Models that depict innovation as a smooth, well-behaved linear process badly misspecify the nature and direction of the causal factors at work. Innovation is complex, uncertain, somewhat disorderly, and subject to changes of many sorts. Innovation is also difficult to measure and demands close coordination of adequate technical knowledge and excellent market judgment in order to satisfy economic, technological, and other types of constraints—all simultaneously. The process of innovation must be viewed as a series of changes in a complete system not only of hardware, but also of market environment, production facilities and knowledge, and the social contexts of the innovation organization.

An Overview of Innovation

This article is an attempt to survey the vast literature on flexibility in manufacturing that has accumulated over the last 10 to 20 years. The survey begins with a brief review of the classical literature on flexibility in economics and organization theory, which provides a background for manufacturing flexibility. Several kinds of flexibilities in manufacturing are then defined carefully along with their purposes, the means to obtain them, and some suggested measurements and valuations. Then we examine the interrelationships among the several flexibilities. Various empirical studies and analytical/optimization models dealing with these flexibilities are reported and discussed. The article concludes with suggestions for some possible future research directions.

https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=1080305

Flexibility in Manufacturing: A Survey

Many economic problems are naturally modeled as a game of incomplete information, where a player’s payoff depends on his own action, the actions of others, and some unknown economic fundamentals. For example, many accounts of currency attacks, bank runs, and liquidity crises give a central role to players’ uncertainty about other players’ actions. Because other players’ actions in such situations are motivated by their beliefs, the decision maker must take account of the beliefs held by other players. We know from the classic contribution of Harsanyi (1967–1968) that rational behavior in such environments not only depends on economic agents’ beliefs about economic fundamentals, but also depends on beliefs of higher-order – i.e., players’ beliefs about other players’ beliefs, players’ beliefs about other players’ beliefs about other players’ beliefs, and so on. Indeed, Mertens and Zamir (1985) have shown how one can give a complete description of the “type” of a player in an incomplete information game in terms of a full hierarchy of beliefs at all levels. In principle, optimal strategic behavior should be analyzed in the space of all possible infinite hierarchies of beliefs; however, such analysis is highly complex for players and analysts alike and is likely to prove intractable in general. It is therefore useful to identify strategic environments with incomplete information that are rich enough to capture the important role of higher-order beliefs in economic settings, but simple enough to allow tractable analysis. Global games, first studied by Carlsson and van Damme (1993a), represent one such environment. Uncertain economic fundamentals are summarized by a state θ and each player observes a different signal of the state with a small amount of noise. Assuming that the noise technology is common knowledge among the players, each player’s signal generates beliefs about fundamentals, beliefs about other players’ beliefs about fundamentals, and so on. Our purpose in this paper is to describe how such models work, how global game reasoning can be applied to economic problems, and how this analysis relates to more general analysis of higher-order beliefs in strategic settings.

/pdf/global-games-theory-and-applications-1lch3df46c.pdf

Global Games: Theory and Applications

This paper gives a survey of the various forms of Pontryagin’s maximum principle for optimal control problems with state variable inequality constraints. The relations between the different sets of optimality conditions arising in these forms are shown. Furthermore, the application of these maximum principle conditions is demonstrated by solving some illustrative examples.

A survey of the maximum principles for optimal control problems with state constraints

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics.

Differential Games in Economics and Management Science

In this paper, we deal with the problem of sequencing parts and robot moves in a robotic cell where the robot is used to feed machines in the cell. The robotic cell, which produces a set of parts of the same or different types, is a flow-line manufacturing system. Our objective is to maximize the long-run average throughput of the system subject to the constraint that the parts are to be produced in proportion of their demand. The cycle time formulas are developed and analyzed for this purpose for cells producing a single part type using two or three machines. A state space approach is used to address the problem. Both necessary and sufficient conditions are obtained for various cycles to be optimal. Finally, in the case of many part types, the problem of scheduling parts for a specific sequence of robot moves in a two machine cell is formulated as a solvable case of the traveling salesman problem.

Sequencing of Parts and Robot Moves in a Robotic Cell

We consider a class of nonlinear dynamic economic models in
 which the actual realizations of a certain variable (e.g., price) depend
 on the agents' expectations about this variable. We define a consistent
 expectations equilibrium (CEE) by the property that the sample average
 and the sample autocorrelations of the realizations of the actual law
 of motion equal the average and the autocorrelations of the perceived law
 of motion. Along a CEE agent's expectations are thus self-fulfilling in
 terms of the observable sample average and sample autocorrelations.
 Restricting ourselves to the case in which beliefs are described by
 an AR(1) process, we study existence and stability of three different
 types of CEE: steady-state, two-cycle, and chaotic. We illustrate how
 these equilibria can emerge in the nonlinear cobweb model. Learning
 dynamics based on sample average and sample autocorrelations are
 introduced and stability of CEE under this learning process is
 investigated.

Consistent expectations equilibria

Competitive dynamic advertising: A modification of the Case game

In this paper, we develop a theoretical framework for the common business practice of rolling horizon decision making. The main idea of our approach is that the usefulness of rolling horizon methods is, to a great extent, implied by the fact that forecasting the future is a costly activity. We, therefore, consider a general, discrete-time, stochastic dynamic optimization problem in which the decision maker has the possibility to obtain information on the uncertain future at given cost. For this non-standard optimization problem with optimal stopping decisions, we develop a dynamic programming formulation. We treat both finite and infinite horizon cases. We also provide a careful interpretation of the dynamic programming equations and illustrate our results by a simple numerical example. Various generalizations are shown to be captured by straightforward modifications of our model.

Gerhard Sorger

Papers

Differential Games in Economics and Management Science

Sequencing of Parts and Robot Moves in a Robotic Cell

Consistent expectations equilibria

Competitive dynamic advertising: A modification of the Case game

A theory of rolling horizon decision making