Conditions 1 and 2 define optimality in a more basic sense than that required by expected utility maximization because they do not entail the specification of any probability distribution over the set of conjectured prices.

To check experimentally whether participants comply with the two conditions characterizing prior-free optimal behavior, in every period, besides choosing a sales price, each subject had to specify a set of the others' average price that he considered as possible and the profits he aimed to achieve for each conjectured price.

When payments were based on conjectured prices, the payoff of a seller participant was given by [W.sub.i] = 180 - 10[min.sub.[c.sub.i] [member of] [C.sub.i]] [absolute value of [[bar.p].sub.i] - [c.sub.i]].

In fact it is also conjectured that for every n, there are n consecutive primes in arithmetic progression; at the time of writing, the longest such string consists of 10 primes (see Caldwell, 2004b).

When they are not, consider the smallest natural number d such that [P.sub.k] + d is prime; Reo Fortune conjectured that the numbers d are themselves prime: they are called the fortunate numbers (Golomb, 1981).

It had long been conjectured that there is an algorithm whose duration is a polynomial function of the number of digits in the given number p.

Scientists have

conjectured that chemicals called morphogens may help orchestrate embryonic development by turning on or off genes in specific sets of cells at different times.

More than three centuries ago, French mathematician Pierre de Fermat

conjectured that all numbers of this form are prime -- that is, divisible evenly only by themselves and 1.