Dynamic Game Theory Research Articles

Monitoring policies to prevent oil spills: lessons from the theoretical literature

This paper analyzes the policies implemented by the US Coast Guard for regulating transfers of oil in US harbors, specifically, we evaluate those monitoring and enforcement programs aimed at ensuring that the necessary levels of care and maintenance are observed during the routine transfer of oil between shore facilities and either tankers or barges. Our aim is to bring to the attention of policy makers and others interested in the regulation of pollution some of the insights to be gained from dynamic game theory. In particular, we discuss the punitive value of selective and repeated monitoring, which can be used as a cheap way of enforcing observance of regulations. We conclude with some suggestions for policy improvements.

Moving horizon Nash strategies for a military air operation

Dynamic game theory has recently received considerable attention as a possible technology for formulating control actions for decision makers in an extended complex enterprise that involves an adversary. Examples of such enterprises are very common in military operations. Enterprises of this type are typically modeled by a highly nonlinear discrete time dynamic system whose state is controlled by two teams of decision makers each with a different objective function and possibly with a different hierarchy of decision making. Because of the complexity of such systems, the traditional solutions from dynamic game theory that involve optimizing objective functions over the entire time horizon of the system are computationally extremely difficult, if not impossible, to derive. We discuss a solution approach where at each step the controllers limit the computation of their actions to a short time horizon that may involve only the next few time steps. This moving horizon solution, although suboptimal in the global sense, is very useful in taking into account the possible near-term control actions of the adversary. To illustrate this solution methodology, we consider an example of an extended military enterprise that involves two opposing forces engaged in a battle.

Dynamical systems game theory II: A new approach to the problem of the social dilemma

The “social dilemma” is a problem inherent in forming and maintaining cooperation among selfish individuals, and is of fundamental importance in the biological and social sciences. From the viewpoint of traditional game theory, the existence of the social dilemma necessarily implies degeneration into selfish behavior as the numbers of members in a community increases, unless there exists some external power. In the real world, however, cooperation is often formed and maintained merely through mutual interactions, without the influence of an external power. To answer questions concerning appearance and maintenance of cooperative behavior in societies, we study what we call the “Lumberjacks’ Dilemma (LD) game”, as an application of the dynamical systems (DS) game theory presented in [Physica D 147 (2000) 221], which can naturally deal with the dynamic aspects of games. Dynamical processes that lead to the formation and maintenance of cooperation, which is often observed in the real communities, are realized in our model. The mechanism underlying this formation and maintenance is explained from the DS game point of view, by analyzing the functional dependence of the attractor of the game dynamics on a parameter characterizing the strategy. It is demonstrated that norms for cooperation are formed as strategies that are manifested as specific attractors of game dynamics. The change in the stability of this cooperative behavior as the number of members increases is also discussed. Finally, the relevance of our study to cooperation seen in the real world is discussed.

Game-theoretic modeling and control of a military air operation

An attrition-type discrete-time dynamic model is formulated for two opposing forces, labeled Blue and Red, engaged in a military air operation. The Blue force consists of combat air units and its objective is to destroy a fixed target, such as an airport or a bridge, which Is being defended by the Red force. The Red force consists of ground troops and air defense units. We model the objective functions for each side and identify the associated constraints on the control and state variables. We employ a two-level hierarchy of command and control for each force. An example scenario illustrating the implementation of this approach using concepts from non-zero sum dynamic game theory is presented.

Dynamical systems game theory and dynamics of games

A theoretical framework we call dynamical systems game is presented, in which the game itself can change due to the influence of players’ behaviors and states. That is, the nature of the game itself is described as a dynamical system. The relation between game dynamics and the evolution of strategies is discussed by applying this framework. Computer experiments are carried out for simple one-person games to demonstrate the evolution of dynamical systems with the effective use of dynamical resources.

Evolution and control system design. The evolutionary game

The idea of mimicking biological processes has produced a number of useful engineering tools. This article does not advocate another biological approach to solving engineering problems, but rather it introduces some ideas about the evolutionary process that should appeal to those interested in dynamical systems, optimization, stability, and game theory. Understanding the evolutionary process involves all of this and more. We explore how an evolutionary process can take place in a set of differential equations, and examine some interesting links between stability and optimization. One of the interesting paradoxes we explore is how a hill-climbing algorithm can end up at a stable local minimum and why this might have important implications in understanding speciation. Finally, we examine some connections between evolution and control system design.

An Objective-Based Framework for Motion Planning under Sensing and Control Uncertainties

The authors consider the problem of determining robot motion plans under sensing and control uncertainties. Traditional approaches are often based on methodology known as preimage planning, which involves worst-case analysis. The authors have developed a gen eral framework for determining feedback strategies by blending ideas from stochastic optimal control and dynamic game theory with traditional preimage planning concepts. This generalizes classical preimages to performance preimages and preimage planning for de signing motion strategies with information feedback. For a given problem, one can define a performance criterion that evaluates any executed trajectory of the robot. The authors present methods for selecting a motion strategy that optimizes this criterion under either nondeterministic uncertainty (resulting in worst-case analysis) or probabilistic uncertainty (resulting in expected-case analysis). The authors present dynamic programming-based algorithms that nu merically compute performance preimages and optimal strategies; several computed examples of forward projections, performance preimages, and optimal strategies are presented.

Robust tracking enhancement of robot systems including motor dynamics: a fuzzy-based dynamic game approach

A robust tracking control design of robot systems including motor dynamics with parameter perturbation and external disturbance is proposed in this study via adaptive fuzzy cancellation technique. A minimax controller equipped with a fuzzy-based scheme is used to enhance the tracking performance in spite of system uncertainties and external disturbance. The design procedure is divided into three steps. At first, a linear nominal robotic control design is obtained via model reference tracking with desired eigenvalue assignment. Next, a fuzzy logic system is constructed and then tuned to eliminate the nonlinear uncertainties as possibly as it can to enhance the tracking robustness. Finally, a minimax control scheme is specified to optimally attenuate the worst-case effect of both the residue due to fuzzy cancellation and external disturbance to achieve a minimax tracking performance. In addition, an adaptive fuzzy-based dynamic game theory is introduced to solve the minimax tracking problem. The proposed method is appropriate for the robust tracking design of robotic systems with large parameter perturbation and external disturbance. A simulation example of a two-link robotic manipulator driven by DC motors is also given to demonstrate the effectiveness of proposed design method's tracking performance.

Explaining supplier-buyer partnerships: a dynamic game theory approach

Car manufacturers are introducing new purchasing policies in the European automotive industry. Aggregation of parts to form complete prefabricated systems is becoming the prominent way for suppliers to increase their competitiveness. This change implies new organizational arrangements between car manufacturers and suppliers to reflect a new relationship between traditionally adversarial firms. Using a game-theoretic approach, we emphasize, in this paper, that a partnership can only be accomplished, when the present uncertainty between the car manufacturer and the supplier can be drastically reduced. We show through a dynamic game construct and a case study how trust between suppliers and assemblers can be forged.

Dynamic noncooperative game theory

Dynamic noncooperative game theory

Dynamic Decisions in a Laboratory Setting

Many economic models involve a trade-off between current and future rewards. For example, in neoclassical one-sector growth models there is a trade-off between immediate consumption and investment for future consumption. In sequential job search models of labor economics, workers must decide between continuing their job search at a cost or accepting the best wage offered so far. In oligopoly models of tacit collusion, firms decide whether or not to defect from collusive behavior, and the defection leads to short-term benefit but future punishment. These models are all dynamic in the sense that an action at one stage influences the available actions or rewards at a future stage. Many such examples fall into the class of dynamic programming problems and for large classes of such problems, techniques for finding optima are well understood. Less well understood, however, are the decisions which individuals actually make in such dynamic settings. This is an empirical issue which lends itself to the methodology of laboratory investigation. There have already been a number of experiments in which subjects face a sequence of related decisions. Examples include the asset market studies of Camerer and Weigelt [3] and Smith, Suchanek, and Williams [13]. predictions of dynamic game theory have been tested extensively, for example, in the contexts of the centipede game by McKelvey and Palfrey [9], of the repeated prisoner's dilemma by Selten and Stoecker [11] and Andreoni and Miller [1] and of bargaining by Ochs and Roth [10]. Dynamic job search has been studied by Cox and Oaxaca [4] and two armed bandits have been studied by Banks, Olson, and Porter [2]. In the market and game theory studies the decisions made by subjects are complicated by the strategic aspects of the games; subjects' decisions must take into account the strategies they expect the other players to use. In asset markets, subjects seem to have difficulty making decisions and speculative bubbles frequently result. As noted by McCabe, Rassenti, and Smith [8], The robust tendency of laboratory stock markets to produce bubbles is attributable to the myopic trading behavior of subjects. In effect, subjects fail to act according to the backward induction

THE CONSERVATION AND MANAGEMENT OF HIGH SEAS FISHERY RESOURCES UNDER THE NEW LAW OF THE SEA

The Agreement, arising from the recently concluded U.N. Conference on Straddling Fish Stocks and Highly Migratory Fish Stocks, calls for the management of these transboundary resources to be undertaken through regional fisheries management organizations. This paper represents a first attempt to analyze the optimal economic management of straddling/highly migratory stocks under the to‐be‐established regional organizations. Dynamic game theory, commonly used in analyzing the management of “shared” fishery resources, is brought to bear.An obvious question to be raised is whether the analysis applied to “shared” fish stocks management is sufficient for the purpose of examining the management of straddling/highly migratory fish stocks. The analysis is not sufficient for the purpose of examining the cooperative management of straddling/highly migratory fish stocks, because, in contrast to “shared” fish stock management, there is no guarantee that the number and nature of joint exploiters of the resource, in the aforementioned regional organization, will be constant through time. It is the existence of what is termed the “New Member Problem” which most clearly distinguishes the management of straddling/highly migratory fish stocks from the management of “shared” fish stocks. The paper discusses several approaches to addressing the “New Member Problem.”

Policy Windows and Two-Level Games: Explaining the Passage of Acid-Rain Legislation in the Clean Air Act of 1990

Because of the transboundary nature of most environmental problems, environmental policy often lies at the intersection of domestic and international forces. Yet, because domestic and international issues are usually examined with different sets of theories and models, we tend to explain the policy process and outcome by emphasizing only one arena. Analysis of domestic policy is often dominated by process models, whereas scholars of international relations tend to apply rational models to explain state behavior. We apply Kingdon's ‘policy windows’ model of agenda setting and Brams's dynamic game theory framework to the development of acid-rain legislation enacted by the USA in the Clean Air Act of 1990. We compare the explanations of these theories with the work of other analysts, as well as with perceptions of policymakers by using data from interviews of policymaking elites in Canadian and US government, industry, and interest groups. It is demonstrated that process models and models of strategic interaction can complement each other, providing improved explanations of policy outcomes.

The Choice of Fiscal Policy Settings under Alternative Inflation Targets

This paper considers an open-loop Nash game between independent monetary and fiscal authorities. The monetary authority is concerned solely with achieving a desired rate of inflation. The fiscal authority has multiple objectives defined by specific preference parameters. A dynamic game theory approach is used to analyse the impact of different inflation targets on the long-term level of public debt, on the level of government expenditure, and on the dynamic path of the economy.

Formula omitted] control design in bilinear systems: a tensor formal series approach

In this paper, the H ∞ disturbance attenuation problem of bilinear system is discussed. Dynamic game theory is used to solve this bilinear minimax problem. The solvability of H ∞ disturbance attenuation in bilinear system is also discussed. The techniques of tensor products and formal power series are employed to solve the nonlinear Bellman-Isaac differential equation. Furthermore, the convergence for the tensor formal series approach of this H ∞ control problem is discussed, and the radius of convergence for this H ∞ control to be well defined is also obtained.

Superinfection and the evolution of parasite virulence

Earlier ideas that parasites evolve toward becoming harmless to their hosts have, in recent years, given way to more analytic studies, focused on the 'basic reproductive rate', R0, of individual parasites. In general, the biology of the parasite life cycle will lead to constraining relations between virulence (parasite-associated host death or reduction in fertility) and transmissibility: the maximum R0 may then be attained by virulence being high, or low, or at some intermediate level, depending on the details of the constraining relations. Such studies have not generally included superinfection (where an already-infected host is infected by another parasite). Here we propose a general, but simple, model of superinfection, which is amenable to analytical treatment. In such models selection does not simply act to maximize R0; superinfection leads to selection for higher levels of virulence, highly polymorphic parasite populations and very complicated dynamics. We calculate the equilibrium distribution of parasite strains and the maximum level of virulence that can be maintained by superinfection. We also note the equivalence between our 'superinfection model' and recent approaches to the study of the meta-population dynamics of multi-species interactions.

H∞ Control Design in Bilinear Systems: A Tensor Formal Series Approach

Dynamic game theory and the tensor formal series approac:h are proposed to cope with the H∞ disturbance attenuation problem of bilinear system. The techniques of tensor products and formal power seriea are employed to solve the nonlinear partial differential Bellman-Isaac equation. The convergence for the tensor formal series approach of this control problem is discussed, and the radius of convergence for this H∞ control to be well dcfined is also obtained. The solution for the H∞ bilinear disturbance attenuation problem is shown to be exilt for small initial conditions. Furthermore, for large initial states one must choose a small horizon time tf to meet the desired disturbance attenuation level γ.

A note on the Replicator Equations of dynamical game theory

The Replicator Equations introduced by Maynard Smith and Price [1] are examined in the continuous form given by Taylor and Jonker [2]. A simple, explicit classification of the stable classes for three competing strategies is given in terms of the system parameters.

Dynamic tariffs with asymmetric information

Recent developments in dynamic game theory are applied to determine when two countries can sustain freer trade given that they determine trade policies non-cooperatively. Countries know their own level of protection, but not the other country's level of protection. Using import trigger strategies, cooperation (in the form of low tariffs) can be supported, although there are periodic reversionary (high tariff) episodes. However, if terms of trade trigger strategies are used, cooperation does not occur.

Foraging, vigilance and risk of predation in birds—a dynamic game study of ESS

A dynamic multi-period game theory model is developed to study evolutionary stable scanning strategies of birds foraging in flocks. Scanning, while foraging, is carried out to detect attacking predators. In our model there is a chance that birds are killed by predators during foraging days. After each loss of a flock mate the remaining birds face the following foraging day in a smaller flock. The model has non-unique solutions. The evolutionary stable scanning rates may be constant over the foraging season, or they may show a monotonic decreasing trend with time. The former ESS solution does not depend on the future survival probabilities, and is independent of the future flock dynamics. Hence, the scanning rates depend on the current flock size only. The latter ESS solution is interpreted as follows. A loss of a flock mate decreases the future survival of each remaining bird. Hence, the birds increase their scanning rates to take care of their flock mates and to face the future predator attacks in a bigger flock. The choice between the ESS solutions depends on the behavior of the birds at the end of the foraging season. The scanning rates depend on the behavior of the predators.