Top

Social Choice and Welfare

Published in:

08-06-2019 | Original Paper

Dominance of contributions monitoring in teams

Authors: Parimal K. Bag, Peng Wang

Published in: Social Choice and Welfare | Issue 3/2019

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In team problems it has been previously argued that there is no loss to the principal from monitoring team output compared to monitoring of individual contributions, a result known as monitoring equivalence. Optimal output monitoring, however, sometimes required up front payment from the agents to the principal. By introducing limited liability (LL) on the part of agents that rules out positive monetary transfers to the principal, it is shown that the principal strictly benefits by monitoring individual contributions. Positive rent of the lowest type under output monitoring with LL implies there will be a dominating contributions monitoring contract that further transfers some of this rent to the principal. Thus, unlimited agent liability is necessary for the equivalence result.

previous article Equilibrium competition, social welfare and corruption in procurement auctions

next article Dilemma with approval and disapproval votes

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Exceptions could be law firms or a group of medical doctors in private practices where junior partners may have to pledge compensation at the start in case the firm (or the group) does not perform well. Simon Grant suggested this example.

Vander Veen (1995) observed that McAfee–McMillan’s equivalence result should break down if the agents are risk averse.

There are other differences as well that will become clear in the model section.

See the discussion of Holmström (1982) conjectures below.

Thus, our limited liability restriction is weaker: ex post participation constraint implies limited liability but not necessarily the other way around.

Strausz (2006) had argued that in most principal-agent applications, focusing on deterministic mechanisms can be justified so long as the optimal (deterministic) mechanism satisfies a “no-bunching” condition. To our knowledge no such result is available in the principal-multi-agent setting, which is our focus.

Note that the payment to agent i is restricted to depend only on i’s contribution. Admittedly this weakens the principal’s hand but given that ultimately we are going to show dominance of contributions monitoring, allowing a more general payment function that depends on other agents’ contributions as well would retain the dominance result if not strengthen it further.

Note that there are multiple equilibria for each type of contract, all leading to the same contributions and principal’s payoffs. In particular, we do find optimal contracts such that payments under contributions monitoring are all positive. As can be clearly seen later, the optimal contract under contributions monitoring in Table 2 is also optimal without imposing the limited liability constraint.

Similar to contributions monitoring, there are multiple solutions for the optimal payment under output monitoring without limited liability. Multiplicity of optimal payments will also be observed under contributions and output monitoring when limited liability applies, but only one set of optimal contributions is obtained for each case.

A more natural mechanism would be to give a non-negative reward so long as i’s contribution is at least \({\bar{y}}_{i}({\hat{z}}_{i},\hat{\mathbf{z }}_{-i})\) and zero reward otherwise. All our analysis will hold for this alternative mechanism.

Note that the actual implementation of the punishing contract involves all non-negative ex post payments.

After setting the lower bound of the team production technology at 0, e.g., when all team members put in 0 effort output is low (with probability 1), we ran more simulations which show that the dominance result still holds. Thus, the lower bound assumption is not necessary for our dominance result.

In fact, it is easy to see that in our model the lowest type of every agent would earn a positive rent under limited liability, so long as one justifiably ignores the extreme contract in which an agent receives zero payments for all output realizations. See the discussion following Assumption 1 and Proposition 3. Thus, a stronger version of Proposition 3\(^\prime \) can be established.

In fact, for any feasible output monitoring contract, except for the ‘null contract’, we can find a dominating contributions monitoring contract. Thus, the existence result is not essential for our dominance result.

Unlike in contributions monitoring, under output monitoring the principal has to penalize all following a deviation because he won’t be able to tell who has deviated.

The latter requirement is fulfilled so long as the downward-adjusted payment does not fall below the cost of the suggested contribution \(y^c_{i}({\hat{z}}_{i}^\prime , \mathbf{z }_{-i})\) by the true type \({\bar{z}}_i\).

Note that the reductions in type \({{\bar{z}}}_i\)’s deviation payment that were carried out earlier for \(({\hat{z}}_{i}^\prime ,z_{-i})\) reported profiles, the same reductions will happen when the true type is \({{\hat{z}}}_i^\prime \) and the reported profiles are the same \(({\hat{z}}_{i}^\prime , \mathbf{z }_{-i})\). That is, the same reductions apply to both sides of (A.8).

Che Y-K, Yoo S-W (2001) Optimal incentives for teams. Am Econ Rev 91:525–541CrossRef

Gershkov A, Winter E (2015) Formal vs. informal monitoring in teams. Am Econ J Microecon 72:27–44CrossRef

Holmström B (1982) Moral hazard in teams. Bell J Econ 13:324–340CrossRef

Khalil F, Lawarrée J (1995) Input versus output monitoring: who is the residual claimant? J Econ Theory 66:139–157CrossRef

Laffont JJ, Martimort D (2002) The theory of incentives: the principal-agent model. Princeton University Press, Princeton, ISBN 0-691-09183-8

McAfee RP, McMillan J (1991) Optimal contracts for teams. Int Econ Rev 32:561–577CrossRef

Myerson R (1982) Optimal coordination mechanisms in generalized principal-agent problems. J Math Econ 10:67–81CrossRef

Ollier S, Thomas L (2013) Ex post participation constraint in a principal-agent model with adverse selection and moral hazard. J Econ Theory 148:2383–2403CrossRef

Rahman D (2012) But who will monitor the monitor? Am Econ Rev 102:2267–2297CrossRef

Raith M (2008) Specific knowledge and performance measurement. Rand J Econ 39:1059–1079CrossRef

Strausz R (2006) Deterministic versus stochastic mechanisms in principal-agent models. J Econ Theory 128:306–314CrossRef

Vander Veen TD (1995) Optimal contracts for teams: a note on the results of McAfee and McMillan. Int Econ Rev 36:1051–1056CrossRef

Varian H (1990) Monitoring agents with other agents. J Inst Theor Econ 146:153–174

Title: Dominance of contributions monitoring in teams
Authors: Parimal K. Bag
Peng Wang
Publication date: 08-06-2019
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 3/2019
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-019-01193-7

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 3/2019

Dissatisfied with life or with being interviewed? Happiness and the motivation to participate in a survey

Correction to: Relationally equal treatment of equals and affine combinations of values for TU games

Dilemma with approval and disapproval votes

Using the Borda rule for ranking sets of objects

Evidence reading mechanisms

Strategyproof judgment aggregation under partial information