Gaming and game theory are two extremely different yet highly related disciplines. It is of considerable use to a practitioner of either of these disciplines that he be aware of the relationship of one to the other. This paper attempts to provide a sketch of game theory for those whose prime concern is gaming.
The usefulness of group theoretic methods in solving integer programming (IP) problems is extended by procedures for controlling the size of the groups. The main procedure given shows how an optimal linear programming basis can be altered to reduce the magnitude of its determinant thereby reducing the size of the group induced by the basis. An adaption of Benders' mixed IP algorithm is given which uses these methods. Some limited computational experience is given.
A cursory survey of the theory of games is presented. The basic models for games in extensive form, normal form, and characteristic function form are discussed, and some generalizations and extensions of these models are mentioned briefly. Some general remarks about the applicability of the theory are made in §2, and a few-specific applications are referred to in sections subsequent to the description of the particular models. Mention is made throughout this paper to the other game theoretic articles in this issue in an attempt to place them somewhat within this outline of the subject.
Many manufacturing firms produce component parts both for assembly into new products and to meet orders for spare parts. An inventory model for this situation would involve two types of demands: probabilistic demand as spares and deterministic (or scheduled) withdrawals as components for assembly. Relevant costs would include a setup cost for replenishment orders, inventory carrying costs, and backorder costs. An analytical model approximating these characteristics is formulated. An optimal dynamic program for the periodic review case is briefly discussed; this policy is extremely costly to implement, however. Two feasible operating policies are considered in the paper: a continuous review (Q, r)-type policy and a simple periodic review scheduling heuristic. The paper concludes with sample economic comparisons of the cost of the (Q, r)-type policy and the heuristic policy for a set of numerical examples.
This paper is a case study in the development, implementation and evaluation of the delphi technique, which systematically makes use of expert judgment in generating manpower forecasts. The study was conducted in a large national retail organization on professional manpower. The results of the delphi technique are compared with results generated by conventional regression based models and the actual experience of the organization, which serves as the criterion. The study also analyzes the Informational elements used by experts during the delphi procedures and develops a model based on these elements. The usefulness of the delphi in generating manpower forecasting models is also discussed.
One of the important methodological problems concerning the application of decision analysis to complex problems is the restrictiveness of existing techniques for systematically assessing multiattributed utility functions valid for decision making under uncertainty. This is the problem addressed in this paper. Operational assumptions are postulated about the decision maker's preferences for multiattributed consequences, and functional forms of utility functions satisfying these assumptions are derived. The results are a number of representation theorems which simplify the assessment of the utility function provided the requisite assumptions hold. A special case of these results is the well-known additive utility function. A procedure to verify the appropriateness of the necessary assumptions is included.
A class of queueing problems is introduced in which each customer can purchase preferential treatment by making a payment. Each customer is assumed to select his payment so as to minimize his own expected cost, without regard for global considerations. A payment policy determines a customer's payment as a function of the information available. A payment policy is said to be stable if no one customer can reduce his expected cost by deviating from it, provided that all other customers follow it. The existence of stable payment policies which are not globally optimal is demonstrated in examples based on the M/M/1 queue.
This paper presents an algorithm for determining the minimum cost schedule of tasks in a critical path network in which task cost-time curves may be concave. A computer program for the case of cost-time curves that are piecewise linear in two segments is described, and a numerical example is presented.
It is generally agreed that the minimax solution to a two-person zero-sum matrix game is intuitively satisfactory. Now in many applications of game theory, a game is not described a priori in matrix (or “normal” or “strategic”) form, but rather in extensive form, i.e., by its rules. A game described in such a way may be reduced to a matrix game by means of the concept of “strategy.” If, moreover, it is of perfect recall, then all mixed strategies, and in particular the optimal strategies of each player, are equivalent to behavior strategies. The usual conclusion from these considerations is that for 2-person 0-sum games in extensive form, the minimax solution is intuitively satisfactory; and that in games of perfect recall, in particular, the players would do well to play in accordance with optimal (minimax) behavior strategies. In this paper we shall discuss some examples that, we believe, cast doubt on these conclusions.