Secure Implementation Experiments: Do Strategy-proof Mechanisms ...

elatively better than a non-secure one). In a real world application, the subjects may become
confused about the rules of the game and the payoffs. We leave for the future the task of
studying how noise can be minimized in practical applications. But we believe that overly
pessimistic conclusions about the future of mechanism design, which some researchers have
drawn based on the poor performance of non-secure mechanisms in laboratory experiments,
may not be justified at this point. Our experiment suggests that there is no inherent flaw in the
game theoretic predictions that would rule out all possible practical applications. 20
In practical applications, mechanisms should not be too complex, due to the finite
information processing capacity of the players. It turns out that requiring secure
implementation does not lead to more complex mechanisms: attention can be restricted to
revelation mechanisms without loss of generality (Saijo, Sjöström and Yamato, 2003). By
Proposition 1, the efficiency condition and strategy-proofness essentially pin down the
revelation mechanism in the public goods environment. In order to compare the performance of
two efficient strategy-proof revelation mechanisms, one that is secure and one that is not, the
environment (specifically, the set of valuation functions) has to vary across treatments (as in
Treatment P versus Treatment S). In our experiment, we do not think this matters too much,
because the presentation of the payoff tables was similar in the two treatments. Still, in other
situations it may be possible to make interesting comparisons of the performance of secure
versus non-secure mechanisms in the same environment. This is left for future experiments.
Recently, Chen (2005) and Chen and Gazzale (2004) study whether mechanisms based
on supermodularity conditions achieve convergence to Nash equilibria through learning. They
find supermodular mechanisms converge significantly better than non-supermodular
mechanisms in experiments. It would be interesting to investigate the role of supermodularity
in accomplishing convergence to dominant strategy equilibria. It is easy to check that
20 In contrast, if the secure mechanism had performed poorly in our experiment, this would have suggested that, no
matter how well the mechanism could be explained to the participants, practical applications of mechanism design
would have little hope of success.
32