BoundedRationality_TheAdaptiveToolbox.pdf

218
game/ choice prob.
S&A2: A2 B2
A1 (2,4) (6,0)
B1 (3,3) (1,5)
S&A8: A2 B2
A1 (8,0) (3,8)
B1 (0,5) (5,3)
S&A3k: A2 B2
A1 (3,7) (8,2)
B1 (4,6) (1,9)
S&A3u: A2 B2
A1 (3,7) (8.2)
B1 (4,6) (1,9)
M&L: A2 B2
A1 (3,-3) (-1,1)
B1 (-9,9) (3,-3)
Ido Erev and Alvin E. Roth
Data
A1
A2
eq.
Basic
reinforcement
(1par)
Predictions
Roth/Erev
(RE)
(3 par)
a^-g-r-g
A1 at eq.
A2ateq.
T] D D Q-e- 1
A & A a A A
•B-O O D O D D
FP-like
(4 par)
Figure 12.1 Repeated 2^2 games (S&A: Suppes and Atkinson 1960; M&L: Malcolm
and Lieberman 1965). In the top four games, each payoff unit increases the probability of
winning by l/6inS&A2,by l/8inS&A8,andby l/10inS&A3kandS&A3u. In the fifth
game, payoffs were directly converted to money. Each cell in the left-hand column presents
the experimental results: the proportion of A choices over subjects in each role
(grouped in 5 to 8 blocks) as a function of time (200-210) trials in all cases. The three
right-hand columns present the models' predictions in the same format. The equilibrium
predictions are presented at the right-hand side of the data cells. Adapted from Erev and
Roth (1998b).
L2 Average Updating
The propensity of Player n to play strategy; at trial t + 1 is a weighted average of
the initial propensity (qnj (1)) and the average payoff obtained by Player n from
playing j in the first t trials (AVEnj(t)). The weight of the initial propensity is a
function of an initial strength parameter N(l) and the number of time Player n
chose strategy; (CnJ(t)). Specifically,
CAD + NiV/m,,
c^t)
+AVE * {t) CJ(t) + N(l)/mn ' ( 12 - 2 >
«M~«UcJFZ* +A1 *'