Decision Makers Best Choice: an Investigation into the Efficiency of Search Strategies with Partial Information

Rank oriented models do not assume that we can exactly quantify the value of an alternative. They do not even assume that we know anything about the distribution of the utility, loss or other observable quantities characterizing an alternative’s utility. We only assume that we are able to rank the alternatives drawn. However the necessity to introduce search cost in our considerations seem to diminish the practical value of these strategies. It seems not to be possible anymore to confine ourself to ordinal utility functions (see [Janko, 2010]). In the models to be considered now we assume that it is possible to observe a value which we call price characterizing the alternative. Also we assume that the price distribution is known. Using the Bayesian approach we only assume knowledge of the distribution and not of the parameters of the price distribution. We shall consider here the multinomial distribution only. We shall give analytical results for the special case of the discrete uniform-distribution. M. Rothschild has treated the problem of searching for the lowest price when the distribution of prices is multinomial [Rothschild, 1976]. It is well known that the family of Dirichlet distributions is a conjugate family for observations which have a multinomial distribution. It must be emphasized that using the multinomial distribution we assume prior knowledge of the maximal value of observable offers. Let the prior density function of the multinomial probabilities