# conjecture

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## conjecture

A conclusion that is not proved but rather is assumed from incomplete evidence; a guess or speculation.
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Yet, we are rather confident that this argument lacks relevance in our setting: in order to improve their chance of earning money, our seller participants could report several conjectures and aspirations without having to forego profits resulting from their conjectured prices.
Our experiment implements a multi-period triopoly market where, in every period, each seller participant must (1) choose one price, (2) specify a finite set-valued conjecture about the average price of his two current competitors, and (3) form a profit aspiration for each conjectured price.
This allows us to investigate whether the likelihood of revising depends on the received feedback and, if participants engage in revisions, what they revise more often (their conjectured prices, their profit aspirations, or their own price).
These two conditions are rather sensible: the first simply requires that sellers should best respond to their own set of conjectures; the second postulates that each specified aspiration must be achievable and not too moderate, that is, it must fully exhaust the profit potential allowed by the corresponding conjectured price and the chosen price.
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.
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
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.
French mathematician Henri Poincare conjectured 99 years ago that, just as in the case of surfaces, any dosed three-dimensional space in which loops can be tightened to a single point is really a three-dimensional sphere.

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