Learning, Words and Actions: Experimental Evidence on Coordination-Improving Information

This payoff structure coincides with treatment 1 in the seminal contribution by Beard and Beil (1994), who were the first to study subjects’ behavior under varying stakes in a sequential move game. They found that 66% (from 20% to even 80% across treatments, with an average of 54.5%) of player As prefer the mistrustful choice , while the preference to maximize own gains is almost universal (97.8%) among subjects in the role of player B who are trusted by their partners. These results were confirmed on Japanese subjects in Beard, Beil, and Mataga (2001). Goeree and Holt (2001) applied the strategy method to the decision of player Bs. When asked what they would do if player A chose , the odds that player Bs would choose vary from 53 to 100% depending on the relative payoffs of each action. The rate of secure choices from subjects in the role of player As varies from 16 to 80%.

See, e.g. Cooper, DeJong, Forsythe, and Ross (1992), Crawford (1998), Charness (2000), Duffy and Feltovich (2002), Duffy and Feltovich (2006), and Blume and Ortmann (2007).

Although the original Rosenthal conjecture concerns a one-shot game, Beard and Beil note in their original paper (pp. 261 and 262) that it seems equally valid for a repeated game, and that learning through experience may affect people’s behavior independently of payoff-related factors.

See Crawford (1998) for an earlier survey of the theoretical and experimental literature on cheap-talk, Ellingsen and Ostling (2010) for a detailed survey of the evidence in Stag Hunt games, Cooper, DeJong, Forsythe, and Ross (1992) and Charness (2000) for a comprehensive experimental study.

There are still few papers that implement this kind of feedback information. Bracht and Feltovich (2009) apply these two treatments in the Gift-Exchange Game. The results show a striking contrast between treatments: while observation is effective in reinforcing cooperation, the effect of communication visibly lags behind. See also Celen, Kariv, and Schotter (2010) for further discussion on the effects of communication and observation on strategic behavior in the lab.

Given the payoff structure of this game, one hypothesis is that social preferences explain player Bs’ behavior. In fact, even if the payoff dominant issue is reached, player B always earns less than player A: it could then be that player Bs take into consideration relative payoffs rather than their own earnings (see, e.g. Fehr and Schmidt (1999)). We have tested this hypothesis through companion experiments, reported in Jacquemet and Zylbersztejn (2011), in which the baseline treatment is compared with a treatment that equalizes payoffs between players in the Pareto–Nash equilibrium. We unambiguously reject the hypothesis that aversion to inequality is enough to account for player Bs’ striking behavior.

Experimental results from Charness and Dufwenberg (2006, 2008) substantiate the idea that impersonal messages, prefabricated by the experimenter, work effectively in coordination games, whereas in trust games a more customized free-form communication seems to be needed. Similarly, Bochet, Page, and Putterman (2006) find that free-form communication yields higher efficiency in a VCM game than numerical messages.

The recruitment uses Orsee (Greiner 2004); the experiment is computerized through software developed under Regate (Zeiliger 2000).

This 50–50 spread of genders is purely incidental.

Disciplines such as economics, engineering, management, political science, psychology, mathematics applied to social science, mathematics, computer science, sociology.

Heteroscedasticity is due to the linear probability specification. Even if the data generating process was i.i.d (i.e. , and and ) the model entails that: .

All p-values presented in the section below are associated with statistics computed according to this HC3 procedure. We also ran robustness checks by implementing the HC1 correction, which generally leads to lower estimated standard errors. Our choice is thus conservative as regards our ability to find significant differences in behavior. Based on a correction closely related to the HC3 procedure, Angrist and Lavy (2009) find an inflation of the cluster-robust standard errors by 10 up to 50%.

Fisher’s exact test does not reject the null hypothesis that player Bs’ decisions in round 1 come from the same distribution in all treatments (1.000). Model 3 in Table 4 suggests that the average proportion of decisions r in rounds 2–10 does not significantly differ from the initial round BT in either treatment: 0.952; CT: 1.000, OT: 0.318. Finally, on the basis of Model 1 in Table 4, we also test a joint hypothesis that the means in all treatments are statistically different in rounds 2–4 through : ⋂ . No difference arises either in this early stage ( 0.925), or in rounds 5–7 (0.932) or rounds 8–10 (0.917).

Based on Model 3, we assess the effect of observation against baseline through tests of . The differences are insignificant as regards reliance (), cooperation () coordination () and type I errors ().

We use Model 1 to test the joint hypothesis that in every triplet of rounds –2–4, 5–7 and 8–10 – a given outcome is equally frequent in both treatments, that is H₀: (CT + CT_rounds2–4 = OT + OT_rounds2–4)⋂(CT + CT_rounds5–7 = OT + OT_rounds5–7)⋂(CT + CT_rounds8–10 = OT + OT_rounds8–10). We find p = 0.688 for reliance, p = 0.669 for cooperation, p = 0.360 for coordination, p = 0.531 for type I error, and p = 0.949 for type II error.

Note, this way of separating player Bs implies that the first group comprises only those players who constantly played r before the current interaction. As a result, any player B with a perfect record who chooses l once in the game drops out from this category permanently, and becomes B_IP ever after.

None of these differences are significant, though: testing H₀ : CT_ReassMess = OT_PerfRep gives p = 0.475 for cooperation, p = 0.383 for coordination, p = 0.572 and p = 0.326 for type I and type II errors, respectively.

All comparisons made in this paragraph are based on tests of H₀: CT_NonReassMess = OT_ImPerfRep in the regressions in Table 6.

These results are obtained through an additional -test for equality of coefficients. For instance, in the latter case we test H₀: H(r) × PH[0;0.5[ = H(l) × PH[0;0.5[ in regression in column 3.

These results are obtained through additional tests for equality of coefficients in the regression in column 6: H₀: H(l) × PH(1) = H(l) × PH[0.5; 0.7[ and H₀: H(l) × PH(1) = H(l) × PH[0.7; 0.9[, respectively.

Due to this conditioning on historical behavior, we use observations from rounds 2–10.

The differences in reliability between both types of player Bs, shown in the second column of Table 9, are statistically significant according to our parametric test for equality of proportions, with p-values equal to 0.052, 0.002, 0.002, 0.050 for subsequent rows.

This paper is a revised version of CES Working Paper no. 2010–64. We thank Ibrahim Ahamada, Juergen Bracht, Timothy Cason, Boğaçhan Çelen, Gary Charness, Nick Feltovich, Pierre Fleckinger, Guillaume Fréchette, Nobuyuki Hanaki, Frédéric Koessler, Michal Krawczyk, Stéphane Luchini, Andreas Ortmann, Drazen Prelec, Stéphane Robin, Jean-Marc Tallon, and Erik Wengström for inspiring discussions; participants in numerous conferences, workshops and seminars for insightful comments; Maxim Frolov for his technical assistance in running the experiments, as well as financial support from University Paris 1 and the Paris School of Economics. Nicolas Jacquemet acknowledges the support of the Institut Universitaire de France. Adam Zylbersztejn is grateful to the State of Sao Paulo Research Foundation (FAPESP), the Collège des Ecoles Doctorales de l’Université Paris 1 Panthéon-Sorbonne, the Alliance Program and the Columbia University Economics Department for their support..