Engelbert J. Dockner

A Dynamic Theory of Conjectural Variations

This paper explores the relationship between dynamic oligopolistic competition and static conjectural variations equilibria. Using an infinite horizon adjustment cost model, the author demonstrates that any steady state closed-loop (subgame-perfect) equilibrium coincides with a conjectural variations equilibrium. In the case of linear demand and quadratic costs, the dynamic conjectures consistent with closed-loop steady state equilibria are negative, constant, symmetric, and vary continuously with the discount rate (and the adjustment cost parameter) in an interval between the static consistent conjectures and zero (Cournot). Copyright 1992 by Blackwell Publishing Ltd.

Tractable classes of nonzero-sum open-loop Nash differential games: Theory and examples

This paper identifies some classes ofN-person nonzero-sum differential games that are tractable, in the sense that open-loop Nash strategies can be determined, either explicitly or qualitatively in terms of a phase-diagram portrait. The classes are characterized by conditions imposed on the Hamiltonians. Also, the underlying game structures needed to satisfy these conditions are characterized.

On the optimality of limit cycles in dynamic economic systems

The purpose of this paper is to derive conditions for the optimality of a limit cycle in a dynamic economic system and to interpret them economically. A fairly general two-state continuous-time nonlinear optimal control problem is considered. It turns out that for this class of models three different economic mechanisms can be identified as the possible source of limit cycles. One relates to an intertemporal substitution effect expressed in terms of complementarity over time, the second one is a dominating cross effect between the state variables of the system (i.e., the capital stocks in our model), and the third one is positive growth at the equilibrium.

Noncooperative solutions for a differential game model of fishery

Abstract In this paper a generalization of Gordon-Schaefers fishery resource model to a duopoly is presented. The resulting noncooperative game is solved analytically as well as numerically by using the equilibrium concepts of Nash and Stackelbewrg. It turns out that in both cases the player with the smaller unit costs is able to choose a higher catch rate than his opponent. Furthermore it is shown that the game is Stackelberg-dominant. In the Stackelberg case any information disadvantage in the sense of Stackelberg fellowership can be eliminated by a more efficient technology.

Analysis of Nash equilibria in a class of capital accumulation games

In a simple capital accumulation game we study existence and dynamic properties of the cooperative solution, two kinds of Markov perfect equilibria (MPE), and a trigger strategy equilibrium. In the cooperative solution the stock always converges towards a steady state. This property is shared by our first MPE, whereas the second type of MPE may result in complicated dynamics. A Pareto comparison of both MPE depends on the parameter specifications but can turn out either way. Finally, we show how the players can achieve the efficient payoffs of the cooperative solution as an equilibrium outcome by using trigger strategies.

Tariffs and quotas under dynamic duopolistic competition

Abstract This paper analyzes tariffs and quotas in a differential game model of duopolistic competition. For a homogeneous good, equal import tariffs and quotas are compared with respect to resulting domestic prices. The open-loop and closed-loop (subgame perfect) equilibria are derived. The open-loop game leads to domestic price equivalence; however, the closed-loop game does not, unless firms are myopic or the number of domestic firms becomes large. Thus, we prove that the equivalence for static Cournot competition does not carry over to the dynamic case.

Forecasting Time-dependent Conditional Densities: A Semi-non- parametric Neural Network Approach

In _nancial econometrics the modelling of asset return series is closely related to the estimation of the corresponding conditional densities[ One reason why one is interested in the whole conditional density and not only in the conditional mean is that the conditional variance can be interpreted as a measure of time!dependent volatility of the return series[ In fact\ the mod! elling and the prediction of volatility is one of the central topics in asset pricing[ In this paper we propose to estimate conditional densities semi! non!parametrically in a neural network framework[ Our recurrent mixture density networks realize the basic ideas of prominent GARCH approaches but they are capable of modelling any continuous conditional density also allowing for time!dependent higher!order moments[ Our empirical analysis of daily FTSE 099 data demonstrates the importance of distributional assumptions in volatility prediction and shows that the out!of!sample fore! casting performance of neural networks slightly dominates those of GARCH models[ Copyright 1999 John Wiley + Sons\ Ltd[

On the relation between dynamic oligopolistic competition and long-run competitive equilibrimn

Summary In this paper we consider a dynamic oligopolistic model where the demand curve is described by a first—order differential equation which relates at each point in time the price of the commodity, the rate of change of the price, and the outputs of all firms in the market. The linear dynamic demand equation is considered as a first—order price adjustment mechanism. Open—loop, feedback and closed—loop Nash equilibria are derived. The corresponding stationary solutions are compared to the static Cournot equilibrium price and the competitive equilibrium price. It is demonstrated that for the “limiting game” (when the constant speed of adjustment reaches infinity) only the stationary open—loop price converges to the static Cournot price. The stationary feedback and a particular closed—loop solution converge to a price which is below the static Cournot price. For the limiting game when the number of firms goes to infinity the Nash equilibrium prices (independent of the information structure assumed) converge to the long—run competitive equilibrium.

Leaders, Followers, and Risk Dynamics in Industry Equilibrium

We study the distinct impacts of own and rival actions on risk and return when firms strategically compete in the product market. Contrary to simple intuition, a competitor’s options to adjust capacity reduce own-firm risk. For example, if a rival possesses a growth option, an increase in industry demand directly enhances profits but also encourages value-reducing competitor expansion. The rival option thus acts as a natural hedge. Within the industry, we obtain endogenous differences in expected returns. In a leader-follower equilibrium, own-firm and competitor risks and required returns move together through contractions and oppositely during expansions, providing testable new predictions.

The AURORA financial management system: Model and parallel implementation design

The AURORA financial management system under development at the University of Vienna is a modular decision support tool for portfolio and asset–liability management. It is based on a multivariate Markovian birth-and-death factor model for the economic environment, a pricing model for the financial instruments and an objective function which is flexible enough to express risk aversion.The core of the system is a large scale linear or convex program, which due to its size and structure is well suited for parallel optimization methods.As the system is still at an early stage of development, the results are preliminary in nature. Only a few types of financial instruments are handled and just two types of objectives are considered. The parallel optimization modules are still in the development phase.