But, even if a seller participant wants to maximize the expectation of his experimentally designed monetary payoff, he should (1) predict the others' average price as accurately as possible because his conjectures enter in the [W.sub.i] part of Equation (5), (2) given these conjectures, choose a rationalizable price because specifying a price that cannot be rationalized by any probability distribution over [C.sub.i], in the attempt of lowering one's own actual profit and satisfying the condition in the third addend of Equation (5), would not be beneficial, and (3) set each aspiration level equal to the profits attainable given the chosen price and the corresponding conjectured price.
Observed Prices, Conjectured Prices, and Aspiration Profiles
Let [absolute value of [C.sub.i]] denote the cardinality of the elicited set [C.sub.i], that is, the number of player i's conjectured prices.
(10) Thus, the increase in the number of conjectured prices is associated with a decrease in the dispersion of conjectures and aspirations.
The boxplots in Figure 1 provide descriptive statistics on the distributions of stated prices and average conjectured prices (i.e., ([[summation].sub.[c.sub.i] [member of] [C.sub.i]] [c.sub.i]) /[absolute value of [C.sub.i]]) over all periods.
Turning to average conjectured prices (Figure 1B), the median and the mean values are, respectively, 6.50 and 6.69 in the first period, and 7.25 and 7.22 in the last period.
Although the average conjectured prices are, typically, lower than 8, are conjectures accurate?
Table 1 reports the percentage of subjects whose conjectured prices are such that [[bar.p].sub.-i] lies in their convex hull.
Do the profit aspirations of the satisficing participants exhaust the full profit potential allowed by their chosen price and their conjectured prices?
Overall, 76.54% of the satisficing participants specify at least one aspiration that is lower than the profits attainable given the chosen price and the corresponding conjectured price.
The observation that aspirations are adjusted more frequently than conjectured and stated prices applies also to across period-revisions.