Abstract
This paper investigates experimentally the effects of communication in distinct games with complete information. We design four games resulting from the interaction between two incentive elements: strategic complementarity and coordination. These incentive elements allow to analyse the use of cheap talk as an efficiency-enhancing and coordinating device. We implement a restricted communication protocol (one-sided, optional, and closed-form) in repeated settings with fixed partners. Our findings provide robust evidence about how cheap talk interacts with incentives to explain strategic behaviour in a dynamic way. As expected, cheap talk increases efficiency under complementarity incentives, and the coordination level under coordination incentives. As novelty, the use of limited communication in repeated interactions has led to identify specific time-varying message profiles as the most effective messages in the coordination games. While the content of messages is explained by the complementarity incentives, faithfulness to credible messages is determined by the coordination incentives.
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Data Availability Statement
The dataset and the raw zTree files are available from the authors upon request.
Notes
In the Online Supplementary Material, we present the benchmark model (Section S.1), an additional descriptive and econometric analysis (Section S.2), and the experimental instructions (Section S.3).
Strategic complementarity is related to the positive effect of a change in a player’s choice on the marginal payoff of the other player (see Cooper, 1999; Eichberger and Kelsey, 2002 or Potters and Suetens, 2009 ). We say that strategies are non-complementary if a player cannot increase her payoff when the other player changes her action. See Morris and Shin (2002) and Nagel (1998) for alternative ways to introduce strategic complementarity in a BCG.
In section S.1 of the Online Supplementary Material, we characterise a general model and derive the properties of each game by setting specific values for two payoff function parameters.
Indeed, as we let subjects choose up to two decimals, the game has 3 symmetric equilibria: \(\{0,0\}\), \(\{0.01,0.01\}\) and \(\{0.02, 0.02\}\). From the viewpoint of payoff saliency in the lab, the difference between them is insignificant. Hence, we will assume that the Compl Non-Coord game has a unique Nash equilibrium given by \(\{0,0\}\).
Cooper and Kühn (2016) find that the effectiveness of one-way communication may be higher in sequential settings where players have future opportunities to modify previous actions or renegotiate messages. These authors compare the relative effectiveness of two communication protocols (limited messages vs. chat) in two-period sequential games. They allow subjects to communicate successively, so that messages can express intentions about contingent strategies (first-period actions and second-period actions as a function of the first-period outcome).
Besides, the optional protocol allows to identify those subjects who resort to secret handshakes to reach coordination. In games with private information, recent literature incorporates optional communication as a way of distinguishing between distinct behavioural models when players’ preferences are not aligned: preference for truth-telling, lying aversion, etc. (see, for example, Goeree and Zhang 2014 or Cai and Wang 2006). An example of optional communication in complete information games can be found in Andersson and Wengström (2012). In our experiment, the motivations for keeping silent depend on the specific game; for instance, in the Non-Compl Non-Coord game, rational players have incentives to avoid communication, so that non-rational players take more time attempting to capture the strategic features of the game.
In the game-theoretic sense, rationality assumes that players’ decisions are the result of maximising their own selfish payoff functions conditional on their beliefs about the other players’ optimal behaviour (see, Bicchieri 2004).
Yet, in the Non-Compl Coord game, all equilibria but 0 are “weak”, since players are indifferent between playing the equilibrium and deviating downwards. Hence, the sender has no strict preferences for playing the announced number if she (the sender) thought the receiver would believe her. Here, we can say that the messages are weakly credible.
Not only can a deceitful message have a psychological cost of lying for the sender, but also it can have the (small) effort of thinking about it. This could reduce the chance of sending deceitful messages when collusion is not expected.
Further results are presented at the treatment level in section S.2 in the Online Supplementary Material (see Table S.2 and Figures S.2 and S.3).
First-round data seem to indicate that players initially fail to completely comprehend the specific game they are playing. This can be due to the cumbersome frame used in the instructions.
Models M1 and M2 are panel data regressions where the dependent variable is the individual choice ([0, 100]). Models M3 and M4 are probit panel data models at the couple level where the dependent variable is a dummy that takes value 1 if the two members of a couple coordinate in a given period and 0 otherwise. All the models shown in Table 2, and Tables 4 and 5, are estimated with random effects and standard errors are corrected for clustering at the couple level (when individual data are utilized) due to the bias introduced by the fixed-matching procedure (see, Liang and Zeger 1986). To control for individual unobservable characteristics, we include the first-period value of the dependent variable in each regression. Therefore, to study the treatment effects and control for individual heterogeneity, we estimate random-effects panel models, rather than fixed-effects, and include initial decisions as independent variables.
For individual choices, we also tested for alternative specifications using random-effects two-limit Tobit models, with the dependent variable doubly censored at 0 and at 100. The estimates are fairly similar to those of the standard panel data model. We settle on the standard model, because it allows to control for couple effects.
We estimate linear regression models for choices and probit regression models for coordination. All of them use data at the couple level (in the case of choices, the average of the two numbers).
SURE tests for the equality of the coefficients of Compl give significant differences: for instance, for \(\beta _{\textsc {Compl}} (M9) = \beta _{\textsc {Compl}} (M10)\), \(\chi ^2 (1)= 13.75\), \(p< 0.001\).
In Sect. S.2 of the Online Supplementary Material, we provide additional analysis in Table S.3 and Figures S.5–S.9.
Recall that the sender of each couple is randomly selected at the beginning of the experiment and maintains that role along the six periods. Thus, we have 100 senders in total, 25 by treatment. Out of 100 senders, 12 subjects never send a message, and 35 subjects send messages in all periods.
A two-sided test for equality of proportions gives a result of \(z=0.505\), \(p= 0.610\). By treatment, the only case where there are significant differences between roles is Non-Compl Coord Comm: 72.5% for senders vs. 56.9% for receivers, \(z=2.34\), \(p=0.019\).
Models M13 and M14 present probit panel models to estimate the probability of submitting a message, models M15 and M16 give the panel data regressions for the message values submitted by the senders, and models M17 and M18 estimate the probability of being faithful (sender or receiver) by choosing the same number as the message value. The new explanatory variables are the following: (1) the initial values of the corresponding dependent variables (First Period Message, First Period Faith. and First Period Mess. Value); (2) the message content (Mess. Value) and its interaction terms with the design variables (Value\(\times\) Compl and Value\(\times\) Coord); and (3) the player role (Sender), a dummy that takes value 1 for the sender and 0 for the receiver.
The decreasing trend in faithfulness can be explained by simply pondering that the repetition of the game increases the chance of facing unfaithful behaviour of a player’s partner, which seems to be a dealbreaker for subjects. That is, a player is less likely to behave faithfully as the accumulated experience of unfaithful responses given by her partner increases along time. See Table S.4 in the Online Supplementary Material where the coefficient of Past Partner Unfaithfulness is negative.
Notice that, in our baseline game, the winner’s payoffs are fixed (50 points, 25 points in the case of a tie). Hence, in Non-Compl Non-Coord, the average profits must be exactly 25 points regardless of the communication condition.
We estimate three pairs of panel data models: (i) for profits at the couple level (models M19 and M20); (ii) for likelihood of coordinating on any outcome (models M21 and M22); and (iii) for likelihood of coordinating on equilibrium (models M23 and M24). Equil. Coord is a dummy variable that takes value 1 when subjects coordinate at an equilibrium strategy [any number in the Coord games and (0,0) in the Non-Coord games]. As explanatory variables, we include: (i) the corresponding first-period values of the dependent variables; (ii) a dummy for the use of pre-play communication, Message Use; (iii) two dummies for the extreme values of messages 0 and 100, Mess0 and Mess100, and (iv) the number of past instances of unfaithfulness at the couple level, Past Unfaithfulness. In the second model of each pair, we incorporate the interaction terms of the communication variables with Compl and Coord.
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Acknowledgements
The authors gratefully acknowledge the support of the editor and the valuable reports of two anonymous referees which have considerably improved the final version of the paper. We also thank Peter Moffatt, Subhasish Modak Chowdhury, Anders Poulsen, Enrique Fatás, and Miguel Angel Meléndez-Jiménez for helpful comments and suggestions. This research benefited from financial support supplied by the Spanish Ministry of Science (grants RTI2018-097620-B-I00 and MEC-ECO2014-52345P) and the Junta de Andalucía (Grant SEJ-08065).
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Jiménez-Jiménez, F., Rodero Cosano, J. Experimental cheap talk games: strategic complementarity and coordination. Theory Decis 91, 235–263 (2021). https://doi.org/10.1007/s11238-020-09795-9
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DOI: https://doi.org/10.1007/s11238-020-09795-9