Leon A. Petrosyan

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.

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.

Subgame Consistent Solutions for a Class of Cooperative Stochastic Differential Games with Nontransferable Payoffs

Subgame consistency is a fundamental element in the solution of cooperative stochastic differential games. In particular, it ensures that the extension of the solution policy to a later starting time and any possible state brought about by prior optimal behavior of the players will remain optimal. Recently, mechanisms for the derivation of subgame consistent solutions in stochastic cooperative differential games with transferable payoffs have been found. In the case when players’ payoffs are nontransferable, the derivation of solution candidates is extremely complicated and often intractable. In this chapter, subgame consistent solutions are derived for a class of cooperative stochastic differential games with nontransferable payoffs.

Subgame-consistent cooperative solutions in randomly furcating stochastic differential games

The paradigm of randomly-furcating stochastic differential games incorporates additional stochastic elements via randomly branching payoffs in stochastic differential games. This paper considers dynamically stable cooperative solutions in randomly furcating stochastic differential games. Analytically tractable payoff distribution procedures contingent upon specific random realizations of the state and payoff structure are derived. This new approach widens the application of cooperative differential game theory to problems where the evolution of the state and future environments are not known with certainty. Important cases abound in regional economic cooperation, corporate joint ventures and environmental control. An illustration in cooperative resource extraction is presented.

Bargaining in Dynamic Games

A regularization method is proposed, which enables time-consistent bargaining procedures to be constructed.

Subgame-consistent cooperative solutions in randomly furcating stochastic dynamic games

Abstract In the analysis of cooperative stochastic dynamic games a stringent condition–subgame consistency–is required for a dynamically stable solution. A cooperative solution is subgame consistent if an extension of the solution policy to a subgame starting at a later time with a feasible state brought about by prior optimal behavior would remain optimal. This paper considers subgame consistent cooperative solutions in randomly furcating stochastic discrete-time dynamic games. Analytically tractable payoff distribution procedures contingent upon specific random realizations of the state and payoff structures are derived. In computer modeling and operations research discrete-time analysis often proved to be more applicable and compatible with actual data than continuous-time analysis. This is the first time that a subgame consistent solution for randomly-furcating stochastic dynamic games has been obtained. It widens the application of cooperative dynamic game theory to discrete-time problems where the evolution of the state and future payoff structures are not known with certainty.

COALITIONAL SOLUTION OF A GAME-THEORETIC EMISSION REDUCTION MODEL

In this paper the problem of allocation over time of total cost incurred by coalitions of countries in a coalitional game of pollution reduction is considered. The Nash equilibrium in the game played by coalitions is computed and then the value of each coalition is allocated according to some given mechanism between its members.

Subgame consistent cooperative solution for NTU dynamic games via variable weights

In cooperative dynamic games a stringent condition-subgame consistency-is required for a dynamically stable solution. In particular, a cooperative solution is subgame consistent if the optimality principle agreed upon at the outset remains in effect in any subgame starting at a later stage with a state brought about by prior optimal behavior. Hence the players do not have incentives to deviate from the previously adopted optimal behavior. For the first time, subgame consistent solutions in cooperative dynamic games with non-transferable payoffs/utility (NTU) using a variable payoff weights scheme is analyzed. A solution mechanism for characterizing subgame consistent solutions is derived. The use of a variable payoff weights scheme allows the derivation of subgame consistent solutions under a wide range of optimality principles. The analysis widens the application of NTU cooperative dynamic games through the provision of a dynamically stable solution.

Collaborative Environmental Management

After decades of rapid technological advancement and economic growth, alarming levels of pollution and environmental degradation are emerging globally. Due to the geographical diffusion of pollutants, the unilateral response of one nation or region is often ineffective. Reports portray the situation as an industrial civilization on the verge of suicide, destroying its environmental conditions of existence, with people being held as prisoners on a runaway catastrophe-bound train. Though global cooperation in environmental control holds out the best promise of effective action, limited success has been observed. This is the result of many hurdles, ranging from commitment, monitoring, and sharing of costs to disparities in future development under the cooperative plans. One finds it hard to be convinced that multinational joint initiatives, like the Kyoto Protocol, can offer a long-term solution because there is no guarantee that participants will always be better off within the entire extent of the agreement. More than anything else, it is due to the lack of these kinds of incentives that current cooperative schemes fail to provide an effective means to avert disaster. This is a “classic” game-theoretic problem.