David W. K. Yeung

A model of industrial pollution in a stochastic environment

Abstract Standard models of pollution abatement assume that pollution accumulation occurs in a deterministic pattern as a by-product of the production process. Governmental intervention often occurs in the form of taxation or mandatory abatement controls to reduce inefficiency caused by incomplete markets. In this paper we assume that the accumulation effect of pollution may be stochastic due, for instance, to the random absorption capacity of the ecosystem. Furthermore, we assume that the level of pollution may vary with input use as well as output level. We proceed to analyze properties of a policy for efficient social management of competitive firms which generate pollution.

Stochastic differential game model of a common property fishery

The paper presents a stochastic differential game model of a common-property commercial fishery and determines a feedback Nash equilibrium of the game. Closed-form expressions for the value functions, the equilibrium harvesting strategies, and stationary distributions of the fish stock are derived. Sensitivity analyses with respect tot he model parameters are carried out. The paper also considers equilibrium outcomes under joint maximization and surplus maximization. In the latter case, an optimal market size (i.e., number of firms) is identified.

A cooperative stochastic differential game of transboundary industrial pollution

Though cooperation in environmental control holds out the best promise of effective actions, limited success has been observed because existing multinational joint initiatives fail to satisfy the property of subgame consistency. A cooperative solution is subgame consistent if the solution optimality principle is maintained in any subgame which starts at a later time with any feasible state brought about by prior optimal behaviors. This paper presents a cooperative stochastic differential game of transboundary industrial pollution with two novel features. The first feature is that industrial production creates short-term local impacts and long-term global impacts on the environment. Secondly, a subgame consistent cooperative solution is derived in this stochastic differential game together with a payment distribution mechanism that supports the subgame consistent solution. This is the first time that pollution management is analyzed in a cooperative stochastic differential game framework under these novel features.

Dynamically stable corporate joint ventures

As markets continue to become global and firms become more international, corporate joint ventures provide firms with opportunities to rapidly create economies of scale and learn new skills and technologies that would be very difficult for them to obtain on their own. However, it is often observed that after a certain time of cooperation, some firms may gain sufficient skills and technology that they would do better by breaking up from the joint venture. This is the well-known problem of time inconsistency. In this paper, we consider a dynamic joint venture which adopts the shapley value as its profit allocation scheme. A compensation mechanism distributing payments to participating firms at each instant of time is devised to ensure the realization of the shapley value imputation throughout the venture duration. Hence time-consistency is attained, and a dynamically stable joint venture results. Extension of the analysis to a stochastic environment is also made. It is the first time that stable joint venture is analyzed both deterministically and stochastically in a dynamic environment.

A differential game of industrial pollution management

This paper explores a differential game between a policy maker and a profit maximizing entrepreneur in which production generates pollution. The government levies a pollution tax on output and uses the tax received for pollution abatement. The entrepreneur determines the level of output. A feedback Nash equilibrium is derived. Using more specific functional forms, the game is extended to cover the multiple firm case.

Infinite-Horizon Stochastic Differential Games with Branching Payoffs

In this paper, we consider infinite-horizon stochastic differential games with an autonomous structure and steady branching payoffs. While the introduction of additional stochastic elements via branching payoffs offers a fruitful alternative to modeling game situations under uncertainty, the solution to such a problem is not known. A theorem on the characterization of a Nash equilibrium solution for this kind of games is presented. An application in renewable resource extraction is provided to illustrate the solution mechanism.

Interest rate and output price uncertainty and industry equilibrium for non-renewable resource extracting firms

We establish convexity of a nonrenewable resource extracting agents value function in the future interest rate, a random variable. A preference by the agent for future interest uncertainty follows. A rational expectations, m identical firm industry equilibrium is characterized and the links between interest rate uncertainty and output price uncertainty are investigated.

Rank Size Distribution of International Financial Centers

The observation that global finance is concentrated in only a small number of international centers and cities has raised the question if worldwide financial integration is being achieved at the expense of increased international urban inequality. This article examines the spatial organization of stock markets for some forty-five cities. While New York, London, and Tokyo are undisputed hosts to the largest stock markets in the world, the analysis shows that inequality among international financial centers and cities has diminished between 1980 to 1999 with increased competition from regional financial centers and emerging markets.

Randomly-Furcating Stochastic Differential Games

This paper presents a class of games — designated as Randomly Furcating Stochastic Differential Game — in which random shocks in the stock dynamics and (future) stochastic changes in payoffs are present. Since future payoff are not known with certainty, the term “randomly furcating” is introduced to emphasize that a particularly useful way to analyze such a situation is to assume that payoffs change at any future time instant according to (known) probability distributions defined in terms of multiple-branching stochastic processes. New and significant mathematical results are obtained, under which it becomes possible to characterize the conditions under which previously unsolvable games can be solved. Two illustrations are provided.

Subgame Consistent Cooperative Solution of Dynamic Games with Random Horizon

In cooperative dynamic games, a stringent condition—that of subgame consistency—is required for a dynamically stable cooperative solution. In particular, under a subgame-consistent cooperative solution an extension of the solution policy to a subgame starting at a later time with a state brought about by prior optimal behavior will remain optimal. This paper extends subgame-consistent solutions to dynamic (discrete-time) cooperative games with random horizon. In the analysis, new forms of the Bellman equation and the Isaacs–Bellman equation in discrete-time are derived. Subgame-consistent cooperative solutions are obtained for this class of dynamic games. Analytically tractable payoff distribution mechanisms, which lead to the realization of these solutions, are developed. This is the first time that subgame-consistent solutions for cooperative dynamic games with random horizon are presented.