# The Role of Framing, Inequity and History in a Corruption Game: Some Experimental Evidence

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Methodology

#### 2.1. Experimental Design and Procedures

#### 2.2. Treatments and Research Questions

Firms offered a bribe in 107 out of 170 cases (63%) and the average bribe offered was 6.73 experimental dollars.The bribe was accepted by the official in 82 cases out of 107 (77%).Out of the 82 cases where the firm offered a bribe and the official accepted, the citizen decided to punish in 59 cases (72%) at an average punishment amount of 8.76 experimental dollars.

#### 2.3. Hypotheses

**Hypothesis 1:**

**Hypothesis 2:**

**Hypothesis 3:**

## 3. Results

#### 3.1. Overview

#### 3.2. Analysis of the Role of Framing, History and Inequity Aversion

#### 3.3. Bribe and Acceptance Behavior

_{i1}, …, Z

_{iT}) or ${X}_{i}$ = (X

_{i1}, …, X

_{iT}) as independent variables to obtain unbiased coefficient estimates 10. This correction is suggested by Wooldridge (2002, pp. 493–495) [42] for dynamic panel data models of this nature.

#### 3.4. Punishment Behavior

## 4. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A: Instructions for the Loaded Inequitable Treatment

## Instructions

## General

## Detailed Instructions for Firms

## Detailed Instructions for Officials

## Detailed Instructions for Citizens

**multiplied**by 3, and the payoffs of the Official and the Firm will be reduced by this tripled amount. Your payoff will be reduced by $P, the amount of punishment you have chosen. The exact payoffs will be: Firm gets 58 + 3B − 3P, Official gets 30 + 3B − 3P, and Citizen gets 80 − 7B − P. If you decide not to punish, then the payoffs will be: Firm gets 58 + 3B, Official gets 30 + 3B, and Citizen gets 80 − 7B.

## Appendix B: Instructions for the Neutral Inequitable Treatment

## Instructions

## General

## Detailed Instructions for Player A

## Detailed Instructions for Player B

## Detailed Instructions for Player C

**multiplied by 3,**and the payoffs of Player A and Player B will be reduced by this tripled amount.

**Your payoff will be reduced by G experimental dollars, the amount of money you have chosen to give up**. The exact payoffs will be: Player A gets 58 + 3T − 3G, Player B gets 30 + 3T − 3G, and Player C gets 80 − 7T − G. If you decide not to give up any money, then the payoffs will be: Player A gets 58 + 3T, Player B gets 30 + 3T, and Player C gets 80 − 7T.

## References

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^{1}Alatas et al. (2009a) [2] use the same game, undertaken across the four different locations, to look for gender differences in behavior. Alatas et al. (2009b) [3] look at differences in behavior in this game between Indonesian students and Indonesian civil servants. These two papers are not immediately relevant to our study and hence we refrain from elaborating on them.^{2}We chose the random re-matching protocol in our repeated game set-up in order to preserve the essence of one-shot interactions while allowing for learning and gathering experience. Andreoni and Croson (2008) [9], make this point, albeit in the context of public goods games, by stating: “A common way to deal with this has been to rematch subjects randomly into groups for each iteration of the game, hence forming a repeated single-shot design and avoiding the repeated-game effects.” Further, as Kreps, Milgrom, Roberts and Wilson (1982) [10] and Benoit and Krishna (1985) [11] note, the subgame perfect equilibrium in the one-shot stage game may not necessarily be an equilibrium under fixed matching even with finitely repeated play.^{3}This is the same conversation rate as in Cameron et al. (2009). At the time the experiments were run in 2007 NZ $1 was roughly equivalent to US $0.77.^{4}In the most recent CPI, published in 2015, New Zealand is 4th while Australia is 13th. New Zealand was ranked second in each of the previous three years. Australia has typically ranked somewhere around 10th in each of those years.^{6}It is important to note the following. For firms, taking this average is easy since all we need to do is to look at whether a particular firm offered a bribe or not in each of the ten rounds. However, for each official, we average over acceptance decisions only in those cases when a bribe was offered and the official had a decision to make: whether to accept or reject; similarly, for citizens we look at only those cases, when the bribe was offered and accepted and the citizen actually had a decision to make. This implies that, while we have the same numbers of firms, officials and citizens in each treatment, for the officials and the citizens the actual number of observations over which we are averaging will differ from one subject to another.^{7}Compared to the Loaded inequitable treatment, there is greater inequity between the firm and the official in the Loaded equitable treatment. It is possible, along the lines of the results reported by Jiang et al. (2015) [24], that the changing inequity in the payoffs of the firms and the officials also played a role in the firm’s decision to offer a bribe or not. We thank an anonymous referee for pointing this out.^{8}We note that these observations are not independent and this is likely contributing to the high significance levels; but the general point is still valid. Given that the earnings from not bribing is constant, we use a t-test here.^{9}As a robustness check, we re-ran our regressions with standard errors clustered at the level of individual subjects. The results are similar. We report non-clustered standard errors because Cameron and Miller (2015) [39] argue that in order to obtain precise estimates with clustering one requires a large number of clusters and fixed size in each cluster. This is not really true in our case. We do not have many clusters and our cluster sizes vary. Cameron and Miller (2015) argue that performance can deteriorate significantly with a relatively small number of clusters and/or where the cluster size is not fixed.^{10}The results for $B{O}_{i0}$, ${Z}_{i}$, $B{A}_{i0}$ and ${X}_{i}$ estimated coefficients are not reported in the tables.^{11}In terms of the interaction between treatments and round, we note that the variables are not demeaned. Given that the regression includes both main treatment effects and treatment*round interactions, the main treatment effects reflect the treatment difference in a hypothetical round 5.5.^{12}Taking logs generates more precise results. The results are similar if we take levels; the only difference without logs is that we have less significant estimated effects. The joint log likelihood for the two-part model with a random effects maximum likelihood regression on a log-normal model presented in Table 4 is −125.72, the joint log likelihood for the two-part model with a random effects maximum likelihood regression on the actual bribe amount is −1029.44, and the joint log likelihood for two-part model with a random effects Tobit model is −897.46. This shows that the model we presented in Table 4 provides the best fit for our data.^{13}If a firm does not offer a bribe in round t-1, the value for lag ln(bribe amount) is replaced with the log-normal of the bribe amount in the most recent round before that. An anonymous referee correctly pointed out that this is a strong assumption and suggested that this may affect our estimates; e.g., by increasing the distance between the lagged bribe amount and the bribe amount for firms that are less likely to bribe at all. We thank the referee for raising this point. But, we could not find or think of another way to deal with missing observations. We had to choose a particular way of addressing this and to us, it made sense, to insert the last value experienced by an individual as the lagged value.^{14}Likelihood ratio test shows this specification is better than one without additional interaction terms between treatment dummies and bribe amount (${\chi}^{2}$ (3) = 10.28, p = 0.0163).^{15}Likelihood ratio test shows this specification is better than one with additional interaction terms between treatment dummies and bribe amount (${\chi}^{2}$ (3) = 4.34, p = 0.2275).^{16}The joint log likelihood for the two-part model with a random effects maximum likelihood regression on a log-normal model presented in Table 4 is −338.20, the joint log likelihood for two-part model with a random effects maximum likelihood regression on the actual bribe amount is −730.72, and the joint log likelihood for two-part model with a random effects Tobit model is −637.12. This shows that the model we present in Table 4 provides the best fit for our data.

**Figure 3.**(

**A**) Evolution of the bribe rate over ten rounds; (

**B**) Evolution of the acceptance rate over ten rounds; (

**C**) Evolution of the punishment rate over ten rounds.

Treatments | Abbreviation | Number of Subjects (Number of F-O-C Triplets) | Exchange Rate | Number of Plays of the Stage Game |
---|---|---|---|---|

Treatment 1 (Control treatment) Loaded language with different conversion rates | Loaded inequitable | 51 (17) | Firm: Exp$60 = NZ$1 Official: Exp$40 = NZ$1 Citizen: Exp$30 = NZ$1 | 170 |

Treatment 2 Neutral language with different conversion rates | Neutral inequitable | 60 (20) | Firm: Exp$60 = NZ$1 Official: Exp$40 = NZ$1 Citizen: Exp$30 = NZ$1 | 200 |

Treatment 3 Loaded language with uniform conversion rate | Loaded equitable | 42 (14) | Firm, Official, Citizen: Exp$40 = NZ$1 | 140 |

Treatment 4 Loaded language with different conversion rates and history | Loaded inequitable plus history | 57 (19) | Firm: Exp$60 = NZ$1 Official: Exp$40 = NZ$1 Citizen: Exp$30 = NZ$1 | 190 |

TOTAL | 210 (70) | 700 |

One-Shot Game in Cameron et al. 5 | This Study Round 1 only | This Study Average over 10 Rounds | ||||
---|---|---|---|---|---|---|

Melbourne | Singapore | New Delhi | Jakarta | |||

% of firms bribing | 87.8 | 83.6 | 93.3 | 78.3 | 58.8 | 62.9 |

% of officials accepting | 88.9 | 96.1 | 92.9 | 78.7 | 60.0 | 76.6 |

% of citizens punishing | 42.2 | 57.1 | 21.2 | 59.5 | 66.7 | 72.0 |

**Table 3.**Results of Wilcoxon ranksum tests for bribe, acceptance and punishment rates; average over ten rounds by individual.

Panel 1: Impact of Framing | ||||

Loaded inequitable (n = 17) | Neutral inequitable (n = 20) | p-Value | ||

% of firms bribing | 62.9 | 98 | 0.0001 | |

Bribe amount if chose to bribe | 6.67 | 6.85 | 0.71 | |

% of officials accepting | 78 | 90 | 0.10 | |

% of citizen punishing | 73 | 55 | 0.14 | |

Punishment amount if chose to punish | 8.5 | 6.7 | 0.08 | |

Panel 2: Impact of Inequity in Initial Endowments | ||||

Loaded inequitable (n = 17) | Loaded equitable (n = 14) | p-Value | ||

% of firms bribing | 62.9 | 79 | 0.22 | |

Bribe amount if chose to bribe | 6.67 | 6.20 | 0.16 | |

% of officials accepting | 78 | 72 | 0.18 | |

% of citizen punishing | 73 | 71.2 | 0.76 | |

Punishment amount if chose to punish | 8.5 | 7.8 | 0.35 | |

Panel 3: Impact of History of Past Plays | ||||

Loaded Inequitable (n = 17) | Loaded Inequitable Plus History (n = 19) | p-Value | ||

% of firms bribing | 62.9 | 77.9 | 0.23 | |

Bribe amount if chose to bribe | 6.67 | 6.23 | 0.37 | |

% of officials accepting | 78 | 76.6 | 0.95 | |

% of citizen punishing | 73 | 73.3 | 0.98 | |

Punishment amount if chose to punish | 8.5 | 7.3 | 0.31 |

(1) Bribe (0/1) | (2) Log-Normal Bribe Amount | (3) Accept (0/1) | (4) Punish (0/1) | (5) Log-Normal Punishment Amount | |
---|---|---|---|---|---|

Neutral inequitable dummy | 4.19 ** (1.86) | −0.02 (0.07) | −1.67 (1.26) | −1.91 * (1.11) | −0.32 (0.27) |

Loaded inequitable plus history dummy | 0.19 (0.62) | 0.02 (0.08) | −0.40 (1.17) | −0.27 (1.19.) | −0.14 (0.30) |

Loaded equitable dummy | 1.45 * (0.76) | −0.07 (0.08) | −2.66 ** (1.28) | −1.06 (1.17) | −0.15 (0.32) |

Round | −0.07 (0.05) | 0.01 (0.01) | 0.04 (0.07) | −0.26 ** (0.13) | −0.03 (0.03) |

Neutral inequitable * Round | −0.25 (0.21) | 0.001 (0.01) | −0.13 (0.09) | 0.23 * (0.14) | 0.05 (0.04) |

Loaded inequitable plus history * Round | 0.03 (0.07) | −0.01 (0.01) | −0.16 * (0.09) | 0.02 (0.15) | 0.04 (0.05) |

Loaded equitable * Round | −0.14 (0.09) | 0.01 (0.01) | −0.04 (0.11) | 0.17 (0.15) | 0.04 (0.05) |

Lag bribe (0/1) | −0.72 *** (0.27) | −0.003 (0.04) | --- | --- | --- |

Lag bribe with acceptance (0/1) | 1.00 *** (0.33) | 0.04 (0.03) | --- | --- | --- |

Lag bribe with punishment (0/1) | −0.71 ** (0.30) | −0.03 (0.02) | --- | --- | --- |

Lag ln(bribe amount) | --- | 0.20 *** (0.05) | --- | --- | --- |

Bribe amount | --- | --- | 0.02 (0.12) | 0.27 *** (0.07) | 0.05 * (0.03) |

Neutral inequitable * Bribe amount | --- | --- | 0.42 ** (0.17) | --- | --- |

Loaded inequitable plus history * Bribe amount | --- | --- | 0.18 (0.15) | --- | --- |

Loaded equitable * Bribe amount | --- | --- | 0.50 *** (0.19) | --- | --- |

Lag acceptance (0/1) | --- | --- | −0.005 (0.26) | --- | --- |

Lag acceptance with punishment (0/1) | --- | --- | −0.36 * (0.21) | --- | --- |

Lag Punishment (0/1) | --- | --- | --- | 0.25 (0.24) | --- |

Lag ln(punishment amount) | --- | --- | --- | --- | 0.37 *** (0.06) |

Constant | 0.69 (0.53) | 1.17 *** (0.14) | 1.93 (1.37) | 3.50 * (2.01) | 0.37 (0.43) |

Log likelihood | −215.09 | −89.37 | −195.97 | −171.89 | −166.31 |

N | 630 | 496 | 488 | 346 | 223 |

© 2016 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 (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Chaudhuri, A.; Paichayontvijit, T.; Sbai, E. The Role of Framing, Inequity and History in a Corruption Game: Some Experimental Evidence. *Games* **2016**, *7*, 13.
https://doi.org/10.3390/g7020013

**AMA Style**

Chaudhuri A, Paichayontvijit T, Sbai E. The Role of Framing, Inequity and History in a Corruption Game: Some Experimental Evidence. *Games*. 2016; 7(2):13.
https://doi.org/10.3390/g7020013

**Chicago/Turabian Style**

Chaudhuri, Ananish, Tirnud Paichayontvijit, and Erwann Sbai. 2016. "The Role of Framing, Inequity and History in a Corruption Game: Some Experimental Evidence" *Games* 7, no. 2: 13.
https://doi.org/10.3390/g7020013