Incentives in Teams

Why Teams?

* Complimentary - foster coordination and cooperation in an organisation
* Allows specialisation to occur and specialisation to be used to the max
* But:
	+ Difficult to identify individual effort from the team effort
	+ Difficult to evaluate individual effort from team effort

Pay for "Team"-Performance

* Team Output can only usually be measured aggregately and individual effort is not seen
* The externalities of teamwork is from the interaction between the team members
	+ Complementaries occur when the team works together and it benefits the entire team
	+ A team working together as a sum is better than the individuals
	+ One member putting in effort improves the team in general

* This creates a problem of freeriding
	+ The actions of one individual benefits the group so this is the case of a private provision of a public good.
	+ Since the entire team benefits, some members of the team shall not contribute as they can benefit from the team effort itself.
	+ As a result, the team members that contributed will not be rewarded accordingly for the disproportionate effort they put in.
	+ Lack of coordination may also be a cause of free-riding as work is not distributed properly over the team members.

First Best Effort(in partnerships) and reducing free-riding

* Partnerships mean that output is shared among the team members
* Output/Revenue is a1+a2+a3+....an
* Cost per worker is 1/2\*a^2
* Marginal team output dP/da = Marginal personal cost dC/da => Team-surplus maximising output
* Suppose output is shared among the team by s1+s2+s3+.....sn = 1
* So a given worker's utility is = si(a1+a2+a3......an) - 1/2\*ai^2
* Worker puts in the effort du/da = dC/da = ai = si
* Whenever si < 1, worker will under-provide effort
* Inducing first best effort to prevent freeriding would involve giving all of the profit to the workers which is not desirable
	+ Question solving
	+ the objective is finding a\*, the optimum hours that the worker will put in as work
	+ Surplus is R - total personal Cost
	+ Maximise S to find optimum a\*
	+ utility function is revenue share - personal cost
	+ For finding a\* in a freeriding situation, we differentiate the utility function of the worker to find a\*
	+ the utility function for this is the same, Revenue share - personal cost
* Make pay system so that workers get paid only if they put in effort ~> Quota system
* This makes each worker pivotal
	+ Question solving burning money:
		- Worker utility function has two branches - one if the target is met and the other if the target is not
		- If not met the utility will be 0 - personal cost. Otherwise it would be revenue share - personal cost.
		- Revenue = (number of employees,n-1)\*optimal worker hours + worker's working hour a
		- Personal share would be above divided by 1/n
		- Compare revenue share gained to personal cost to find best response
		- Think slowly!
	+ Drawback of steep team incentives
		- If everyone puts in one unit of output, the output will be shared completely among workers
		- But if one worker puts in no effort, the output becomes n-1
		- The output is not there. What happened to it? Does it get destroyed? Are the nonworking members of the team rewarded with the output(Budget Breaking).
		- Multiple equilibria - workers work as long as they believe the other will work
		- Based on belief that others will work so if the belief is weak, worker will not put in work
		- Weak self-enforcing equilbrium
		- Budget Breaking as Debt Financing
		- Firm takes a loan of D with a commitment to repay it with a guarantee (bonus?) of b to each worker
		- D = n - nb
		- If output is at least n, then firm repays D and pays each worker b
		- If output exceeds n, excess is paid to workers equally
		- If unable to make enough, bankruptcy and firm owned by creditor
		- Bankruptcy ensures that work is done by the team members

Pay for Individual and Group-Performance

* How much to base compensation on group-performance or individual performance?
* Individual performance better for measuring individual behaviour
* Group performance allows individuals to take into account of their individual behaviour on the team
* Pay on group performance may improve individual behaviour
* RPE - Relative Performance Evaluation, performance of an individual evaluated in terms of another person's performance, promotes non-cooperation. Performance of others increase, pay of individual decreases. Used for: Benchmarking and Tournaments
* JPE - Joint Performance Evaluation, performance of an individual evaluated in terms of the performance as a team, promotes cooperation. Performance of others increase, pay of individual increases. Useful for: Internalising externalities and fostering cooperation
* Benchmarking
	+ Two risk averse workers exist P1 = a1 + e(common risk) and P2 a2 + e(common risk)
	+ Profit = sum of efforts = a1 + a2
	+ Basing pay on individual effort/performance means worker bears risk
	+ Comparing each worker to average performance eliminates the risk P1 - (P1+P2)/2
	+ Firm can induce first best effort in spite of workers risk aversion
	+ Comparing performance to others filters out common noise and infers lower risk to workers and increase individual incentives
* Cooperation vs Incentive
	+ Paying for group performance incentivises cooperation and internalising externalities for the benefit of the group
	+ But since group performance is evaluated for individual pay, there is a possibility of free-riding
	+ Tradeoff between internalising externalities and free-riding
	+ Individual performances of P1 = a1 + ya2, P2 = a2 + ya1
	+ Private cost = 1/2\*a^2
	+ Firm pays with individual performance APi and other team member performance BPj
	+ utility of worker 1, u1 = (A-B)P1 + B(P1+P2) - 1/2\*a^2
	+ firm pays B for joint performance and A-B for individual performance
	+ How would a worker change in individual and group pay?
	+ u1 = A(a1+ya2) + B(a1+ya2) - 1/2\*a^2 = (A+By)a1 + (By+A)a2 - 1/2\*a^2
	+ worker 1 thus puts in effort A+By with individual pay increasing performance and group pay change effect depends on the externality

Focused vs Broad based incentives

* Read slides
* TDR Broad based is better