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Bargaining Theory and Fairness

A Theoretical and Experimental Approach Considering Freedom of Choice and the Crowding-out of Intrinsic Motivation

Crüger, Arwed

Volkswirtschaftliche Schriften, Vol. 527

(2002)

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Abstract

Two new bargaining games, called "Freedom to Punish (FTP)" and "Right and Choice to Punish (RAP)", are developed, analyzed and tested by means of an experimental implementation. Hypotheses about behavior are developed, discussed and tested. The central hypotheses are aimed at the importance of freedom of choice, on the difference between the FTP game and the RAP game, and on the crowding-out of intrinsic motivation. As might have been expected, fairness plays a role in both games, represented by the frequent appearances of equal splits as well as by the frequent rejections of unfair offers.

In addition to that, fairness was crowded out by the new Institution of a veto power decision, confirming the importance of the institutional setting for behavior. Contrary to the few veto power sales in the RAP game, an amazingly high number of receivers refrained from veto power in the FTP game. This significant difference has clearly been attributed to the different information conditions and the existence of a bonus. This bonus can be interpreted in terms of freedom of choice, and exploits a value for the freedom to choose for the first time in experimental economics.

Table of Contents

Section Title Page Action Price
List of Contents 5
List of Figures 9
List of Abbreviations 12
List of Variables and Design Parameters 13
A. Introduction 15
I. Motivation and Research Objectives 15
II. Overview and Contents 17
B. Research on Bargaining Games 19
I. Bargaining Games and Related Games 20
1. The Ultimatum Game 20
2. The Dictator Game 20
3. The Impunity Game 21
4. The Cardinal Impunity Game 21
5. Cardinal Ultimatum Games 22
6. The Best Shot Game and the Best Shot Mini Game 23
7. An Auction Market Game 23
8. Prisoner’s Dilemma 24
II. Comparisons Between Related Types of Games 24
1. Experimental Results on Ultimatum and Dictator Bargaining 26
2. Basic and Advanced Designs for Ultimatum Experiments 27
3. Experiments with Dictator Games and Other Games 31
III. A Summary of Research Results 36
C. Fairness and Intrinsic Motivation 41
I. The Concept of Intrinsic Motivation 41
II. Experimental Approaches Towards Intrinsic Motivation 42
III. Aspects of Fairness 42
IV. Referring to a Fairness Norm 44
V. Relevant Factors for a Social Norm of Fairness 48
1. The Level of Competitiveness 48
2. The Level of Social Distance 50
3. Annoyance as a Key Factor 50
4. Determinants for a Level of Annoyance 52
VI. Another Implementation of Fairness 53
VII. Putting the Factors Together 55
D. Freedom of Choice 58
I. The Basic Concept 58
1. Instrumental and Intrinsic Importance 58
2. Negative and Positive Freedom 59
3. Alternative Spaces, Functionings, and Capabilities 60
4. The Famine Example 60
II. Axiomatic Modeling of Freedom of Choice 63
III. Modeling Freedom of Choice with a Simple Game 63
IV. A Summary on Freedom of Choice 64
E. The Two Games and Their Experimental Realization 66
I. Freedom to Punish 68
1. The Structure of the Game 68
2. The Game Theoretic Solution of the FTP Game 70
II. Right and Choice to Punish 71
1. The Structure of the Game 72
2. The Game Theoretic Solution of the RAP Game 73
III. Differences and Similarities Between the Two Games 74
IV. The Experimental Realization 74
V. The Experimental Procedure 76
F. Experimental Design for the FTP Game 77
I. Design Approach for the Experiment 78
1. Treatment Variables 79
2. Designs with a Low Proportional Bonus: A and Β 79
3. The Design Without a Bonus: C 80
4. The Design with a Low Constant Bonus: D 81
5. The Design with a High Constant Bonus: E 82
6. Designs with a Constant Price: F, G and Η 82
II. Alternative Designs 83
G. Experimental Results for the FTP Game 85
I. An Overview of the Decisions in the FTP Game 85
1. The Veto Power Decisions 85
2. The Proposals 87
3. The Acceptance Decisions 93
4. Payoffs and Efficiency 95
II. Design Background and Hypothesis Approach 96
III. Statistical Analysis for the FTP Game 97
1. The Veto Power Decisions 97
a) General Tendencies for the Veto Power Decisions 98
b) Analysis of the Veto Power Decisions 98
c) Graphical Illustration of the Veto Power Decisions 104
2. The Proposals 105
a) General Tendencies for the Demand Decisions 105
b) Analysis of the Demand Decisions 106
c) Graphical Illustration of the Demand Decisions 110
3. The Acceptance Decisions 111
IV. General Results of the FTP Game 113
1. Interpretation of the Behavior Towards Freedom of Choice 113
2. Overall Outcomes of the FTP Game 114
H. Experimental Design for the RAP Game 116
I. Design Approach for the Experiment 117
1. Treatment Variables 118
2. Design I with a Small Bonus, a Fair and a Greedy Distribution 119
3. Design II with a Small Bonus, a Greedy and a Very Greedy Distribution 121
4. Design III with a High Bonus, a Fair and a Greedy Distribution 122
5. Design IV with a High Bonus, a Greedy and a Very Greedy Distribution 123
6. Playing a Subgame 124
II. Alternative Designs 125
I. Experimental Results for the RAP Game 127
I. An Overview of the Decisions in the RAP Game 127
1. The Veto Power Decisions 127
2. The Proposals 129
3. The Acceptance Decisions 133
4. The Subgames 135
5. Behavior Types for Proposers and Receivers 136
6. A Strategy Tournament 139
7. Payoffs and Efficiency 144
II. Design Background and Hypothesis Approach 146
III. Statistical Analysis for the RAP Game 147
1. Differences Between the FTP Game and the RAP Game 148
2. The Veto Power Decisions 149
3. The Proposals 151
4. The Acceptance Decisions 158
5. The Subgames 159
IV. General Results of the RAP Game 161
1. Interpretation of the Behavior Towards a Crowding-Out 161
2. Overall Outcomes of the RAP Game 162
J. Summary 164
Bibliography 166
Subject Index 174