Two workers, Conrad and Dina produce 5*E units of output each working individually where E is the amount of effort that they provide. Dina's output working individually is 5*E_DI and Conrad's output working individually is 5*E_CI. The subscript "I" denotes effort working individually and the subscript "T" denotes effort working on a team.

If they work as a team and coordinate their effort, their joint output as team is

Team Output = 2*(E_DT + E_CT)².

The team output is greater than the sum of the individual outputs so long as E_DT + E_CT > 10.

The amount of effort Dina and Conrad provide depends on their incentives. With a bonus contract that is percentage of output (x%), the marginal return to output from a unit of additional effort working individually is 5 for all levels of E_DI and E_CI and the marginal bonus to the individuals from an additional unit of effort is x%*5. With team production, the two workers split the credit for the output, so the marginal return to an additional unit of effort is 2*(E_D + E_C) and the marginal bonus for an additional unit of effort is x%*2*(E_D + E_C).[1]

So the two workers have weaker incentives when placed on a team which could eliminate the benefits of creating a team unless Conrad is confident that Dina will put forth a certain level of effort and vice versa.

How would you modify the objective bonus contract to make Conrad is confident that Dina will put forth a certain level of effort and vice versa?

Notes: There are somethings that you are not allowed to do. You cannot play Santa Claus with the shareholder's money and make x% larger. You cannot switch to a subjective bonus program because it is prohibitively costly to measure Dina and Conrad's effort in team setting.

[1] The team output is 2*(E_DT + E_CT)². The individual's share for performance purposes is half of the total: (E_DT + E_CT)². The marginal return to a unit of effort is the derivative of individual's share with respect to effort.