Voluntary Teaming and Effort



Discussion Papers 745

5 Experimental results

In the VOLUNTARY ASYM treatment, team remuneration is chosen by both players and thus
realized in as many as 72 percent of all periods. Again, this is in sharp contrast to the sub-
game-perfect equilibrium of the game with its specific parametrization. The relative frequen-
cy of team remuneration in this treatment exhibits a tendency to increase over time. When we
compare the first set of 15 periods to the last set of 15 periods, we observe an increase that is
significant at the 5-percent level (Wilcoxon test).

In the subgame-perfect equilibrium of the VOLUNTARY ASYM treatment only the high-cost
player has an interest in choosing team remuneration. Thus, we hypothesize that high-cost
players tend to choose team remuneration more often than low-cost players. We find support
for this hypothesis in that the high-cost players chose team remuneration in 89 percent of all
periods while the low-cost players chose team remuneration in 78 percent of all periods. In six
of the eight independent groups the high-cost player chooses team remuneration more often
than the low-cost player. This replicates the empirical finding of Hamilton, Nickerson and
Owan (2003).

Conclusion 1: Participants do choose team remuneration, contradictory to the subgame-
perfect equilibrium solution of the game.

Prediction 2: Participants choose the optimal effort level under private remuneration.

In the VOLUNTARY SYM treatment, the average effort over all periods with private remunera-
tion is 45.27 (standard deviation of 16.81) and is not significantly different from 45, the opti-
mal effort in the case of private remuneration (binomial test). This might be interpreted as
evidence in favor of the participants' rationality. However, only about one half (52 percent) of
all individual decisions under private remuneration are exactly 45. Participants tend to learn
the optimal effort, though: the percentage of optimal private-effort choices increases from 47
in the first set of 15 periods to 63 in the last set of 15 periods. This increase is significant at
the 10-percent level (Wilcoxon test).

In the VOLUNTARY ASYM treatment, the average private effort of the low-cost players is
34.87 (standard deviation of 9.88), which is not significantly different from the optimal level
of 35 (binomial test), and the average private effort of the high-cost players is 27.22 (standard
deviation of 15.58), which is not significantly different from the optimal level of 28 (binomial
test). However, on the aggregate, only 51 percent of the effort choices by the low-cost players
and 46 of those by the high-cost players are optimal. Pooling low-cost and high-cost players

13



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