Discussion Papers 745
2 The model
I e 1 + e 2 I 2
Max T - Ci = 11-------I - ki 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 ki
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 = 2ki
2 We equally weigh both players’ profits. By using different weights we find other Pareto optimal solutions.