Subgame Consistent Economic Optimization

Inhaltsverzeichnis

1. Frontmatter

2. Chapter 1. Introduction

   David W. K. Yeung, Leon A. Petrosyan

   Abstract

   The most appealing characteristic of the perfectly competitive market is perhaps the postulation that individually rational self-maximizing behaviors bring about group (Pareto) optimality. Hence the market is regarded as an effective means to allocate economic resources efficiently. However, a competitive market will fail to provide an efficient allocation mechanism if there exists an imperfect market structure, externalities, imperfect information, or public goods. These phenomena are prevalent in the current global economy. As a result, though the market is perceived to be the most effective instrument in conducting economic activities, it fails to guarantee its efficiency under many current conditions. Not only have inefficient market outcomes appeared, but gravely detrimental events—such as the worldwide financial crisis and catastrophe-bound industrial pollution problem—have also emerged under the conventional market system.

3. Chapter 2. Dynamic Strategic Interactions in Economic Systems

   David W. K. Yeung, Leon A. Petrosyan

   Abstract

   The recent globalization and emergence of multinational corporations turned many major economic activities into dynamic interactive endeavors. The number of decision makers involved is relatively small and it leads to significant strategic interdependence. With human life being lived over time, and institutions like markets, firms, and governments changing over time, the economic system is definitely a dynamic interactive entity. Section 2.1 provides a general overview of dynamic interactive economic systems. Market outcomes under open-loop equilibria are investigated in Sect. 2.2 and those under feedback equilibria are examined in Sect. 2.3. An extension of the analysis to a stochastic framework is provided in Sect. 2.4.

4. Chapter 3. Dynamic Economic Optimization: Group Optimality and Individual Rationality

   David W. K. Yeung, Leon A. Petrosyan

   Abstract

   The most appealing characteristic of perfectly competitive markets is that individually rational behaviors bring about group (Pareto) optimality in economic resource allocation. However, the market fails to provide an effective mechanism for optimal resource use because of the prevalence of imperfect market structure, externalities, imperfect information, and public goods in the current global economy. As a result, though the market is one of the most effective instruments in conducting economic activities, it fails to guarantee its efficiency under the current arrangement. The noncooperative outcomes characterized in Chap. 2 vividly demonstrate that Pareto optimality could not be achieved by markets. Removing market suboptimality is not just a task of achieving a better alternative, but sometimes it can be an absolute necessity. For instance, efforts to alleviate the worldwide financial tsunami and catastrophe-bound industrial pollution are currently pressing issues.

5. Chapter 4. Time Consistency and Optimal-Trajectory-Subgame Consistent Economic Optimization

   David W. K. Yeung, Leon A. Petrosyan

   Abstract

   The noncooperative games discussed in Chap. 2 fail to reflect all the facets of optimal behavior in n-person market games. In particular, equilibria in noncooperative games do not take into consideration Pareto efficiency or group optimality. Chapter 3 considers cooperation in economic optimization and it is shown that group optimality and individual rationality are two essential properties for cooperation. However, merely satisfying group optimality and individual rationality does not necessarily bring about a dynamically stable solution in economic cooperation because there is no guarantee that the agreed-upon optimality principle is fulfilled throughout the cooperative period. In this chapter we consider dynamically stable economic optimization.

6. Chapter 5. Dynamically Stable Cost-Saving Joint Venture

   David W. K. Yeung, Leon A. Petrosyan

   Abstract

   In this chapter, we consider a common economic activity involving cooperative optimization—joint venture. However, it is often observed that after a certain time of cooperation some firms in a joint venture may gain sufficient skills and technology that they would do better by breaking away from the joint operation. Analysis on time (optimal-trajectory subgame) consistent joint ventures are presented in the following sections.

7. Chapter 6. Collaborative Environmental Management

   David W. K. Yeung, Leon A. Petrosyan

   Abstract

   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.

8. Chapter 7. Dynamically Stable Dormant Firm Cartel

   David W. K. Yeung, Leon A. Petrosyan

   Abstract

   In this chapter, the optimization by cartels that restricts outputs to enhance their joint profit is examined. In particular, we consider oligopolies in which firms agree to form a cartel to restrain output and enhance their profits. Some firms have cost disadvantages that force them to become dormant partners. In Sect. 7.1 a dynamic oligopoly in which there are cost differentials among firms is presented. Pareto optimal output path, imputation schemes, profit sharing arrangements, and time (optimal-trajectory-subgame) consistent solution are derived for a dormant firm cartel in Sect. 7.2. An illustration is shown in the following section. The case when the planning horizon becomes infinite is analyzed in Sect. 7.4, including an illustration with an explicit solution following in the subsequent section.

9. Chapter 8. Subgame Consistent Economic Optimization Under Uncertainty

   David W. K. Yeung, Leon A. Petrosyan

   Abstract

   In many economic problems, uncertainty prevails. An essential characteristic of time—and hence decision making over time—is that though the individual may, through the expenditure of resources, gather past and present information, the future is inherently unknown and therefore (in the mathematical sense) uncertain. There is no escape from this fact, regardless of what resources the individual should choose to devote to obtaining data, information, and to forecasting. An empirically meaningful theory must therefore incorporate time-uncertainty in an appropriate manner. This development establishes a framework or paradigm for modeling game-theoretic situations with stochastic dynamics and uncertain environments over time. Again, the noncooperative stochastic differential games discussed in Chap. 2 fail to reflect all the facets of optimal behavior in n-person market games. Therefore cooperative optimization will generally lead to improved outcomes. Moreover, similar to cooperative differential game solutions, dynamically stable solutions of cooperative stochastic differential games have to be consistent over time. In the presence of stochastic elements, a very stringent condition—that of subgame consistency—is required for a credible cooperative solution. In particular, the optimality principle agreed upon at the outset must remain effective in any subgame starting at a later time with a realizable state brought about by prior optimal behavior.

10. Chapter 9. Cost-Saving Joint Venture Under Uncertainty

    David W. K. Yeung, Leon A. Petrosyan

    Abstract

    In this chapter, we consider a cost-saving joint venture in the presence of stochastic elements. Section 9.1 formulates a dynamic cost-saving corporate joint venture in a stochastic environment and characterizes its subgame consistent solutions. An explicitly solvable illustration is given in Sect. 9.2. A characterization of the Shapley Value solution to a stochastic cost-saving joint venture is presented in Sect. 9.3 and a payoff distribution procedure leading to a subgame consistent solution is computed. Extensions to infinite-horizon ventures are formulated with explicit illustrations in the subsequent two sections.

11. Chapter 10. Collaborative Environmental Management Under Uncertainty

    David W. K. Yeung, Leon A. Petrosyan

    Abstract

    In this chapter, we introduce stochastic elements in collaborative environmental management. Similar to the deterministic analysis in Chap. 6, the industrial sector is characterized by an international trading zone involving n nations or regions. Each government adopts its own abatement policy and tax scheme to reduce pollution. The governments have to promote business interests and at the same time have to handle the financing of the costs brought about by pollution. The industrial sectors remain competitive among themselves while the governments cooperate in pollution abatement. Industrial production creates two types of negative environmental externalities. First, pollutants emitted via industrial production cause short-term local impacts on neighboring areas of the origin of production. Examples of these short-term local impacts include passing-by waste in waterways, wind-driven suspended particles in the air, unpleasant odor, noise, dust, and heat generated in the production processes. Second, the emitted pollutants will add to the existing pollution stock in the environment and produce long-term impacts to extensive and far-away areas. Greenhouse-gases, CFC, and atmospheric particulates are examples of this form of negative environmental externality. This specification permits the proximity of the origin of industrial production to receive heavier environmental damages as production increases. Given these neighboring impacts, the individual government tax policy has to take into consideration the tax policies of other nations and these policies’ intricate effects on outputs and environmental effects. In particular, while designing tax policies to curtail their outputs, governments have to consider the inducement to neighboring nations’ output that can cause local negative environmental impacts to themselves.

12. Chapter 11. Subgame Consistent Dormant Firm Cartel

    David W. K. Yeung, Leon A. Petrosyan

    Abstract

    In this chapter, we introduce uncertainty into the dormant-firm cartel discussed in Chap. 7.

13. Chapter 12. Dynamic Consistency in Discrete-Time Cooperative Games

    David W. K. Yeung, Leon A. Petrosyan

    Abstract

    In some economic situations, the economic process is in discrete time rather than in continuous time. The discrete-time counterpart of differential games are known as dynamic games. Bylka et al (Ann. Oper. Res. 97:69–89, 2000) analyzed oligopolistic price competition in a dynamic game model. Wie and Choi (KSCE J. Civ. Eng. 4(4):239–248, 2000) examined discrete-time traffic network. Beard and McDonald (Ann. Int. Soc. Dyn. Games 9:393–410, 2007) investigated water sharing agreements and Amir and Nannerup (J. Bioecon. 8:147–165, 2006) considered resource extraction problems in a discrete-time dynamic framework. Yeung (Ann. Oper. Res. doi:10.1007/s10479-011-0844-0, 2011) examined dynamically consistent collaborative environmental management with technology selection in a discrete-time dynamic game framework. The properties of Nash equilibria in dynamic games are examined in Basar (J. Optim. Theory Appl. 14:425–430, 1974; Int. J. Game Theory 5:65–90, 1976). The solution algorithm for solving dynamic games can be found in Basar (IEEE Trans. Autom. Control AC-22:124–126, 1977; In: Differential Games and Control Theory II, pp. 201–228, 1977). Petrosyan and Zenkevich (Game theory. World Scientific, Singapore, 1996) presented an analysis on cooperative dynamic games in a discrete time framework. The SIAM Classics on Dynamic Noncooperative Game Theory by Basar and Olsder (Dynamic noncooperative game theory, 2nd edn. Academic Press, London, 1995) gave a comprehensive treatment of discrete-time noncooperative dynamic games.

14. Chapter 13. Discrete-Time Cooperative Games Under Uncertainty

    David W. K. Yeung, Leon A. Petrosyan

    Abstract

    In some economic processes in discrete-time, uncertainty may also arise. For instance, Smith and Zenou (Rev. Econ. Dyn. 6(1):54–79, 2003) considered a discrete-time stochastic job search model. Esteban-Bravo and Nogales (Comput. Oper. Res. 35:226–240, 2008) analyzed mathematical programming for stochastic discrete-time dynamics arising in economic systems, including examples in a stochastic national growth model and international growth model with uncertainty. The discrete-time counterpart of stochastic differential games is known as stochastic dynamic games. Basar and Ho (J. Econ. Theory 7:370–387, 1974) examined informational properties of the Nash solutions of stochastic nonzero-sum games. The elimination of the informational nonuniqueness in a Nash equilibrium through a stochastic formulation was first discussed in Basar (Int. J. Game Theory 5:65–90, 1976) and further examined in Basar (Automatica 11:547–551, 1975; In: New trends in dynamic system theory and economics, pp. 3–5, 1979; In: Dynamic policy games in economics, pp. 9–54, 1989). Basar and Mintz (In: Proceedings of the IEEE 11th conference on decision and control, pp. 188–192, 1972; Stochastics 1:25–69, 1973) and Basar (IEEE Trans. Autom. Control AC-23:233–243, 1978) developed an equilibrium solution of linear-quadratic stochastic dynamic games with noisy observation. Again, the SIAM Classics on Dynamic Noncooperative Game Theory by Basar and Olsder (Dynamic noncooperative game theory, 2nd edn. Academic Press, London, 1995) gave a comprehensive treatment of noncooperative stochastic dynamic games. Yeung and Petrosyan (J. Optim. Theory Appl. 145(3):579–596, 2010) provided the techniques in characterizing subgame consistent solutions for stochastic dynamic. Furthermore, they also presented a stochastic dynamic game in resource extraction. Analyses of noncooperative and cooperative discrete-time dynamic games with random game horizons were presented in Yeung and Petrosyan (J. Optim. Theory Appl. forthcoming, 2011). The recently emerging robust control techniques in discrete time along the lines of Hansen and Sargent (Robustness. Princeton University Press, Princeton, 2008) should prove to be fruitful in developing into stochastic dynamic interactive economic models.

15. Backmatter