Decision Making & Negotiations

The article focuses on the author's view on whether consumers can calculate best buys. According to the author, a number of studies have found only a limited incidence of the ability to reason proportionately. Though subjects in these studies were still in their teens, little further development would be probable with their advancement into adulthood. This evidence led to their hypothesis that a significant number of adults would be unable to utilize a proportional reasoning strategy in a simple consumer decision-making context.

Reprinted in Advances in Financial Economics: Volume I (Theory), Bhattacharya and Constantinides (editors), Roman and Allenhead publishers 1986.

Consider a renewal process {Xn, n ≥ 1} for which there is defined an associated sequence of independent and identically distributed random variables {Bn, n ≥ 1} such that Bn is the length of a subinterval of Xn. We show that when attention is restricted only to B-intervals, the asymptotic joint distribution of the residual life and total life of a B-interval is that of a renewal process generated by {Bn, n ≥ 1}.

This paper is a theoretical investigation of equilibrium forward and futures prices. We construct a rational expectations model in continuous time of a multigood, identical consumer economy with constant stochastic returns to scale production. Using this model we find three main results. First, we find formulas for equilibrium forward, futures, discount bond, commodity bond and commodity option prices.

This paper considers the solution of Markov decision problems whose parameters can be obtained only via approximating schemes, or where it is computationally preferable to approximate the parameters, rather than employing exact algorithms for their computation. Various models are presented in which this situation occurs. Furthermore, it is shown that a modified value-iteration method may be employed, both for the discounted version and for the undiscounted version of the model, in order to solve the optimality equation and to find optimal policies.

Recent papers have shown that Π∞k = 1 P(k) = limm→∞ (P(m) ... P(1)) exists whenever the sequence of stochastic matrices {P(k)}∞k = 1 exhibits convergence to an aperiodic matrix P with a single subchain (closed, irreducible set of states). We show how the limit matrix depends upon P(1).

For the multi-server queue with Poisson arrivals and general service times we present various approximations for the steady-state probabilities of the queue size. These approximations are computed from numerically stable recursion schemes which can be easily applied in practice. Numerical experience reveals that the approximations are very accurate with errors typically below 5%. For the delay probability the various approximations result either into the widely used Erlang delay probability or into a new approximation which improves in many cases the Erlang delay probability approximation.

We examine the relative effects of several service order disciplines on important operating characteristics of queues in which customers request a random number of servers. This class of queues is characterized by customers who cannot begin service until all required servers are available. We show that for many systems in this class, it is possible to define a new service order disciplien which is more efficient than FIFO with respect to one or more measures such as expected waiting time, probability of delay, etc.