LEARNING MODELS
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play. In almost all cases, they find that the best Žmaximum-likelihood. version of
the model is quite different from the restricted versions, and that the former is
significantly better than any of the latter.
We will look at four data sets, each of which comes from an experiment
involving a simultaneous-move game. Two were used by Erev and Roth: Erev
and Roth’s Ž1998. ‘‘Matching Pennies’’ game and Ochs’s Ž1995. 2=2 games.
The other two were used by Camerer and Ho: Mookherjee and Sopher’s Ž1997.
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=6 constant-sum games, and Van Huyck, Battalio, and Beil’s Ž1991. median-
action game. As we did in Section 4.1 with the asymmetric-information game
data, we look at the models’ abilities to predict individual decisions. As before,
we attempt to limit the reliance of the models on unobservable initial propensi-
ties or beliefs by not comparing predictions of behavior with actual play in early
rounds. For each data set, we compare model predictions with play from round
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1 through the last round of play, with the exception of the data from van Huyck
et al., whose experiment only lasted ten rounds; we consider rounds 3 through
0 of this data set. The data we examine range from 75% to 96% of each
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experiment. For comparison, and in order to examine the plausibility of our
assumption that initial propensities or beliefs are drowned out by the time we
reach the rounds at which we look, we also consider the data from a smaller
subset of rounds of each experiment Žroughly the last 50% of each experiment..
As a basis for comparison, in addition to the RE and BA models, we
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consider stationary equilibrium Žif the equilibrium is unique., the INŽ0.75.
model in which players repeat their previous action with probability 0.75 and
play each other action with equal share of the remaining 0.25 probability, and
the INŽ1rm. model in which players play each of the m possible actions with
equal probability. For each of these models, we report in Table VII the MSD,
POI, and lnŽL. scores, as well as the posterior probability of each model Žagain,
given that one of these models is the correct one. and the rounds considered.
According to both MSD and lnŽL. Žand thus posterior probability., RE is
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the best for characterizing Erev and Roth’s data, but it is only slightly better
than the INŽ0.75. model according to MSD, and worse according to POI. Even
the best BA model fares worse than RE according to all three criteria, but it
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nonetheless improves upon the stationary equilibrium prediction. None of
these results changes when we look at rounds 251᎐500 rather than 11᎐500.
Ochs’s data present a somewhat weaker case for the RE model; according to
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MSD, it outperforms the rest of the models, and the best BA model is even
worse than the INŽ0.75. model. On the other hand, according to POI, RE is
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worse than BA and only slightly better than INŽ0.75.. According to lnŽL., RE is
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worse than BA and both inertial models; as with POI, the BA model outper-
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The best BA model is determined separately for each data set, time frame, and criterion, again
using a grid search. The optimal values of and ␦ vary greatly between experiments and between
criteria; and vary somewhat between time frames. For example, using the longer time frame and the
lnŽL. criterion, the best BA model is BAŽ0.791,y0.133. for the Erev and Roth data set,
BAŽ0.612,0.236. for the Ochs data set, BAŽ31.0,y27.6. for the van Huyck et al. data set, and
BAŽ0.556,0.153. for the Mookherjee and Sopher data set.