# Inequality Aversion and Reciprocity in Moonlighting Games

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Design

**Figure 1.**Strategy space of the game (blue for Treatment 1 and orange for Treatment 2). The emphasized circles denote the status quo payoff distribution. Player 1 may move to another distribution by taking (empty circle of same color) or sending money (filled circle of same color). Player 2 may punish or reward by moving along the corresponding lines in the indicated directions.

## 3. Predictions

Model | Prediction |

Inequality aversion | T1: Player 2 does not punish after Player 1 has sent and does not sent after Player 1 has taken. T2: Player 2 does not punish after any action of Player 1. |

Fehr-Schmidt | T1, T2: Player 2 either equalizes payoffs or does nothing. |

Naive reciprocity | T1, T2: Player 2 does not punish after Player 1 has sent and does not send after Player 1 has taken. |

Dufwenberg-Kirchsteiger general | Kind equilibrium: Player 2’s sent amount in T2 > T1, but sending is less likely. Unkind equilibrium: Player 2’s punishment in T2 > T1. |

Dufwenberg-Kirchsteiger linear | See above, but only extreme amounts should be observed (sending all or punish the maximum). |

Falk-Fischbacher | T2: No punishment should be observed. Under reasonable assumptions Player 2’s sent amount in T2 > T1. |

Cox-Friedman-Sadiraj | Player 2’s sent amount in T2 ≥ T1 and Player 2’s punishment in T2 ≤ T1. For similar budget sets Player 2’s sent amount in T1 > T2 and Player 2’s punishment in T2 > T1. |

## 4. Results

#### 4.1. Overview

**Table 2.**Player 2 behavior in the Moonlighting-game with almost equal endowments (Treatment 1). DecTx and DecSy are the decisions of Player 2 after Player 1 has taken x EMU or sent y EMU, respectively, where sending y implies gains of 3y for Player 2. A positive value indicates the number of EMU sent back, a negative value the number of reduction points assigned, where each reduction point costs 3 EMU to player 1.

Treatment 1 | |||||||

Subject(s) | DecT9 | DecT6 | DecT3 | DecT0 | DecS3 | DecS6 | DecS9 |

3,7,9,27,31,33,37,43,45 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | 0 | 0 | 0 | –3 | 0 | 0 | 0 |

5 | 0 | 0 | 0 | 0 | 5 | 10 | 15 |

11 | –8 | –6 | –3 | 0 | 0 | 0 | 0 |

13 | –8 | –4 | –3 | –1 | 3 | 6 | 9 |

15 | –5 | –4 | –3 | 2 | 3 | 5 | 8 |

17 | 0 | 0 | 0 | 0 | 3 | 3 | 3 |

19 | 0 | 0 | 0 | 0 | 3 | 0 | 0 |

21 | –3 | –3 | 3 | 0 | 3 | 6 | 9 |

23 | –6 | –4 | –2 | 0 | 1 | 3 | 5 |

25 | 0 | 0 | 0 | 0 | 3 | 6 | 9 |

29 | –3 | –2 | –1 | 0 | 0 | 0 | 0 |

35,41 | –3 | –2 | –1 | 0 | 3 | 6 | 9 |

39 | –4 | –3 | –2 | 0 | 6 | 9 | 12 |

**Table 3.**Player 2 behavior in the Moonlighting-game with unequal endowments (Treatment 2). DecTx and DecSy are the decisions of Player 2 after Player 1 has taken x EMU or sent y EMU, respectively, where sending y implies gains of 3y for Player 2. A positive value indicates the number of EMU sent back, a negative value the number of reduction points assigned, where each reduction point costs 3 EMU to player 1. Subject 59 is apparently confused.

Treatment 2 | |||||||

Subject(s) | DecT9 | DecT6 | DecT3 | DecT0 | DecS3 | DecS6 | DecS9 |

51,55,57,63,65,67,69,71,81,95 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

53 | 0 | 0 | 0 | 0 | 5 | 10 | 15 |

59 | 7 | –2 | –4 | 2 | –3 | 6 | 5 |

61 | –2 | –1 | –1 | 0 | 0 | 1 | 1 |

73 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

75 | –8 | –6 | –3 | 0 | –3 | –3 | 3 |

77 | 0 | 0 | 0 | 0 | 1 | 2 | 3 |

79 | –8 | –7 | –6 | 15 | 22 | 27 | 33 |

83 | –2 | 0 | 0 | 0 | 1 | 2 | 3 |

85 | 13 | 19 | 25 | 31 | 43 | 55 | 67 |

87 | –8 | –7 | –6 | 0 | 12 | 15 | 18 |

89 | –3 | –2 | –1 | 0 | 3 | 6 | 9 |

91 | –3 | –3 | –3 | 0 | 0 | 0 | 0 |

93 | –1 | –2 | 1 | 0 | 3 | 2 | –2 |

97 | –5 | –4 | –3 | –2 | 5 | 8 | 10 |

**Result 1**: If inequality aversion and reciprocity agree, after Player 1 has taken money in Treatment 1, most of the behavior is consistent. If inequality aversion and reciprocity predict different behavior, after Player 1 has taken money in Treatment 2, most of the observed non-selfish behavior is inconsistent with inequality aversion.

**Result 2**: Even when Player 2 sends money to Player 1, this is almost never eliminating inequality.

#### 4.2. Statistical Tests for the Role of Inequality Aversion

**Result 3**: Across treatments, if the actions by Player 1 are the same but the resulting inequality differs, the reactions by Player 2 do not differ significantly.

#### 4.3. Statistical Tests for the Role of Intuitive Notions of Reciprocity

**Result 4**: Across treatments, if the actions by Player 1 are different but the resulting inequality is the same, the reactions by Player 2 differ significantly, in line with reciprocity.

#### 4.4. Considering Predictions by the Reciprocity Models

**Result 5**: The qualitative predictions derived for the Dufwenberg-Kirchsteiger and Falk-Fischbacher models are not supported.

#### 4.5. Behavior of Player 1

**Result 6**: Player 1 behavior differs very little across treatments, in contrast to the predictions of inequality aversion.

## 5. Discussion and Concluding Remarks

## Acknowledgements

## References

- Fehr, E.; Schmidt, K.M. A theory of fairness, competition, and cooperation. Quart. J. Econ.
**1999**, 114, 817–868. [Google Scholar] [CrossRef] - Bolton, G.E.; Ockenfels, A. ERC—A theory of equity, reciprocity, and competition. Amer. Econ. Rev.
**2000**, 90, 166–193. [Google Scholar] [CrossRef] - Charness, G.; Rabin, M. Understanding social preferences with simple tests. Quart. J. Econ.
**2002**, 117, 817–869. [Google Scholar] [CrossRef] - Engelmann, D.; Strobel, M. Inequality aversion, efficiency, and maximin preferences in simple distribution experiments. Amer. Econ. Rev.
**2004**, 94, 857–869. [Google Scholar] [CrossRef] - Cox, J.C.; Sadiraj, V. Direct tests of individual preferences for efficiency and equity. Econ. Inq. (Forthcoming).
- Engelmann, D.; Strobel, M. Preferences over income distributions: Experimental evidence. Public Financ. Rev.
**2007**, 35, 285–310. [Google Scholar] [CrossRef] - Cox, J.C. How to identify trust and reciprocity. Game. Econ. Behav.
**2004**, 46, 260–281. [Google Scholar] [CrossRef] - Falk, A.; Fehr, E.; Fischbacher, U. On the nature of fair behavior. Econ. Inq.
**2003**, 41, 20–26. [Google Scholar] [CrossRef] - Falk, A.; Fehr, E.; Fischbacher, U. Testing theories of fairness—Intentions matter. Game. Econ. Behav.
**2008**, 62, 287–304. [Google Scholar] [CrossRef] - Falk, A.; Fehr, E.; Fischbacher, U. Driving forces behind informal sanctions. Econometrica
**2005**, 73, 2017–2030. [Google Scholar] [CrossRef] - Kagel, J.H.; Wolfe, K. Tests of fairness models based on equity considerations in a three-person ultimatum game. Exp. Econ.
**2001**, 4, 203–219. [Google Scholar] [CrossRef] - Bolton, G.E.; Brandts, J.; Ockenfels, A. Measuring motivations for the reciprocal responses observed in a simple dilemma game. Exp. Econ.
**1998**, 1, 207–219. [Google Scholar] [CrossRef] - Berg, J.; Dickhaut, J.; McCabe, K. Trust, reciprocity, and social history. Game. Econ. Behav.
**1995**, 10, 122–142. [Google Scholar] [CrossRef] - Abbink, K.; Irlenbusch, B.; Renner, E. The moonlighting game. J. Econ. Behav. Organ.
**2000**, 42, 265–277. [Google Scholar] [CrossRef] - Fischbacher, U. z-Tree: Zurich toolbox for ready-made economic experiments. Exp. Econ.
**2007**, 10, 171–178. [Google Scholar] [CrossRef] - Dufwenberg, M.; Kirchsteiger, G. A theory of sequential reciprocity. Game. Econ. Behav.
**2004**, 47, 268–298. [Google Scholar] [CrossRef] - Falk, A.; Fischbacher, U. A theory of reciprocity. Game. Econ. Behav.
**2006**, 54, 293–315. [Google Scholar] [CrossRef] - Cox, J.C.; Friedman, D.; Sadiraj, V. Revealed altruism. Econometrica
**2008**, 76, 31–69. [Google Scholar] [CrossRef]

## A. Appendix: Instructions

#### General Instructions

#### Decision of person 1

**tripled**. Hence if person 1 sends 3 EMU, person 2 gains 9 EMU, if person 1 sends 6 EMU, person 2 gains 18, and if person 1 sends 9, person 2 gains 27.

Choice of person 1 | take 9 | take 6 | take 3 | take/send 0 | send 3 | send 6 | send 9 |

EMU person 1 | 26 | 23 | 20 | 17 | 14 | 11 | 8 |

EMU person 2 | 39 | 42 | 45 | 48 | 57 | 66 | 75 |

#### Decision of person 2

Choice of person 1 | take 9 | take 6 | take 3 | take/send 0 | send 3 | send 6 | send 9 |

EMU person 1 | $26+x$ | $23+x$ | $20+x$ | $17+x$ | $14+x$ | $11+x$ | $8+x$ |

EMU person 2 | $39-x$ | $42-x$ | $45-x$ | $48-x$ | $57-x$ | $66-x$ | $75-x$ |

Choice of person 1 | take 9 | take 6 | take 3 | take/send 0 | send 3 | send 6 | send 9 |

EMU person 1 | $26-3y$ | $23-3y$ | $20-3y$ | $17-3y$ | $14-3y$ | $11-3y$ | $8-3y$ |

EMU person 2 | $39-y$ | $42-y$ | $45-y$ | $48-y$ | $57-y$ | $66-y$ | $75-y$ |

**all possible**choices of person 1. So person 2 will decide what to do if person 1 takes 9 EMU, if person 1 takes 6 or 3 EMU, if person 1 sends 3, 6, or 9 and if person 1 neither takes nor sends anything.

#### Questionnaire

- Will you be able to choose more than once?
- If person 1 sends 6 EMU, how much will this cost person 1 and how much will person 2 gain?
- If person 2 assigns 4 reduction points, how much does this cost person 2 and how much will person 1 lose?
- Will person 1 know anything about the choice of person 2 before making a choice?
- Will person 2 be informed about the choice of person 1 before making a choice?
- If at the end of the experiment you have 23 EMU, how much will you get in cash?

© 2010 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Engelmann, D.; Strobel, M.
Inequality Aversion and Reciprocity in Moonlighting Games. *Games* **2010**, *1*, 459-477.
https://doi.org/10.3390/g1040459

**AMA Style**

Engelmann D, Strobel M.
Inequality Aversion and Reciprocity in Moonlighting Games. *Games*. 2010; 1(4):459-477.
https://doi.org/10.3390/g1040459

**Chicago/Turabian Style**

Engelmann, Dirk, and Martin Strobel.
2010. "Inequality Aversion and Reciprocity in Moonlighting Games" *Games* 1, no. 4: 459-477.
https://doi.org/10.3390/g1040459