Voluntary Teaming and Effort

Discussion Papers 745

2 The model

I e 1 + e 2 I 2

Max T - C_i = 11-------I - k_i e².

ii          ii

ei                                   2

The solution is independent of the other player's effort and, thus, implies the following domi-
nant strategy for each player i:

t
_p * * ----

i        4 k_i

The resulting equilibrium profit for player i is:

tt

∏ ** = e ** + — e **          with i = 1, 2 and j = 3 - i.

i4i2j,                                    ,

Consider, now, the first stage of the effort game taking the above solutions into account. If
Πi** > Πi*, then player i chooses team remuneration; if Πi ** < Πi*, then player i chooses
private remuneration. If player i is indifferent regarding team and private remuneration, we
assume that player i chooses private remuneration. Only when both players choose team re-
muneration does the subgame-perfect equilibrium predict team remuneration; in all other
cases, it predicts private remuneration.

2.3 Joint profit maximization

In the case of team remuneration, the two players find themselves in a kind of prisoner's-
dilemma situation: their efforts represent voluntary contributions to the public good team
effort. To some extent, each player has an incentive to take a free ride on the effort of the
other player. The effort levels predicted by the equilibrium in dominant strategies are not
optimal for the team. We find Pareto-optimal team-effort levels by solving the joint profit-
maximization problem: ²

Max t (e₁+e₂)-k₁e₁² -k₂e₂²
e₁, e₂

For each player i, the optimal effort is given by:

t
e ' =-----

^{ei =} 2k_i

² We equally weigh both players’ profits. By using different weights we find other Pareto optimal solutions.

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