Yu-Chi Ho

NONZERO-SUM DIFFERENTIAL GAMES.

The theory of differential games is extended to the situation where there areN players and where the game is nonzero-sum, i.e., the players wish to minimize different performance criteria. Dropping the usual zero-sum condition adds several interesting new features. It is no longer obvious what should be demanded of asolution, and three types of solutions are discussed:Nash equilibrium, minimax, andnoninferior set of strategies. For one special case, the linear-quadratic game, all three of these solutions can be obtained by solving sets of ordinary matrix differential equations. To illustrate the differences between zero-sum and nonzero-sum games, the results are applied to a nonzero-sum version of a simple pursuit-evasion problem first considered by Ho, Bryson, and Baron (Ref. 1).Negotiated solutions are found to exist which give better results forboth players than the usualsaddle-point solution. To illustrate that the theory may find interesting applications in economic analysis, a problem is outlined involving the dividend policies of firms operating in an imperfectly competitive market.

A Bayesian approach to problems in stochastic estimation and control

In this paper, a general class of stochastic estimation and control problems is formulated from the Bayesian Decision-Theoretic viewpoint. A discussion as to how these problems can be solved step by step in principle and practice from this approach is presented. As a specific example, the closed form Wiener-Kalman solution for linear estimation in Gaussian noise is derived. The purpose of the paper is to show that the Bayesian approach provides; 1) a general unifying framework within which to pursue further researches in stochastic estimation and control problems, and 2) the necessary computations and difficulties that must be overcome for these problems. An example of a nonlinear, non-Gaussian estimation problem is also solved.

Ordinal Optimization of DEDS

In this paper we argue thatordinal rather thancardinal optimization, i.e., concentrating on finding good, better, or best designs rather than on estimating accurately the performance value of these designs, offers a new, efficient, and complementary approach to the performance optimization of systems. Some experimental and analytical evidence is offered to substantiate this claim. The main purpose of the paper is to call attention to a novel and promising approach to system optimization.

Differential games and optimal pursuit-evasion strategies

In this paper it is shown that variational techniques can be applied to solve differential games. Conditions for capture and for optimality are derived for a class of optimal pursuit-evasion problems. Results are used to demonstrate that the well-known proportional navigation law is actually an optimal intercept strategy.

Team decision theory and information structures

This tutorial-survey paper introduces the problems of decentralized statistical decision making (team theory) where the decision makers have access to different information concerning the underlying uncertainties. Using a simple thematic example with variations, the paper introduces and explains various concepts and results of team theory as applied to economics, information theory, and decentralized control.

A gradient technique for general buffer storage design in a production line

In this paper, we present a complete and novel solution to the well known buffer storage design problem in a serial production line. The key ingredient of the solution is the efficient calculation of the gradient vector of the throughput with respect to the various buffer sizes. Analytical and experimental results are presented.

Performance evaluation and perturbation analysis of discrete event dynamic systems

This is a conceptual and speculative paper concerning the future development of system and control theory in operational and discrete event systems with particular emphasis to the techniques of perturbation analysis.

Further properties of nonzero-sum differential games

The general nonzero-sum differential game hasN players, each controlling a different set of inputs to a single nonlinear dynamic system and each trying to minimize a different performance criterion. These general games have several interesting features which are absent in the two bestknown special cases (the optimal control problem and the two-person, zero-sum differential game). This paper considers some of the difficulties which arise in attempting to generalize ideas which are well known in optimal control theory, such as theprinciple of optimality and the relation betweenopen-loop andclosed-loop controls. Two types of solutions are discussed: theNash equilibrium and thenoninferior set. Some simple multistage discrete games are used to illustrate phenomena which also arise in the continuous formulation.

Simple Explanation of the No-Free-Lunch Theorem and Its Implications

The no-free-lunch theorem of optimization (NFLT) is an impossibility theorem telling us that a general-purpose, universal optimization strategy is impossible. The only way one strategy can outperform another is if it is specialized to the structure of the specific problem under consideration. Since optimization is a central human activity, an appreciation of the NFLT and its consequences is essential. In this paper, we present a framework for conceptualizing optimization that leads to a simple but rigorous explanation of the NFLT and its implications.

Brief paper: Infinitesimal and finite perturbation analysis for queueing networks

The sample-path pertrubation analysis technique introduced in refs. (1-4) is extended to included finite (and possibly large) pertrubations typically introduced by changes in queue sizes or other parameter. It is shown that there is a natural hierarchy of perturbation analysis which takes care of increasingly large perturbations. Experiments with zeroth (infinitesmal) and first order (finite) pertrubation analysis show that significant accuracy improvement can be obtained with small increase in computational effort.