Abstract
We conduct a multi-round experiment on a punishment game using both the strategy method and the direct-response method. In the game, the sender may make decisions that are either favorable or unfavorable to the receiver, whereas the receiver may reward the favorable decision and/or punish the unfavorable decision. The hot-versus-cold effect is observed in both sender behaviors and receiver behaviors. Under the strategy method, the senders more often adopt decisions that are favorable to the receivers, whereas the receivers impose punishment more frequently than under the direct-response method. We suggest that in the multi-round experiment, the strategic value of punishment dominates the taste for punishment from the perspective of the receiver. According to our explanation based on mental accounting, the utility of imposing punishment is higher under the strategy method than under the direct-response method. Hence, the receiver is more likely to make punishment decisions. This difference in receiver behaviors prompts the sender to make receiver-favorable decisions more frequently under the strategy method.
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Acknowledgements
The authors thank the editors and anonymous referees for their comments and suggestions, which are helpful to improve the paper. Also many thanks to all members of our research group for discussions in regular group meeting. This research is supported by the National Natural Science Foundation of China under Grant 71210002.
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Appendix: Experimental instructions
Appendix: Experimental instructions
Summary We thank you for your participation in this experimental session. Please note that all the information you receive in the experiment is authentic, neither misleading nor deceptive. Please always feel free to inquire the experimenter if you have any questions. You are kindly asked not to talk to other participants during the experiment. Please keep your mobile phone off or muted.
You will receive monetary payoff for the experiment. Your final payoff will be the sum of the experimental payoff and a show-up fee of CNY 10. During the experiment, you will be paired with other participants, and your experimental payoff will be jointly determined by the decisions of yours and your opponents’. Your experimental payoff may differ if you adopt different decisions.
Decision task In each pair of participants, one plays as role A and the other as role B. Each round of decision task consists of three stages.
In the first stage, player A declares an (non-binding) intention of A’s action, i.e. A1 or A2, in the second stage. Player A’s action in the following stage can be either consistent or inconsistent to the declaration. Player B will be informed of the declaration once it has been made.
In the second stage, player A chooses an action between A1 and A2, while player B simultaneously chooses an action between B1 and B2. Once the actions have been determined, the players will be informed of the other party’s action. The following table shows possible payoffs after the second stage. If player B chooses B1, the current decision round terminates without the third stage; otherwise player B chooses B2, and the current decision round proceeds to the third stage.
B1 | B2 | |
|---|---|---|
A1 | A: 2, B: 2 | A: 6, B: 9 |
A2 | A: 2, B: 2 | A: 12, B: 3 |
In the third stage, player B makes a decision based on the results in the second stage. If A has chosen A1, then B may choose either B3 to accept the payoffs determined in the second stage or B4 to change the payoffs. Similarly, if A has chosen A2, then B may choose either B5 to accept the payoffs determined in the second stage or B6 to change the payoffs. The following table shows possible payoffs after the third stage.
Results of stage 2 | Payoffs of stage 2 | Decision in stage 3 | Final payoffs |
|---|---|---|---|
A1, B2 | A: 6, B: 9 | B3 | A: 6, B: 9 |
B4 | A: 8, B: 7 | ||
A2, B2 | A: 12, B: 3 | B5 | A:12, B: 3 |
B6 | A: 2, B: 2 |
Feedback information By the end of each decision round, you will be informed of the results of this round, which include the decisions made by you and your opponent in all the three stages and the corresponding payoffs.
Experimental protocols The experiment will be conducted for 40 rounds. Your role is fixed during the 40 rounds. You will be matched randomly with participants of the opponent role, and will not be matched with the same opponent in two successive rounds. You will be informed of neither the identities nor the historical decisions of your opponents.
Experimental payoff Your experimental payoff is determined by your cumulative payoff during the 40 rounds with conversion coefficient 0.25.
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Zhao, Y., Zhao, X. & Shen, ZJ.M. The hot-versus-cold effect in a punishment game: a multi-round experimental study. Ann Oper Res 268, 333–355 (2018). https://doi.org/10.1007/s10479-017-2412-8
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DOI: https://doi.org/10.1007/s10479-017-2412-8