On the Impact of an Intermediary Agent in the Ultimatum Game
Abstract
:1. Introduction
2. Background
3. Theory and Hypotheses
3.1. Agent Preferences
3.2. Hypotheses
4. Experimental Design
5. Results
5.1. Proposer Behavior
5.2. Responder Behavior
5.3. Agent Behavior
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Instructions for the Experiment
- Setting 1 ‘Nonbinding proposal’: The proposed offer is nonbinding. The agent is not obligated to make the proposed offer.
- Setting 2 ‘Binding proposal’: The proposed offer is binding. The agent is obligated to make the proposed offer.
- Setting 3 ‘Upper Bound’: The proposer sets a binding Upper Bound. The agent is obligated to make an offer equal to or lower than the binding Upper Bound.
- Setting 4 ‘Lower Bound’: The proposer sets a binding Lower Bound. The agent is obligated to make an offer equal to or higher than the binding Lower Bound.
- Payments:
- Proposer choice screen:
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
What is your proposed offer to be paid to the Responder, to be made at your own expense? | | | | | | | | | | |
- Agent choice screen in the Nonbinding proposal condition (the screen in other conditions was slightly modified to reflect the boundaries of the respective condition):
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
What is your offer if the Proposer’s proposed offer is 0? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 1? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 2? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 3? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 4? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 5? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 6? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 7? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 8? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 9? | | | | | | | | | | |
What is your offer if the Proposer’s proposed offer is 10? | | | | | | | | | | |
- Responder choice screen:
Reject | Accept | |
What is your offer if the Proposer’s proposed offer is 0? | | |
What is your offer if the Proposer’s proposed offer is 1? | | |
What is your offer if the Proposer’s proposed offer is 2? | | |
What is your offer if the Proposer’s proposed offer is 3? | | |
What is your offer if the Proposer’s proposed offer is 4? | | |
What is your offer if the Proposer’s proposed offer is 5? | | |
What is your offer if the Proposer’s proposed offer is 6? | | |
What is your offer if the Proposer’s proposed offer is 7? | | |
What is your offer if the Proposer’s proposed offer is 8? | | |
What is your offer if the Proposer’s proposed offer is 9? | | |
What is your offer if the Proposer’s proposed offer is 10? | | |
Appendix B. Investigating Whether the Agent’s Own Proposal in the Proposer’s Role Affects His Response to the Partnered Proposer’s Proposal
Parameter | Unrestricted Menu | Restricted Menu |
---|---|---|
Setting ‘No Bounds’ (440 observations, 40 clusters) | ||
Intercept | 0.859 (1.215) | 0.640 (0.677) |
Proposer’s Proposal | 0.430 * (0.073) | 0.334 * (0.058) |
Agent’s own proposal in proposer’s role | 0.317 (0.185) | 0.553 * (0.127) |
LL | −1022.663 | −906.399 |
Setting ‘Upper Bound’ (440 observations, 40 clusters) | ||
Intercept | 3.931 * (1.363) | −0.744 (0.811) |
Proposal | 0.219 * (0.081) | 0.377 * (0.054) |
Agent’s own proposal in proposer’s role | 0.071 (0.156) | 0.568 * (0.133) |
LL | −563.805 | −619.838 |
Setting ‘Lower Bound’ (440 observations, 40 clusters) | ||
Intercept | −0.069 (1.333) | −0.126 (0.868) |
Proposal | −0.067 (0.134) | 0.288 * (0.069) |
Agent’s own proposal in proposer’s role | 0.612 * (0.193) | 0.723 * (0.192) |
LL | −433.637 | −580.520 |
Pooled settings (1320 observations, 40 clusters) | ||
Intercept | 1.077 (0.872) | 0.378 (0.500) |
Proposal | 0.345 * (0.060) | 0.313 * (0.046) |
Agent’s own proposal in proposer’s role | 0.332 * (0.128) | 0.571 * (0.104) |
LL | −2045.113 | −2152.925 |
Sum of non-pooled LL from the three earlier regressions | −2020.105 | −2106.757 |
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Model 1. The agent’s offer is independent of the proposer’s specification, absent of a binding constraint. |
Model 2. The agent perceives any constraint as a communication and reacts to such communication monotonically and similarly over settings. |
Unrestricted Menu | Restricted Menu | |
---|---|---|
Nonbinding Proposal | 40 participants | 40 participants |
Binding Proposal | 40 participants | 40 participants |
Upper Bound | 40 participants | 40 participants |
Lower Bound | 40 participants | 40 participants |
Manipulation | Description | |
Proposal Format | ||
Nonbinding proposal | The proposal is nonbinding. The agent is not obligated to make the proposed offer. | |
Binding proposal | The proposal is binding. The agent is obligated to make the proposed offer. | |
Upper Bound | The proposer sets a binding Upper Bound. The agent is obligated to make an offer equal to or lower than the upper bound. | |
Lower Bound | The proposer sets a binding Lower Bound. The agent is obligated to make an offer equal to or higher than the lower bound. | |
Menu Display | ||
Unrestricted Menu | The agent is shown the full range of contingent offers for each potential proposal, but is restricted to choosing only qualified offers that do not violate proposer-imposed boundaries | |
Restricted Menu | The agent is shown only the range of qualified offers for each potential proposal that do not violate proposer-imposed boundaries |
Proposal Format | Unrestricted Menu | Restricted Menu |
---|---|---|
Nonbinding proposal | 4.825 (0.354) | 5.125 (0.362) |
Binding proposal | 5.100 (0.377) | 5.125 (0.351) |
Upper Bound | 5.600 (0.347) | 6.000 (0.330) |
Lower Bound | 3.675 (0.344) | 4.400 (0.363) |
F-test for the joint effect of Setting (all 4 settings) | F(3, 156) = 5.36, p = 0.002 | F(3, 156) = 3.46, p = 0.018 |
Proposal Format | Unrestricted Menu | Restricted Menu |
---|---|---|
Nonbinding proposal | 2.750 (0.301) | 2.200 (0.315) |
Binding proposal | 2.750 (0.323) | 2.200 (0.313) |
Upper Bound | 2.725 (0.302) | 2.275 (0.297) |
Lower Bound | 2.400 (0.288) | 2.325 (0.321) |
F-test for the joint effect of setting (all 4 settings) | F(3, 156) = 0.32, p = 0.813 | F(3, 156) = 0.04, p = 0.990 |
Parameter | Unrestricted Menu | Restricted Menu |
---|---|---|
Setting 1 ‘Nonbinding Proposal’ (440 observations, 40 clusters) | ||
Intercept | 2.703 * (0.484) | 3.476 * (0.441) |
Proposal | 0.430 * (0.073) | 0.334 * (0.058) |
LL | −1021.193 | −985.71129 |
Setting 2 ‘Upper Bound’ (440 observations, 40 clusters) | ||
Intercept | 4.400 * (0.707) | 2.768 * (0.483) |
Proposal | 0.219 * (0.081) | 0.360 * (0.057) |
LL | −564.320 | −662.964 |
Setting 3 ‘Lower Bound’ (440 observations, 40 clusters) | ||
Intercept | 2.770 * (0.702) | 2.980 * (0.316) |
Proposal | −0.067 (0.118) | 0.296 * (0.064) |
LL | −454.986 | −629.412 |
Pooled settings (1320 observations, 40 clusters) | ||
Intercept | 2.891 * (0.416) | 3.209 * (0.368) |
Proposal | 0.365 * (0.059) | 0.341 * (0.043) |
LL | −2093.569 | −2298.462 |
Sum of non-pooled LL from the three earlier regressions | −2040.499 | −2278.087 |
F-test for the joint effect of Setting (excluding ‘Binding Proposal’) | F(2, 1314) = 50.38, p < 0.001 | F(2, 1314) = 98.61, p < 0.001 |
F-test for the joint effect of Setting × Proposal | F(2, 1314) = 24.51, p < 0.001 | F(3, 1314) = 42.21, p < 0.001 |
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Haruvy, E.; Roth, Y. On the Impact of an Intermediary Agent in the Ultimatum Game. Games 2022, 13, 43. https://doi.org/10.3390/g13030043
Haruvy E, Roth Y. On the Impact of an Intermediary Agent in the Ultimatum Game. Games. 2022; 13(3):43. https://doi.org/10.3390/g13030043
Chicago/Turabian StyleHaruvy, Ernan, and Yefim Roth. 2022. "On the Impact of an Intermediary Agent in the Ultimatum Game" Games 13, no. 3: 43. https://doi.org/10.3390/g13030043