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The gift of advice: communication in a bilateral gift exchange game

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An Erratum to this article was published on 30 July 2013

Abstract

We augment a standard bilateral gift exchange game so employees can send messages at the same time as choosing an effort level. Employee effort (controlling for wages) is unaffected by allowing messages, but wages dramatically increase. Messages affect wages because employees give managers advice to set higher wages, usually explaining that this will result in higher effort. This advice prompts managers to try higher wages, helping them learn that raising wages increases their payoffs. In a follow-up experiment, we directly provide managers with additional information about the relationship between wages and effort. This too causes wages to increase, but to a lesser extent than allowing messages. Our results highlight the critical role of learning in generating gains from positive gift exchange.

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Notes

  1. Incomplete meaning that workers cannot pre-commit to an effort level and managers have no means of sanctioning low effort either through enforceable incentive contracts or termination of the manager-employee relationship.

  2. The results of Charness and Dufwenberger (2006) imply that wages will be higher if employees can send a message before a wage is chosen since employees can promise to choose a high effort in exchange for a high wage.

  3. For related results see Chaudhuri et al. (2006) and Celen et al. (2010).

  4. See Xiao and Houser (2009) for related results with dictator games. See Wubben et al. (2009) and Van Dijke and De Cremer (2011) for psychology studies of the relationship between communication, emotions, and reciprocity.

  5. In other related work, Noussair and Tucker (2005) study public goods games in which monetary and non-pecuniary punishment are available. Adding non-pecuniary punishment leads to a slight increase in contributions and a more substantial increase in earnings due to lower use of monetary punishments. Non-pecuniary punishment is limited to the assignment of punishment points, so the effects we observe from advice are not possible.

  6. Thirty seconds is long enough for employees to send substantive messages, but not so long that the session grinds to a halt if one employee is especially loquacious. The median length of a message is only 25 characters, but subjects could and did type much longer messages—the longest message was 159 characters, 17 messages had at least 100 characters, and 124 out of 478 messages had at least 50 characters.

  7. Using the functional form of Cox et al. leads to a prediction that adding messages by responders to an ultimatum game should raise rejection rates rather than lowering them as observed by Xiao and Houser (2005). To get the model to correctly predict the effect of responder messages in the ultimatum game, the functional form needs to be modified so the willingness to punish increases, ceteris paribus, as the other player’s payoff increases.

  8. To make the model simple, employees can send a single message which has a fixed cost and imposes a fixed cost (benefit) on the manager if a negative (positive) message is sent. We could have built a more complex version of the model where the employee chooses the intensity of the message. Mathematically, let c(i) be the cost of sending a message with intensity i and let the manager’s benefit (cost) of receiving a positive (negative) message equals its intensity. Assume c′>0 and c″>0. Assuming the second derivative is positive makes it simple to construct examples where a message is sent and positive effort is provided. Similar conclusions can be derived from a model of this sort, but the gain in insight is small relative to the gain in complexity.

  9. This conclusion is based on a t-test using Round 1 data. The t-statistic is 0.772.

  10. To test for statistical significance, we have run t-tests comparing earnings across treatments. We treat the sum of earnings for a subject over the ten round block as a single observation. The earnings of managers (234 vs. 185; t=2.71) and employees (450 vs. 357; t=7.84) are significantly higher at the 1 % level for Rounds 1–10 in the Messages First treatment.

  11. Comparing Rounds 1–10 with Rounds 11–20, the increase in manager payoffs in the Messages Second treatment is statistically significant at the 5 % level (208 vs. 185; t=2.15).

  12. Comparing Rounds 1–10 with Rounds 11–20, the increase in employee payoffs in the Messages Second treatment is statistically significant at the 1 % level (431.3 vs. 357; t=6.39).

  13. Rounds with messages are Rounds 1–10 of Messages First and Rounds 11–20 of Messages Second. Rounds without messages are Rounds 11–20 of Messages First and Rounds 1–10 of Messages Second.

  14. This is shown by modifying Model 2 in Table 2. Define reverse wage = 100—wage and replace wage with reverse wage every place that wage appears. The parameter estimate for “Rounds 11–20” now measures whether effort changes with experience for a wage of 100. The parameter estimate for “Rounds 11–20” equals −6.59 with a standard error of 6.23.

  15. Effort rises slightly for wages in the 80–99 range, but the number of observations is small.

  16. See the estimates for “Messages First, Rounds 6–20” and “Messages Second, Rounds 6–20”.

  17. The two parameters also fail to be jointly significant (F=0.81; 2 d.f.; p=0.44).

  18. 53 % of the messages coded as advice were also coded for negative responses.

  19. Cohen’s κ for the three categories are .92, .71, and .74 respectively.

  20. The non-negligible frequency of positive responses for very low wages is due to sarcasm. Coders were instructed to code what was literally said rather than trying to infer the true meaning. When an employee sends a message of “Thanks!” following a wage of 0, this is coded as a positive response even though we doubt the employee was expressing genuine gratitude.

  21. In other words, managers might care that employees are happy with a high wage or unhappy with a low wage. The messages may help them learn how happy or unhappy the employees are following a specific wage.

  22. We have run a χ 2 test to check whether there is a significant difference in the probability of trying a high wage at some point subject to not choosing a high wage in the first round. The difference between the two treatments is significant at the 1 % level (χ 2=12.02).

  23. These statements are based on tobits regressing wages on period within the 10 period block with communication.

  24. Averaging across coders, advice is given for 15 % of observations in both blocks.

  25. The data used for feedback was drawn with replacement before each session. We constructed the draw to diversify the feedback wages within rounds and to limit repetition of similar feedback wages across rounds. Specifically, in each round of each session there were always at least two wages drawn from each quintile of the wage distribution. With a few exceptions, a manager’s feedback was not drawn from the same quintile of the wage distribution in two consecutive rounds. Subjects were given no details about how the draw was constructed.

  26. Calculating the correlation for each manager’s additional feedback and then averaging across managers, the average correlation observed between wage and effort was 0.51.

  27. For examples of papers where pre-play communication increases cooperation in social dilemmas where cooperation is not consistent with an equilibrium, see Dawes et al. (1977); Isaac and Walker (1988); Charness and Dufwenberger (2006); and Cason and Mui (2009).

  28. For examples see Cooper and Kagel (2005), Kocher and Sutter (2005); and Feri et al. (2010).

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Acknowledgements

We would like to thank Mark Owens and John Kagel for sharing their experimental software with us and Arno Riedl for sharing the raw data from Fehr et al. (1993) with us. Brent Davis, John Jensenius III, Philip Brookins, and David Johnson provided us with valuable research assistance. We would like to thank Jordi Brandts, Dan Friedman, Dan Houser, John Kagel, Quoc Tran, and seminar participants at Florida State University, Georgia State University, the University of Innsbruck, University of California—Santa Cruz, the Economic Science Association meetings, and the Southern Economic Association meetings for providing useful advice.

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Correspondence to John P. Lightle.

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Cooper, D.J., Lightle, J.P. The gift of advice: communication in a bilateral gift exchange game. Exp Econ 16, 443–477 (2013). https://doi.org/10.1007/s10683-012-9347-3

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