Gaming and strategic opacity in incentive provision

• Author: Florian Ederer,Margaret Meyer,Richard Holden
• Published date: 01 December 2018
• DOI: http://doi.org/10.1111/1756-2171.12253
• Date: 01 December 2018

RAND Journal of Economics

Vol.49, No. 4, Winter 2018

pp. 819–854

Gaming and strategic opacity in incentive

provision

Florian Ederer∗

Richard Holden∗∗

and

Margaret Meyer∗∗∗

Westudy the benefits and costs of “opacity” (deliberate lack of transparency)of incentive schemes

as a strategy to combat gaming by better informed agents. In a two-task moral hazard model

in which only the agent knows which task is less costly, the agent has an incentive to focus his

effort on the less costly task. Opaque schemes, which make a risk-averse agent uncertain about

which task will be more highly rewarded, mitigate such gaming but impose more risk. Weidentify

environments in which opaque schemes not only dominate transparent ones, but also eliminate

the costs of the agent’s hidden information.

1. Introduction

A fundamental consideration in designing incentive schemes is the possibility of gaming:

exploitation of an incentive scheme by an agent for his own self-interest to the detriment of

the objectives of the incentive designer. Gaming can take numerous forms, among them (i)

diversion of effort away from activities which are socially valuable but difficult to measure and

reward, toward activities that are easily measured and rewarded; (ii) exploitation of the rules of

classification to improve apparent, though not actual, performance; and (iii) distortion of choices

∗YaleUniversity; florian.ederer@yale.edu.

∗∗University of New South Wales; richard.holden@unsw.edu.au.

∗∗∗Oxford University and CEPR; margaret.meyer@nuffield.ox.ac.uk.

We wish to thank DavidMartimor t (the Editor) and twoanonymous referees for comments and suggestions that greatly

improvedthe article. Weare also g rateful to Philippe Aghion, Sushil Bikhchandani, Simon Board,Patrick Bolton, Jeremy

Bulow,Vince Crawford,Kate Door nik, Mikhail Drugov, Guido Friebel, Edoardo Gallo, Robert Gibbons, Edward Glaeser,

OliverHart, Bengt Holmstr ¨

om, Ian Jewitt,Navin Kartik, Paul Klemperer, Shmuel Leshem, Phillip Leslie, Steven Lippman,

Steven Matthews, John Moore, Andy Newman, In-Uck Park, Charles Roddie, Jesse Shapiro, Ferdinand von Siemens,

Jason Snyder,Alexander Stremitzer, Jeroen Swinkels, and Jean Tirole for helpful discussions and suggestions, as wellas to

seminar participants at Bonn, Boston University,Bristol, Chicago, Columbia, Frankfurt, Georgia Tech, Gerzensee, HBS,

LSE, MIT, Michigan, NES Moscow, Oxford, Queen’s, Rotterdam, UCL, UCLA, USC, and Yale. Holden acknowledges

the Australian Research Council Future Fellowship FT130101159 and the Centre for International Financial Regulation

at UNSW for financial support.

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about timing to exploit temporarily high monetary rewards even when socially efficient choices

have not changed. Evidence of the first type of gaming is provided by Burgess, Propper, Ratto,

and Tominey (2017) and Carrell and West (2010), of the second type by Gravelle, Sutton, and

Ma (2010), and of the third type by Oyer (1998), Larkin (2014), and Forbes, Lederman, and

Tombe (2015).1The costs of gaming are exacerbated when the agent has superior knowledge of

the environment: this makes the form and extent of gaming harder to predict and hence, harder

to deter.

It has been suggested that lack of transparency—deliberate opacity about the criteria upon

which rewards will be based and/or how heavily these criteria will be weighted—can help deter

gaming. This idea has a long intellectual history. It dates back at least to Bentham (1830) who

argued that deliberate opacity about the content of civil service selection tests would lead to the

“maximization of the inducement afforded to exertion on the part of learners, by impossibilizing

the knowledge as to what part the field of exercise the trial will be applied to, and thence making

aptitude of equal necessity in relation to every part.”2

More recently,responding to documented gaming of the highly transparent incentive schemes

which score National Health Service organizations in England according to published lists of

precisely defined performance indicators, Bevan and Hood (2004) argued in the British Medical

Journal, “What is needed are ways of limiting gaming. And one way of doing so is to introduce

more randomness in the assessment of performance, at the expense of transparency.”They invoke

the “analogy [ . .. ] with the use of unseen examinations, where the unpredictability of what the

questions will be means that it is safest for students to cover the syllabus.” They reason that

making it harder for hospitals to predict what performance measures will be used and how they

will be weighted, coupled with hospitals’ risk aversion, will reduce the hospitals’ incentives

for gaming. Similarly, Dranove, Kessler, McClellan, and Satterthwaite (2003) document that

in the United States, report cards for hospitals “encourage providers to ‘game’ the system by

avoiding sick patients or seeking healthy patients or both” and they argue that such gaming is

facilitated by “risk-averse providershaving better information about patients’ conditions” than do

the analysts who compile the report cards. They present evidence that the increased transparency

of incentive schemes for physicians and hospitals providedby report cards increased gaming and

even decreased patient and social welfare.3

The costs of transparency have also been discussed in the context of gaming, by law school

deans, of the performance indicators used by U.S. News to produce its influential law school

rankings. The ranking methodology is transparent and employsa linear scoring r ule incorporating

multiple performance indicators.4There is significant evidence that law schools deploy a range

of strategies that exploit their informational advantage over U.S. News to increase their measured

performance. Examples include cutting the number of full-time students to boost median LSAT

scores and GPAs, creating make-work jobs for their own graduates to inflate the number in

1Burgess et al. (2017) and Gravelle, Sutton, and Ma (2010) study United Kingdom public sector organizations

(an employment agency and the National Health Service, respectively), Carrell and West (2010) use data from post-

secondary education, whereas Oyer (1998), Larkin (2014), and Forbes, Lederman, and Tombe (2015) examine private

sector organizations (salespeople and executives across various industries, enterprise software vendors, and airlines,

respectively).

2Bentham, 1830/2005, Ch. IX, §16, Art 60.1.

3Relatedly, Googlehas experienced manipulation of its search results by some retailers. Although many retailers

have been seeking greater transparency from Google about its search algorithm, Googlehas responded by moving in the

direction of greater opacity to prevent manipulation (Structural Search Engine Optimization, Google Penalty Solutions,

November 4, 2011, www.re1y.com/blog/occupy-google-blog.html). Motivated in part by this debate, Frankel and Kartik

(2014) develop a signalling model of gaming in which the information conveyed bysignals (e.g., prominence in search

results) about agents’ hidden characteristics (e.g., intrinsic relevance to the query) is “muddled” because agents are also

privatelyinfor med about their gaming ability.Other theoretical treatments of gaming of incentive schemes include Jehiel

and Newman (2011) and Barron, Georgiadis, and Swinkels (2017).

4The weights in the scoring rule are quality perception (40%), selectivity (25%), placement success (20%),

and faculty resources (15%) (U.S. News, March 11, 2013, www.usnews.com/education/best-graduate-schools/top-law-

schools/articles/2013/03/11/methodology-best-law-schools-rankings).

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employment, and heavilyadvertising their faculty’s scholarship to U.S.News.5Law scholars (e.g.,

Osler, 2010) have arguedthat g reater opacity in the ranking methodologycould mitigate gaming,

and U.S. Newshas itself signalled its intention to move away from being “totallytransparent about

key methodology details.”6

Finally, one view as to why courts often prefer standards—which are somewhat vague—to

specific rules is that standards mitigate incentives for gaming. For example, Weisbach (2000)

argues that vagueness can reduce gaming of taxation rules, and Scott and Triantis (2006) argue

that vague standards in contracts can improve parties’ incentivesto fulfill the spirit of the contract

rather than focusing on satisfying only the narrowly defined stipulations.

The examples discussed above suggest that “opacity” (i.e., lack of transparency)of incentive

schemes can be beneficial in reducing gaming, especially when agents have superior knowledge

of the environment, when incentive designers care about multiple aspects of performance, and

when gaming takes the form of agents’ focusing efforts on easily manipulableindicators. This line

of argument is, however, incomplete. If agents are risk-averse, then the additional risk imposed

by opaque schemes is per se unattractive to them. Understanding when and why opaque schemes

are used thus requires analyzing the trade-off between their incentivebenefits and their risk costs.

The present article provides such an analysis.

Our analysis incorporates three vital ingredients that are featured in all of our motivating

examples: (i) the agent’s superior information about the environment, (ii) the agent’s risk aversion,

and (iii) the incentive designer’s need for the agent to choose a relatively balanced allocation of

efforts across activities. This suite of ingredients (along with a contractual restriction to incentive

schemes that are ex post linear) delivers two main messages. First,transparent incentive schemes,

even when they involve menus, suffer dramatically from the problem of gaming by the agent.

Second, opaque incentive schemes not only mitigate the problem of gaming but can generate a

higher payoff for the principal.7

In our model, “opacity” corresponds to a lack of transparency about the weights on per-

formance indicators that are used to determine rewards. Motivated by the examples discussed

above, we build on Holmstrom and Milgrom’s (1991) multitask principal-agent model in which

a risk-averse agent performs two tasks, which are substitutes in his cost-of-effort function, and

receives compensation that is linear in his performance on each of the tasks. These linear contracts

(which have been widely studied) are “transparent” in that the agent faces no uncertainty about

the rate at which performance on each of the tasks is rewarded. The principal’s benefit function

is complementary in the agent’sefforts on the two tasks; other things equal, she prefers to induce

both types of agent to choose balanced efforts.8Into this familiar setup, we introduce superior

knowledge of the environment on the part of the agent. There are two types of agent, and only

the agent knows which type he is. One type has a lower cost of effort on task 1, and the other has

a lower cost of effort on task 2.9

The privately informed agent games transparent incentive schemes by choosing effort allo-

cations that are excessively (from an efficiency perspective) sensitive to his private information.

5Law School Rankings Reviewedto Deter “Gaming,” Wall Street Journal, August 26, 2008.

6U.S. News, May 20, 2010, www.usnews.com/education/blogs/college-rankings-blog/2010/05/20/us-news-takes-

steps-to-stop-law-schools-from-manipulating-the-rankings.

7The terms “opaque” and “transparent” may have alternative definitions in other contexts, but here, where we

confine attention to compensation schedules that are ex post linear, an “opaque” incentivescheme will always be one that

leaves the agent, when choosing efforts, uncertain about the incentive coefficients he will face, whereas a “transparent”

scheme will be one under which the agent faces no such uncertainty.

8Our model, like Holmstrom and Milgrom’s(1991), incorporates shocks to measured perfor mance. These shocks

are not essential for our two main messages, given our focus on contracts that are ex post linear. In fact, as shown in

Section 6, our findings about the benefits of opaque incentive schemes would be even stronger in the absence of such

shocks. Nonetheless, it is natural to include them in the analysis; if the agent’s efforts were directly observable by the

principal, then the problem of moral hazard could be trivially solved bya so-called “forcing contract.”

9The analysis would be very similar if the agent types differed with respect to the task on which they weremore

productive.

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