Voluntary Teaming and Effort

Discussion Papers 745

2 The model

If at least one of the players chooses private remuneration, private remuneration is applied:
each player i is paid at the end of the second decision stage, based on his private effort multi-
plied by a constant, p. The private remuneration Pi for each player i is

P_i= pe_i.

Note that we assume t > p. This reflects that in the case of team remuneration the firm has a
cost advantage relative to the case of private remuneration due to reduced monitoring costs.

The effort game ends at the conclusion of the second decision stage. Player i's profit Πi is
determined by his remuneration minus his individual cost of effort:

Π _i=P_i-C_i in the case of private remuneration

Π _i=T_i-C_i in the case of team remuneration

2.2 The subgame-perfect equilibrium

The subgame-perfect equilibrium of the effort game can be found by backward induction. We
start by considering the second decision stage in which each player chooses a profit-
maximizing effort level. We have to distinguish whether private or team remuneration ap-
plies, which depends on the players’ choices in the first stage.

In the case of private remuneration, each player i solves an individual profit-maximization
problem that is independent of the other player's effort choice:

Max P_i-C_i=pe_i-k_ie_i² .
e_i

The resulting optimal effort

e * = P^-

ei      2 ki

implies the profit

p

Π * = — e * .

i2i

In the case of team remuneration, each of the two players, i = 1, 2, independently chooses his
effort to maximize his individual profit, taking the other player's effort into account:

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