onstrated how behavior-based modeling
can substantially improve the ability to
derive credible predictions in these systems. The necessity of behavior-based
modeling is likely to be only magnified
in real-world systems, where players have
to face more uncertainties than in the
lab. We conclude that in order to achieve
desired outcomes in our systems, we
should take into account the way humans, as opposed to rational agents,
make decisions. The challenge for future
research is to appropriately incorporate
in our models insights from the well-established behavioral theories, as well
as new insights obtained from the large
amounts of available behavioral data,
and to design our systems according to
these behaviorally appropriate models.
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Gali Noti is a Ph. D. student in the School of Computer
Science and the Center for the Study of Rationality,
at the Hebrew University of Jerusalem, under the
supervision of Prof. Noam Nisan. Her research is in
the intersection of computer science, economics and
psychology, and specifically she is interested in gaining
insights from human decision-making behavior using
the frameworks of algorithmic game theory, data
science, and machine learning. Gali Noti is supported by
the Adams Fellowship Program of the Israel Academy of
Sciences and Humanities.
© 2017 Copyright held by owners/authors.
Publication rights licensed to ACM
A classic equilibrium-based approach would be to assume the players
reach (approximately) a mixed Nash
equilibrium of the game. This game
has a single mixed equilibrium, in
which the column player must be playing “Left” with a probability p =10/(x+ 1),
so x can be extracted and estimated by
◯ =10/p – 1=10/(0.07+0.61)– 1≈ 13. 7.
Nekipelov et al. suggested to perform the estimation based on the
weaker assumption that the players
(nearly) minimize their regret [ 7]. They
presented this regret-based approach
to econometrics in the specific context
of ad auctions, where estimating bidders’ values from their bids is particularly attractive, but it is in fact general
to most repeated-game scenarios. An
adaptation of their “min-regret” estimation method would calculate for
every possible value of x, what would
have been the regret of the row player,
had the missing parameter been this
value. As in the previous section, the
regret is defined as the difference between the utility that the row player
could have obtained by using the best
fixed strategy in hindsight (and the
other player is still behaving as she
did empirically) and the utility that she
actually obtained under the empirical
play. For example: For x= 13, the row
player’s empirical utility is 0.07∙ 13+
0.04⋅0+0.61⋅ 9+0.28⋅ 10= 9. 20; while had
she always played “Down,” her utility
would have been (0.07+0.61)⋅ 9+(0.04+
0.28)⋅ 10= 9. 32; and had she always played “Up,” her utility would
have been (0.07+0.61)⋅ 13+(0.04+0.28)⋅0
= 8.84. Thus, the row player’s regret is
max( 9. 32, 8.84)– 9. 20=0.12. More generally, one may calculate the regret of the
row player for every possible value of x
(in some grid in some valuation range),
utilEmp(x). The regret of the row player
as a function of the “hidden value” x is
plotted in Figure 2(c). Then, the min-regret method would take as its estimate ◯ the value with the lowest regret,
which (using a grid of integers) is 13 in
Now, let us relax the rational-
ity assumption that underlies both the
equilibrium-based and the min-regret
methods, and take into account be-
havioral results. We first consider the
observation previously described that
humans do seem to minimize regret,
but they do not optimize perfectly. We
then look at the regret curve in Figure
2(c) and notice it is much steeper to the
right of the min-regret point than it is
to its left. Thus, it may seem more likely
that the real value of x is lower than 13
(where the player only loses a bit from
acting the way she did) than that it is
higher than 13 (where the player loses a
lot). We may utilize these observations
by averaging the possible values of x,
with weights that are decreasing with
the regret. Specifically, our “quantal-
regret” estimation method [ 8] takes ex-
ponentially decreasing weights, as fol-
lows: ◯=(∑xe–λ.regret(x)⋅x)/(∑xe–λ.regret(x)). For a
value of (say1) λ= 3 this would evaluate
to ◯≈ 10. 2. As the value of the “regret
aversion” constant λ grows to infinity,
the quantal regret estimate approach-
es the min-regret estimate.
The example we considered is taken
from the results of one of the experimental sessions that Selten and Chmura have
run with human participants [ 9]. 2 For the
curious reader let us reveal that in the actual experiment the value was x= 10, and
indeed in this specific example the estimate of the quantal regret method was
significantly closer to reality than that of
the min-regret method of Nekipelov et al.
[ 7], which in turn was slightly better than
the “classic” equilibrium-based method.
In Nisan and Noti, we showed this is the
usual state of affairs in this 2x2 game
dataset and also in estimating bidders’
values from their bids in our ad auction
dataset [ 8]: The (behavioral) quantal regret method consistently and significantly outperforms the min-regret method
which in turn somewhat outperforms
classic equilibrium-based methods.
The experimental results we have surveyed demonstrate how the common
rationality and equilibrium modeling
assumptions may lead to significant errors in the analyses of computational
strategic systems with human participants. The quantal-regret method dem-
1 In Nisan and Noti, we suggest how to determine the value of λ, and show that the improvement using the quantal regret method is
robust for a wide range of λ values [ 8].
2 The exact setup used in Selten and Chmura
[ 9] is more complex than presented here. For
more details see Nisan and Noti [ 8].