKENHI Grant Number 25380241.

Authors and Affiliations

1. School of Management, Kochi University of Technology, Kami, Japan

   Yoshio Kamijo

2. Economic and Humanities, Kagoshima University, Kagoshima, Japan

   Hiroki Ozono

3. School of Political Science and Economics, Waseda University, Tokyo, Japan

   Kazumi Shimizu

Corresponding author

Correspondence to Yoshio Kamijo.

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