Simone Clemhout

Dynamic common property resources and environmental problems

Problems of interacting common-property resources are set up as stochastic differential games. A class of models is solved where equilibrium closed-loop strategies keep harvest rates proportional to stocks. Corrective taxes, etc., are considered.

A class of trilinear differential games

This paper characterizes a class ofN-person, general sum differential games for which the optimal strategies only depend upon remaining playing time. Such strategies can be easily characterized and determined, and the optimal play can be easily analyzed.

Interactive economic dynamics and differential games

This survey reviews the applications of differential game theory in analyzing issues in the economic literature. The needs of the economic discipline are juxtaposed with the merits of various existing types of differential games. Suggestions are also made as to areas holding great promise for future research.

A Differential Game Model of Oligopoly

Most of the literature on oligopoly deals with profit-maximizing firms engaging in “static” repetitive games. As the number of firms increases, the Nash-equilibrium strategy for each Cournot oligopolist converges to the competitive solution. In a two-person, zero-sum differential game model of duopoly [1] we introduced dynamic elements and explored alternative entrepreneurial goals. The duopolists endeavor to outsell each other subject to a no-loss constraint; the saturation of present markets by past sales and the impact on future goodwill by current advertisement are handled through “state variables.” The differential game formulation [1, 2] offers two advantages: (a) near perfect information leads to frequent existence of pure strategy equilibria and (b) the use of optimal control theory facilitates the characterization of the time structure of an equilibrium. However, the two-person, zero-sum framework is too restrictive while a general theory for solving n-person, non-zero sum differential games has ...

Differential games -- Economic applications

Publisher Summary This chapter discusses the differential games economic applications. Much of the application of N-person, general-sum differential games is in economics, where observed regularities are rarely invariant as in natural sciences. Thus, expenditure patterns in America offer little insights upon the consumption habits in Papua-New Guinea. Out of those differential games that depend on specific function forms (e.g., the linear-quadratic game), useful theoretic examples may be constructed but not the basis for robust predictions. In the case of optimal control, broad conclusions are often obtained by means of the globally analytic phase diagram for those problems with a low-dimension state space. On the other hand, from the viewpoint of economics, there are two distinct types of contributions that differential games can offer. First is regarding the multiplicity of solutions: differential game can yield broad conceptual contributions that do not require the detailed solution(s) of a particular game. Second, there remains an unsatisfied need that differential games may meet. For situations where a single decision maker faces an impersonal environment, the system dynamics can be studied fruitfully with optimal control models. There are analogous situations where the system dynamics is decided by the interactions of a few players. Differential games seem to be the natural tool. What economists wish to predict is not only the details about a single time profile, such as existence and stability of any long run configuration and the monotonicity and speed of convergence toward that limit, but also the findings from the sensitivity analysis: how such a configuration responds to parametric variations.

Equilibrium Patterns for Bargaining Under Strike: A Differential Game Model

Abstract A class of N-person, general-sum differential games is considered for which non-cooperative Nash equilibria can characterize situations such as bargaining during a strike. A subclass of strategies is shown to be playable equilibria. The existence and uniqueness of this subclass, as well as the possibility of profitable recontracting, are analyzed and illustrated with examples. Equilibrium implies that any player will eventually fair as well as if he had accepted the claims of all other players at any earlier time. Possible generalizations are outlined or discussed.

Common-Property Exploitations under Risks of Resource Extinctions

For a renewable resource under the random hazards of extinction, a variational correspondence principle is introduced to show under what conditions, joint optimization can increase both the resource stock in stasis and the survival prospect of the resource. The analysis is independent of the assumption of particular function forms.

On Games of Cake-Eating

Publisher Summary This chapter discusses games of cake-eating. It focuses on a very simple problem in resource economics: the exploitation of a nonrenewable common-property resource. Game theory studies the resolution of conflicting interests among rational individuals. As long as the players differ ever so slightly in their preferences over the way in which the resources should be allocated, some conflict inherently arises. The static common property problem may appear simplistic: players always grab as much as they can. The dynamic version is less straightforward. A player may deny his rival any future consumption only by exhausting all of the resource in one stroke, but then he must accept the same irreversible, total privation for himself, from now on. The simpler problem is known as cake-eating. It is attractive not only because of its utter simplicity. By happy coincidence, this model is structurally a twin of the Ramsey model, known to most economists. Together this pair forms a natural bridge between the control models that are familiar to us all and the differential games that are probably not. For the cake-eating problem, the literature of resource economics contains two traditions; the state variable may be the level of either resources remaining or resources gone.

Endogenous Growth as a Dynamic Game

Dissimilar growth patterns often prevail for economies similar in taste, technology and initial endowment. This may arise from the nature of ‘knowledge capital’, a durable public input, privately accumulated. Its external effect spawns a dynamic game. By a game-theoretic analysis, one obtains a continuum of Markovian-Nash equilibria, some being Pareto-ranked: better coordination means higher growth. The underlying strategical complementarity is shown to be equivalent to the externality of ‘fish war’. The notion of splicing equilibrium is introduced and some open issues are isolated for future studies.

Assessment of consumer research for a valuation of a quality-of-life policy

This paper evaluates the allocation, coordination, priority assignments and new directions in the research efforts towards a consumer policy. The formulation of a consumer policy is an essential component of a quality-of-life policy. It is shown how interdisciplinary efforts could foster this endeavor.The consumer welfare should be central to the political economy system. Thus a detailed analysis of the primary elements that interrelate to produce possible levels of welfare are examined. In depth consideration of the following five points consitute the bulk of the paper: (i) consumer choice and freedom, (ii) controls available to consumers over their environment, (iii) the demographic characteristics of consumer populations over the life-cycle, (iv) the interaction between the individual and the group emerging from the hierarchies of influence at the individual, group and society levels, (v) structure of the markets, degree of concentration and business practices related to sales.As a result of this analysis it can be concluded that several policy measure can redress the balance of power between consumers, business and government, however there is an urgent need for action by the consumers themselves. The initiative for effective social action in consumerism rests in the last resort with the consumers themselves. They can and do form coalitions which can be effective in influencing the course of events.