The experiment is implemented in two stages and has a between-subjects design. In the first stage, subjects are faced with a corruption game, where subjects’ exposure to corruption is randomly varied by increasing the probability of detection. There is also a control group that is not influenced by the corruption framing. The main purpose of the first stage is to create different perceptions of trust and reciprocity among the participants related to the exploitable benefits of corrupt behavior. In the second stage, participants play a public goods game. Players are randomly assigned to one of three groups: (1) a traditional public goods game without the option of punishment; (2) centralized punishment by a leader without counter-punishment; and (3) centralized punishment by a leader with the option of counter-punishment. Using this design, we analyze the impact of monitoring on corruption, the relationship in a public goods game of corruption and cooperation, and the ways in which cooperation can be fostered under different corruption regimes.
Stage 1: the corruption game
The structure of the corruption game follows that proposed by Abbink et al. (2002), where we have a firm (or citizen) that wishes to install a factory next to a river. Among other requirements, the firm needs an environmental certificate from the local government establishing that it does not exceed the limits of pollution to the river. The firm initiates the process of obtaining the certificate with the public official who will be in charge of evaluating the case and determining whether to grant the certificate. The firm has the possibility of offering the official a bribe, to serve as an incentive to grant the certificate. The instructions for all players specify that the granting of a certificate implies a decrease in the cleanliness of the river, in order to make clear the negative social impact of the bribe (Lambsdorff and Frank 2010).Footnote 6 The instructions, delivered individually, indicate the role each player will play in five rounds. The identity of the players in the game is anonymous, and partners play together only once in the course of the game.
Figure 1 shows the sequential steps of the game. The firm (or citizen) moves first. The firm must decide whether to offer a bribe to the public official as an incentive to grant the certificate. If it decides to offer the bribe, the amount t of the bribe must be chosen from its initial endowment, from {0, 1, …, 9}. Besides the amount selected for the bribe, the firm must incur a fixed expense of 2 experimental currency units (ECU) that represents the initial approach to the public official (this is a sunk cost, because the firm must pay it, whether the public official accepts the bribe or not).
After seeing the decision by the firm, the public officials make a decision. If a bribe is offered, they must choose whether to accept it or not. If they decide to accept it, the amount will be deducted from the firm’s account, and three times that amount will be added to their account (Abbink et al. 2002). The public officials must then decide whether to grant the certificate. Granting the certificate implies an effort, because they must justify it to their superiors and complete the necessary paperwork. In this experiment, if the public officials decide to grant the certificate, their payoff is reduced by 6 ECU; if they do not grant it, they keep the entire payoff.
In order to have different corruption scenarios, we randomly assigned the probability of monitoring to one of two values. In the low-monitoring scenario, players have a 5 % probability of getting caught, and in the high-monitoring scenario the probability is 25 %. If players are caught in an act of corruption, they lose their earnings from the round. It is expected that the levels of corrupt behavior are higher with low monitoring because of the greater benefits and lower risks involved. In this first stage, we also include as a baseline a control group that does not play the corruption game.
In this game, the equilibrium for the firm is not to offer a bribe, with the public official not granting the certificate. By backward induction, the firm knows that not granting the certificate is a dominant strategy for the public official. Even if a bribe is offered, it best suits the interests of the public official not to grant the certificate. Firms thus decide not to offer a bribe in the first stage of the game.
Stage 2: the public goods game
In the second part of the experiment, the public goods game, groups of four participants are randomly formed, taking into account each participant’s treatment in the corruption game (whether they participated in a high- or low-monitoring group, or in the control group). This means that all the participants in a group in this stage faced the same treatment in the first stage, and participants are informed of this fact in order to make it clear what kind of partners they might expect. The identity of all players is kept anonymous throughout the game. The players are divided into three groups: (1) the standard public goods game without the option of punishment; (2) centralized punishment by a leader but no counter-punishment; and (3) centralized punishment by a leader with the option of counter-punishment. The new groups play together for five rounds in a partner mode.
The standard public goods game
The standard public goods game consists of a simultaneous assignment decision for each player regarding the initial endowment. The initial endowment is 20 ECU for each participant, and they have two ways to use it: save all or part of it in a personal private account, or invest all or part of it in a shared group project (x). The profitability of the common project is calculated by multiplying the sum of the investments in it by two and dividing it into equal shares among the four participants in each group (\(0.5 \sum\nolimits_{j = 1}^{4} {x_{j} }\)). The payoff for the participants is calculated as follows:
$$\pi_{i} = 20 - x_{i} + 0.5\sum\limits_{j = 1}^{4} {x_{j} }$$
(1)
After the contributions are made by all the members in all groups, players are informed of their earnings for the round and the contribution of their group’s partners. If the participants are rational and selfish, their dominant strategy is not to invest in the common project, but to save their endowment in their private accounts. This happens because players can profit from their partners’ investments in the common project without having to invest in it. If all the players follow this prediction, then none invest in the common project. The best choice in social terms, however, is that all participants invest their endowments in the common project. The profit is then 40 ECU each, a profit of 160 ECU for the group.
However, as previously noted, the literature on public goods games shows some cooperation among players. The average individual contribution starts at around 50 % of the endowment and declines with each round. This behavior is not consistent with the Nash equilibrium, and various researchers have explored why there is cooperation. Among the possible explanations are confusion, altruism (Andreoni 1995), inequity aversion (Fehr and Schmidt 1999), conditional cooperation (Fischbacher et al. 2001), and strategic behavior related to the multi-round setting of the experiment (which includes reciprocity concerns and beliefs about other people’s contributions as in Fischbacher and Gächter 2010). There is no evidence for confusion as a factor in the main result of these games (Andreoni 1995). A recent study shows that multi-round motives are more important than altruism, inequity aversion, and conditional cooperation, but that all of these factors explain cooperative behavior (Yamakawa et al. 2016).
Centralized punishment by a leader but no counter-punishment
The dynamic of this game is similar to the standard public goods game, but a few features are added. Before the first round starts, it is explained to the participants that one player has been exogenously selected. This player (who is not explicitly named as a leader in the experiment) will have the ability to reduce the profits of the partners. It is explained that after all investment decisions have been made in a group, and after all the players know their own profits and the contribution of others, the selected player will decide how much to reduce the others’ profits. There is a cost to doing so, however. Each punishment unit the leader buys delivers three units of punishment to the punished player: if the leader decides to pay 1 ECU to punish another player, the latter’s profit will be reduced by 3 ECU (the leader can use up to 10 ECU to punish each player).Footnote 7 After the leader makes this decision, players learn how many ECU they receive as punishment (but they are not told about the punishment received by others). Then a new round starts. The profit function for players other than the leader is:
$$\pi_{i} = 20 - x_{i} + 0.5\sum\limits_{t = 1}^{4} {x_{t} - 3y_{j} } ,$$
(2)
where y represents the units of punishment received from the leader. The leader’s equation is:
$$\pi_{i} = 20 - x_{i} + 0.5\sum\limits_{t = 1}^{4} {x_{t} - \sum\limits_{j = 1, i \ne j}^{4} {y_{j} } } ,$$
(3)
where the last sum corresponds to the punishment to others.
By backward induction, considering the cost of punishment, leaders decide not to punish others. Taking this into account, the other players have no incentive to invest in the common project at the decision stage. Thus, as in the standard public goods game, the dominant strategy of the players is not to invest in the public good, but to save everything in their private accounts. It is important to note that, given the conditions of the game, it is impossible for the players to coordinate a common strategy.
Centralized punishment by a leader with counter-punishment
This treatment is similar to the previous one, with the added possibility of counter-punishment after the leader has decided on punishment. We add the possibility that punished participants are able to punish the leader in return. However, the cost and value of this counter-punishment is different than the leader’s cost. As before, the leader pays one ECU to punish others three times as much. The cost of the counter-punishment, however, is three times its impact. The idea behind this difference is to reflect the power differential between the leader, representing an institution, and an ordinary player.
As in the previous version of the public goods game, after the leader has decided on the punishment of the rest of the group, the players know their own profit, the contributions to the project by each of the others, and their own punishment. Those players who are punished by the leader must decide whether to apply counter-punishments, taking into account their profits from the round and the cost of counter-punishment. At the end of the round the players will know their final profit after counter-punishment, and then a new round starts. The profit function for players other than the leader is:
$$\pi_{i} = 20 - x_{i} + 0.5\sum\limits_{t = 1}^{4} {x_{t} - 3y_{j} - 3z_{j} \cdot 1(y_{j} > 0)}$$
(4)
with z as the units of counter-punishment of the leader, taking into account its cost (only players who receive punishment can choose a counter-punishment, \(1(y_{j} > 0)\)). The leader’s profit function is:
$$\pi_{i} = 20 - x_{i} + 0.5\sum\limits_{j = 1}^{4} {x_{j} - } \sum\limits_{j = 1, i \ne j}^{4} {y_{j} - \sum\limits_{j = 1, i \ne j}^{4} {z_{j} } }$$
(5)
with the last sum representing the counter-punishment received by the leader.
By backward induction, similar to the other two treatments, it is expected that the costly counter-punishment for the non-leader participants will not be used. Taking this as a given, the leader decides to not punish the rest of the group because of the cost of that punishment. Finally, by having no incentive to cooperate with each other, all the participants decide to save their endowment in their personal accounts.