2. The Model and the Theoretical Predictions
2.1. The Simultaneous Game
2.2. The Sequential Game
2.3. The Choice Game
3. Experimental Design and Procedures
4. Experimental Results
5. Logistic Analysis for the Choice Treatment
6. Discussion and Concluding Remarks
Conflicts of Interest
Appendix A. Instructions
Appendix B. Proofs of Propositions
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Also, in order to explain the observed differences in behavior of senders and receiver in simultaneous and sequential plays, we use a logit agent quantal response equilibrium (logit-AQRE) model, following  and . We present the maximum likelihood estimation results of this model in the online appendix at: http://isaglam.etu.edu.tr/BGOS-2020-Online-Appendix.pdf.
For example, [9,10,11,12,13] among others extend the basic one sender and one receiver model in Crawford and Sobel  by allowing two perfectly informed senders. [14,15,16] consider the case with two imperfectly informed senders while [15,16] also analyze the effects of alternative communication modes, namely simultaneous and sequential transmission of information. A common feature of these extensions is that the policy space is unidimensional, while [17,18,19,20,21,22] consider multidimensional models of cheap talk.
An alternative behavioral explanation for excessive truth-telling is provided by Sánchez-Pagés and Vorsatz  using their baseline and punishment games in  with a modification that the sender in the baseline game additionally has a costly option of remaining silent. They show that overcommunication in the baseline game can be attributed to lying aversion.
Several papers have also studied the robustness of overcommunication phenomenon. For example, Peeters et al.  show that overcommunication of the sender disappears in the presence of rewards, whereas the trust by the receiver increases significantly. Gurdal et al.  analyze the robustness of excessive truth-telling and trust to the intervention of an honest regulator (equivalently to the presence of non-strategic sender types). They show that excessive truth-telling and excessive trust are higher under intervention than under the absence of intervention.
For instance, , and , , constitute an equilibrium.
We consider the observer role so as to check whether our subjects, when they are neither the receiver nor a sender, are able to make correct guesses about the outcomes of the games.
Given that the subjects make choices in the same group for 36 periods, it may be a valid concern that anonymity may have been somewhat disregarded as the repetition could have an effect in the experiment even though the roles are randomly assigned in each period within a group. Since all treatments may be affected to some extent by the repetition, we believe that the differences in treatments are not due to the repetition effect. Moreover, our experimental results indicate that the behavior of the players are not significantly different than the theoretical predictions of the one-shot game in most of the cases (see Section 4). As the choice of running sessions with groups of 4 is essentially done for using non-parametric tests for the receiver behavior in the Choice Treatment, our estimation finding (Result 4 in Section 5) in that regard shows that the receiver values the information acquired in the previous period more than the information acquired in all other past periods in the Choice Treatment. These results imply that the learning effect due to repetition must be minimal.
Looking at the 276 instances during the Choice Treatment, we see that the receivers preferred simultaneous messages in 152 cases (55%) and sequential messages in 124 cases (45%).
The theoretical predictions for the probabilities in the first and last rows are 1/2, whereas the theoretical prediction for the probability that the two senders’ messages are non-conflictive in simultaneous plays is .
The theoretical predictions for the probabilities in the first two rows and the last row are 1/2. The theoretical predictions for the probabilities in all the remaining rows are arbitrary in the interval . To see this, one can check that the probability that sender 2 is truthful when sender 1 is truthful is . Similarly, the probability that sender 2 is truthful when sender 1 lies is . One can also check that the probability that senders are non-conflictive is .
Also, the receiver is statistically significantly the least likely to select simultaneous play if the receiver earned the high payoff in a sequential play in the last period. Also, high ratio of nonconflicting messages in both the Simultaneous and the Sequential Treatment increases the likelihood of simultaneous choice in the Choice Treatment, while the estimated impact is larger in the Simultaneous Treatment than in the Sequential Treatment.
|Table A||Sender 1||Sender 2||Receiver|
|Table B||Sender 1||Sender 2||Receiver|
|Simultaneous Treatment||Choice Treatment|
|% Sender is truthful||54.0 *||49.0 *|
|% Senders are non-conflictive||51.4 **||53.4 **|
|% Non-conflicting messages||58.2 *||50.2 *|
|Sequential Treatment||Choice Treatment|
|% Sender is truthful||53.3 *||52.3 *|
|% Sender 1 is truthful||50.0 *||51.6 *|
|% Sender 2 is truthful when||54.0 **||48.0 **|
|sender 1 is truthful|
|% Sender 2 is truthful when||58.9 **||63.0 **|
|sender 1 lies|
|% Senders are non-conflictive||46.4 **||45.9 **|
|% Non-conflicting messages||54.5 *||62.5 *|
|Simultaneous Messages||Sequential Messages|
|Simultaneous Treatment||59.2 *||Sequential Treatment||52.3 *|
|Choice Treatment||50.7 *||Choice Treatment||48.6 *|
|Simultaneous Messages||Sequential Messages|
|Simultaneous Treatment||56.5 *||Sequential Treatment||59.6 *|
|Choice Treatment||61.3 *||Choice Treatment||55.1 *|
|Number of Times Simultaneous||Number of Subjects|
|Messages Is Preferred|
|% Guesses of Favorable||% Correct|
|Outcome for the Receiver||Guesses|
|Simultaneous Treatment||44.2 *||45.7 *|
|Sequential Treatment||48.2 *||48.2 *|
|Choice Treatment (Simultaneous)||59.1 *||51.2 *|
|Choice Treatment (Sequential)||55.2 *||44.5 *|
|Simwon (1 if previous play was simultaneous and||2.43 **||1.81||1.14||2.27 *||1.72||1.12|
|receiver earned high payoff)||(2.06)||(0.84)||(0.32)||(1.92)||(0.8)||(0.28)|
|Seqwon (1 if previous play was sequential and||0.47 *||0.68||0.43 **||0.43 *||0.67||0.41 **|
|receiver earned high payoff)||(−1.74)||(−0.71)||(−2.41)||(−1.93)||(−0.74)||(−2.44)|
|Simlost (1 if previous play was simultaneous and||1.18||2.02||1.08||1.90|
|receiver earned low payoff)||(0.42)||(1.33)||(0.21)||(1.24)|
|Simwonnc (1 if previous play was simultaneous with||3.67 **||3.67 **||3.70 **||3.68 **|
|nonconflicting messages and receiver earned high payoff)||(1.96)||(1.96)||(2.04)||(2.04)|
|Seqwonnc (1 if previous play was sequential with||0.99||0.88|
|nonconflicting messages and receiver earned high payoff)||(−0.01)||(−0.24)|
|Simlostnc (1 if previous play was simultaneous with||0.72||0.70|
|nonconflicting messages and receiver earned low payoff)||(−0.71)||(−0.77)|
|Seqlostnc (1 if previous play was sequential with||2.05||2.10|
|nonconflicting messages and receiver earned low payoff)||(1.33)||(1.45)|
|Average payoff of the receivers over simultaneous plays,||0.97||0.95||0.90||0.91|
|updated in the Choice Treatment||(−0.14)||(−0.27)||(−0.59)||(−0.51)|
|Average payoff of the receivers over sequential plays,||1.26||1.27 *||1.26 *||1.26|
|updated in the Choice Treatment||(1.47)||(1.76)||(1.67)||(1.61)|
|Ratio of nonconflicting messages in the Simultaneous||8.88||2.88||2.59||2.53||5.26||4.73||4.68|
|Ratio of nonconflicting messages in the Sequential||1.46||1.30||1.27||1.26||1.65||1.72||1.71|
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