On a Dual Control Approach to the Pricing Policies of a Trading Specialist

We consider a market in which there is a specific economic agent or authority who sets the price, and trading takes place out of equilibrium. We call him a marketeer following Clower [8]. A trading specialist is one example of a marketeer whose pricing policies are the main concern of this papem. We assume further that he does not know the exact demand and supply condition that he faces in the market, i.e., he has only imperfect knowledge of the market response to a price he sets. He does have some subjective estimate of the market response as a function of the price he sets. See Arrow [2] for a related topic. Denote by f(p;8) his subjective estimate of the market response (for example, excess demand for the co~ty), where 8 is an element of a known set e . In other ~rds, in the opinion of the marketeer {f(p;@), 8 ~ @} represents a family of possible responses to his setting p . By specifying 8, a specific response is chosen as his estimate. Assume that the true response (unknown to him) corresponds to f(p;8*) + ~ , 8* g 8 ~ where ~ is a random vamiable to be fully specified later. We take 0 to be time-invariant. Therefore~ the actual response may deviate from f(p;8) by: (i) the agent's estimate of the parameter e, being different from the true parameter 8*; and by (ii) the random variable ~ which may be used to represent the effects being Lm]q%own to be systematic to the agent. Various anticipated or systematic trends % such as price expectation on the part of the buyers could be modeled. The probability distribution of is assumed to be known to the agent. The type of consideration to be presented below can be easily extended to the case where the distribution is known imperfectly; for example, up to certain paran~tem values specifying the distributions uniquely. This added generality is not included in the paper, since it represents a straightfor~4ard extension of this paper.