Noisy Clarity: Information, Punishment, and the Enhancement of Trust

Introduction The theory of infinitely repeated prisoner’s dilemma (PD) games provides a framework for predicting which conditions generate sustainable trust and cooperation, such as that needed in ongoing commercial... [ view full abstract ]

Introduction
The theory of infinitely repeated prisoner’s dilemma (PD) games provides a framework for predicting which conditions generate sustainable trust and cooperation, such as that needed in ongoing commercial transactions. Conditions include the level of risk, payoffs, and continuation probability as well as monitoring components, which change the payoff or cost of trust. This basic PD framework has also been used to propose an economic theory of contract enforcement, one which models the relationship between parties to a transaction, the role of information and punishment components, and the existence of third parties providing these services in support of ongoing commercial transactions (Dixit 2004).

However, the theory of infinitely repeated games have been criticized for their inability to make sharp predictions regarding the multiple (non-)cooperative equilibria that may arise (Tirole 1988, Fudenberg & Maskin 1993, Dal Bó & Fréchette 2011). For this reason, a new wave of research has sought to isolate in the effects related to continuation probability (Dal Bó 2005, Bignoni et al. 2015), the quality of the monitoring or public signals (Aoyagi & Fréchette 2009), risk dominance (Dal Bó & Fréchette 2011), noise and uncertainty (Fudenberg et al. 2012), and fixed vs. random matching (Duffy & Ochs 2009). While laboratory experiments offer evidence for the role these factors play in supporting trust and sustaining cooperation, in reality interactions are more complex.

This experimental study seeks to approximate more closely infinitely repeated PD games to the reality of repeated transactions by framing the trust decision in commercial terms and introducing “equilibrium” noise into the interaction.

Theoretical Framework and Hypotheses
A third-party contract enforcement mechanism may be modeled as two repeated PD games with an intermediary who charges a fee for an information or punishment service, or both (Dixit 2004). A testable model predicts that the client of a third-party provider will act honestly if F < (H – C) - r (W – H). In other words, if the fee (F) for the third-party service is greater than the payoff from acting honestly (H) minus the return from cheating (C) minus the discount rate (r) for a one-time win (W) minus the payoff for honesty (H), then the intermediary will honor the contractual commitment.

Yet there is the possibility that the third party can double-cross a client in collaboration with the client’s counterparty. In this case, the most a third party could earn is a portion of the one-time payoff (W – H), forever losing future fees from the cheated client. For the third party to act honestly, the fee must be greater than the discount rate (r) of the payoff of winning (W) minus what could have been earned from acting honestly (H), or F > r′ (W – H). Model variations may capture differences between acting as an information or punishment intermediary as well as different client behavior types (e.g., trustworthy, untrustworthy, opportunist). Yet this model does not account for different types of information and punishment.

In commercial transactions, information components include information about the counterparty’s history as well as monitoring of activities in the ongoing transaction. Punishment may come from counterparties or from third parties. One may reason that an intervention in which parties were forced to interact for a period of time but could rate one another’s behavior – thus providing both second-party information as well as the opportunity to punish by damaging the other’s reputation – would generate more trust compared to a “control” interaction free of ratings (H1). Yet if one were to introduce, alongside ratings, the opportunity to opt out of an ongoing interaction at any moment, this trust gain may be offset, thus predicting decreased trust or cooperation compared to the ratings treatment due to the existence of loss aversion (H2) (Kahneman & Tversky 1979, 1992). On the other hand, if punishment were increased by including a systemic response that would suspend for one round of play the two players with the lowest rating, then one would predict increased cooperation, due to the completeness of the contract enforcement mechanism, compared to the ratings treatment (H3).

Unlike typical infinitely repeated PD experiments in which a single abstract payoff matrix is provided, this experimental manipulation framed the interaction in commercial terms (e.g., you have the opportunity to partner with this person to produce in the garment industry) while randomly rotating one of five commercial dilemmas, each with distinct “equilibrium indices” (i.e., with payoffs making some dilemmas more or less likely for generating cooperation, as predicted by theory). The hypothesis was that the strength of the contract enforcement conditions would override any isolated trust or cooperation prediction based on payoff matrices (H4).

Study Design
A total of 31 experimental sessions were conducted with 248 undergraduates or 8 each per treatment session: Control, Rating, Opt Out, and Suspension. Each session consisted of 8 students who were randomly matched in each round or supergame. Within each supergame, players were provided details on their “rules of the game,” which included playing a round of five games with their counterparty, with a 50% chance of continuation for each additional game thereafter. The rationally expected number of games per supergame was thus 6. A total of 217 supergames consisting of 1291 games or 2582 decisions were played during the 31 sessions.

Results
HLM analysis, with clustered errors at the session level, revealed that the suspension treatment generated higher statistically significant levels of cooperation, with log odds of 2.44 times more than control, 1.79 more than rating, and 3.22 more than opt out (see Table 1). Likewise, the log odds of cooperation for rating are 1.35 more than control and 1.75 more than opt out. While the log odds for control were higher than opt out (1.27), they were not significant.

As with previous PD experiments, there existed an end-game effect in which players were more likely to defect the closer they came to the end of the mandatory five-game period. Thereafter, it was possible to measure the formation of a trust equilibrium following the fifth game. Figure 1 highlights the drop-off occurring until the fifth game and the formation of a sustainable trust equilibrium for some players, with the percentage of cooperation for rating and suspension higher than that for control and opt out. Although the suspension intervention generated nominally higher overall levels of trust than the rating treatment, differences in the level of trust generated beyond the fifth game were not significant. However, the differences in trust between rating and suspension compared to control and opt out were statistically significant (p-value < 0.05).

While results supported H1-H4, findings contradicted that predicted by H5. Despite noise and the influence of conditions, when aggregating treatments the relative equilibrium predictions held, though not in absolute terms, demonstrating compression at the extremes (see Table 2).

Furthermore, disaggregation suggests that contract enforcement mechanisms, rather than eliminating sensitivities to individual payoff structures may actually be critical for enhancing “rational” trust and cooperation decisions (see Table 3). The sharpest relative demarcation or “kink” between the likelihood of trust/not trust occurred in both the rating and suspension treatments (between dilemmas 2 and 3), with both registering statistical significance. On the other hand, there was no statistical significance between dilemmas in the control and opt out treatments.

Conclusion
This framed PD experiment offers empirical evidence for the specific information and punishment components needed to support commercial trust and cooperation, as well as the nature of their combination. However, while these components generated trust higher than that predicted by game theory, there was also evidence that contract enforcement mechanisms enhanced the rationality of trust and cooperation in relative (as opposed to absolute) predicted terms. Future analysis will examine the information mechanisms and dynamics contained in the subjects’ ratings while generating new hypotheses about the relationship between contract enforcement conditions and the sustainability of trust in commercial transactions.