Agent Motivation and Principal Anticipation: Non-Monotonicity, Intentions, and Other Factors

Abstract

We design an experiment to test what motivates agents to choose higher effort and how well principals anticipate agent responses. Principals rank five contracts where a higher ranking increases the likelihood of a contract's implementation. In one treatment, those rankings remain hidden from agents; in the other, agents view the rankings. Agent response to contract structure and monetary incentives largely conforms to our predictions: agents demonstrate a preference for monotonic contracts over non-monotonic contracts, and the vast majority responds favorably to contracts where high effort is a best response. Surprisingly, offering a flat contract that exactly compensates agents for effort performs no better than offering nothing. Principals, however, poorly anticipate agent response to contracts, regardless of the observability of rankings. Additionally, although differences in observable rankings only affect agent behavior in minor ways, principals' rankings between the two treatments indicate principals believed different rankings would significantly influence agents when observable.

Keywords:

• Principal-agent problems
• non-monotonicity
• experimental economics
• contract theory
• intentions

JEL Classification:

• D86
• D91
• J33

Acknowledgments

We would like to thank Collin Weigel for helping us with the SoPHIE software and participants of the 2018 ESA North American meetings for feedback and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Table 1. Probabilities, effort, and revenue.

Notes

1 In Hvide’s (2002) tournament model where agents chose both risk and effort, agents choose excessive risk in equilibrium without a non-monotonic contract.

2 For example, an investing agent could guarantee moderate returns from investing in a well-researched portfolio (high effort) but many of the highest returns only come from overly risky investments.

3 Expected payoff from either effort selection by the agent is the same in both.

4 Flannery and Roberts (2018) shows a tendency of agents to take costly effort when there is a monotonic contract that is close to incentivizing them, indicating either a lack of precision in determining the optimal choice or a willingness to reward principals who were attempting to compensate them appropriately for effort. Lukas (2017) shows similar behavior in a two-period game where principals rarely offer the appropriate non-monotonic contract, and agents behave as though they have been incentivized to choose high effort anyway.

5 Additionally, all three experiments used difficult probabilities for the subjects to comprehend such as 23% and 43% and all had two periods in their design instead of just one as ours does. While the optimality of a non-monotonic contract in our experiment comes from a state with a payoff invariant to effort level, in Lukas (2007), Brosig, Lukas, and Riechmann (2010), and Lukas (2018), it derives from correlation between the two periods.

6 See Johnson and Mislin (2011) for a meta-analysis.

7 If we replaced the revenue of the MEDIUM outcome with 34, instead of the current 36, the only profitable monotonic contract with whole numbers that incentivizes high effort would be (0,16,17), the lowest paying one since the payment to the agent for the MEDIUM outcome must be 16 to encourage high effort.

8 See Brandts and Charness (2011) for a survey of the literature on the strategy method.

9 See Fehr and Schmidt (1999) and Bolton and Ockenfels (2000) for models of fairness.

10 See the ‘Optimal Contracting’ section Flannery and Roberts (2018) for more details.

11 Some students also received extra credit in a course for participating. Those students received extra credit for simply showing-up and the decisions of the students in the experiment only affected monetary payments, not the amount of extra credit received.

12 However, when principals rank (0,0,0) lowest, agents do not have the opportunity to respond to it.

13 Standard deviations of the pooled data provided in parentheses below each value.

14 The largest difference occurs in the eighth round where 26 of 35 subjects chose high effort in response to the non-monotonic contract in the observable treatment while only seventeen of thirty-one responded with high effort in the hidden treatment; however, this difference is not even significant at the 10% level (two-sided Fisher's Exact Test, p = 0.1241).

15 Significance occurs below the one percent level when comparing (0,16,20) to (6,14,22), (12,12,12), and (0,0,0) using pairwise McNemar tests, with the exception of round 6 where the p-value comparing it to (6,14,22) is 0.0124. The maximum p-value comparing (0,16,20) to (12,12,12) and (0,0,0) equals 0.000145 in round 7 and 0.000647 in round 6, respectively.

16 Frequency of high effort differed significantly in rounds 1,2,5,7, and 8 with p-values of 0.0578,0.0077,0.0334,0.0956, and 0.0578, respectively.

17 Significance occurred at the 1% level for (0,0,0) and (12,12,12) with a maximum p-value in round 2 of 0.000465 and in round 7 of 0.000967, respectively. Each round (2,18,14) and (6,14,22) differed at the 5% level except once in round 2, where the difference between them only yields a p-value of 0.1336.

18 (6,14,22) significantly differs from the (0,0,0) and (12,12,12) contracts at the 5% level in all but one of eight rounds and two of eight rounds, respectively. In rounds 1 and 7, the difference between (6,14,22) and (12,12,12) gave a p-value of 0.1655 and 0.0956 (significant at 10% level) while in round 8 the difference between (6,14,22) and (0,0,0) gave a p-value of 0.0956 (significant at 10% level).

19 A minimum p-value of 0.102470 occurs in rounds 6 and 7 for these contracts.

20 The number of observations is smallest for (0,0,0) and (12,12,12) since so many principals ranked them worst.

21 Standard deviations of the pooled data provided in parentheses below each value.

22 We omit other comparisons such as first best ranking high effort proportions versus second, third, and fourth due a lack of observations.

23 None of the differences were significant with the largest difference occurring in the third round only yielding a p-value of 0.1642 (Two-sided Fisher's Exact Test).

24 However, as with the (0,16,20) contract, there is not a significant difference in any round with the largest difference occurring in the first round, giving a p-value of 0.1034 (Two-sided Fisher's Exact Test).

25 Other differences were all higher responses when (0,0,0) was ranked lowest: 0.017 for (12,12,12), 0.007 for (6,14,22), and 0.0035 for (2,18,14). Principal intentions seemed to have little discernible impact on agent choice.

26 The highest rated contract is scored as a 1 and lowest rated contract is scored as a 5.

27 Rounds 6-8 had p-values of 0.0155, 0.0174, and 0.0252, respectively, while the smallest p-value of rounds 1-5 occurred in round 5 and equals 0.2040.

28 See Appendix A.

29 Using a Two-sided Fisher's Exact Test, this difference is significant in rounds 1, 4, and 8 with p-values of 0.0055, 0.0791, 0.0266, respectively.

30 In addition, (6,14,22) is ranked in the top 2 more often in every round while (12,12,12) is ranked in the top 2 more often in every round except the first in the observable treatment compared to the hidden treatment. None of the differences are significant with a minimum p-value of 0.2201 for (6,14,22) in round 1 and 0.189 in round 8 for (12,12,12) (Two-sided Fisher's Exact Test).

31 Kendall's Tau Rank Correlation Test, τ= -0.593 and τ= -0.794 with p-values of 0.0595 and 0.0113 for the observable and hidden treatment, respectively.

32 Kendall's Tau Rank Correlation Test, τ= -0.564, p = 0.0842

33 Kendall's Tau Rank Correlation Test, τ = 0.667, p = 0.0327

34 In the hidden treatment, the principals, in the role of agents of the practice rounds, responded to (2,18,14), (6,14,22), (12,12,12), (0,0,0), and (0,16,20) with high effort rates of 0.758, 0.403, 0.145, 0.130, and 0.806. In the open treatment, the principals, in the role of agents of the practice rounds, responded to (2,18,14), (6,14,22), (12,12,12), (0,0,0), and (0,16,20) with high effort rates of 0.620, 0.586, 0.246, 0.311, and 0.705.

35 For example, if the revenue from the MEDIUM outcome was below 33 and a third (as opposed to the current 36), no profitable monotonic contract exists for the principal that encourages the agent to choose high effort as discussed previously in the Experimental Design section.

36 Assuming both the principal and agent act as profit maximizers.

Additional information

Funding

This work was supported by an internal research grant at Missouri State University under Grant F07333.