Generalized Model of a Stochastic Common Property Fishery Differential Game: A Numerical Study

Robust Markov Perfect Equilibria in a Dynamic Choice Model with Quasi-hyperbolic Discounting.- Stochastic Differential Games and Intricacy of Information Structures.- Policy Interactions in a Monetary Union: An Application of the OPTGAME Algorithm.- The Dynamics of Lobbying Under Uncertainty: On Political Liberalization in Arab Countries.- A Feedback Stackelberg Game of Cooperative Advertising in a Durable Goods Oligopoly.- Strategies of Foreign Direct Investment in the Presence of Technological Spillovers.- Differential Games and Environmental Economics.- Capacity Accumulation Games with Technology Constraints.- Dynamic Analysis of an Electoral Campaign.- Multi-Agent Optimal Control Problems and Variational Inequality Based Reformulations.- Time-consistent Equilibria in a Differential Game Model with Time Inconsistent Preferences and Partial Cooperation.- Interactions Between Fiscal and Monetary Authorities in a Three-Country New-Keynesian Model of a Monetary Union.- Subgame Consistent Cooperative Provision of Public Goods Under Accumulation and Payoff Uncertainties.

This paper constructs a non-cooperative/cooperative stochastic differential game model to prove that the optimal strategies trajectory of agents in a system with a topological configuration of a Multi-Local-World graph would converge into a certain attractor if the system’s configuration is fixed. Due to the economics and management property, almost all systems are divided into several independent Local-Worlds, and the interaction between agents in the system is more complex. The interaction between agents in the same Local-World is defined as a stochastic differential cooperative game; conversely, the interaction between agents in different Local-Worlds is defined as a stochastic differential non-cooperative game. We construct a non-cooperative/cooperative stochastic differential game model to describe the interaction between agents. The solutions of the cooperative and non-cooperative games are obtained by invoking corresponding theories, and then a nonlinear operator is constructed to couple these two solutions together. At last, the optimal strategies trajectory of agents in the system is proven to converge into a certain attractor, which means that strategies trajectory are certainty as time tends to infinity or a large positive integer. It is concluded that the optimal strategy trajectory with a nonlinear operator of cooperative/non-cooperative stochastic differential game between agents can make agents in a certain Local-World coordinate and make the Local-World payment maximize, and can make the all Local-Worlds equilibrated; furthermore, the optimal strategy of the coupled game can converge into a particular attractor that decides the optimal property.

This paper is concerned with a new model of linear-quadratic mean-field stochastic Stackelberg differential game with one leader and two followers, in which only the leader is allowed to stop her strategy at a random time. By employing the backward induction method, the state equation is divided into two-stage equations. Then, the open-loop Stackelberg solution is obtained by using the maximum principle and the verification theorem. In a special case, with the help of Riccati equations, the open-loop Stackelberg solution is expressed as a feedback form of both the state and its mean.

Stochastic differential games are considered in a non-Markovian setting. Typically, in stochastic differential games the modulating process of the diffusion equation describing the state flow is taken to be Markovian. Then Nash equilibria or other types of solutions such as Pareto equilibria are constructed using Hamilton--Jacobi--Bellman (HJB) equations. But in a non-Markovian setting the HJB method is not applicable. To examine the non-Markovian case, this paper considers the situation in which the modulating process is a fractional Brownian motion. Fractional noise calculus is used for such models to find the Nash equilibria explicitly. Although fractional Brownian motion is taken as the modulating process because of its versatility in modeling in the fields of finance and networks, the approach in this paper has the merit of being applicable to more general Gaussian stochastic differential games with only slight conceptual modifications. This work has applications in finance to stock price modeling which incorporates the effect of institutional investors, and to stochastic differential portfolio games in markets in which the stock prices follow diffusions modulated with fractional Brownian motion.

Optimization of Investment and Reinsurance Strategy of an Insurer Based on Stochastic Differential Game and Multi-Vasicek Model

Optimal control for transboundary pollution under ecological compensation: A stochastic differential game approach

This paper deals with a class of equilibria which are based on the use of memory strategies in the context of continuous-time stochastic differential games. In order to get interpretable results, we will focus the study on a stochastic differential game model of the exploitation of one species of fish by two competing fisheries. We explore the possibility of defining a so-called cooperative equilibrium, which will implement a fishing agreement. In order to obtain that equilibrium, one defines a monitoring variable and an associated retaliation scheme. Depending on the value of the monitoring variable, which provides some evidence of a deviation from the agreement, the probability increases that the mode of a game will change from a cooperative to a punitive one. Both the monitoring variable and the parameters of this jump process are design elements of the cooperative equilibrium. A cooperative equilibrium designed in this way is a solution concept for a switching diffusion game. We solve that game using the sufficient conditions for a feedback equilibrium which are given by a set of coupled HJB equations. A numerical analysis, approximating the solution of the HJB equations through an associated Markov game, enables us to show that there exist cooperative equilibria which dominate the classical feedback Nash equilibrium of the original diffusion game model.

In this chapter, we will deal with zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games, via the dynamic programming principle.In Sect. 4.1, we are concerned with basic concepts and definitions and we introduce stochastic differential games, referring to (Controlled MarkovProcesses and viscosity solutions, 2nd edn. Springer, New York 2006), XI. Then, using a semi-discretization argument, we study the DPP for lower- and upper-value functions in Sect. 4.2. In Sect. 4.3, we will consider the Isaacs equations, via semigroups related to DPP. In Sect. 4.4, we consider a link between stochastic controls and differential games via risk sensitive controls.

This chapter introduces the theory of deterministic and stochastic differential games, including the dynamic optimization techniques, (stochastic) differential games and their solution concepts, which will lay a foundation for later study.

Environmental policy instruments in an international duopoly with feedback investment strategies

Over the last two decades, differential game (DG) models have been used extensively to study such issues in dynamic environments as competitive advertising and pricing for new products in the marketing literature, capacity investments in the energy industry, government's subsidy policy in new technology, and monetary and fiscal policies in economics. Recently, a number of papers have applied DGs to treat dynamic interactions between the channel members in decentralized supply chains. This review focuses on these applications. Specifically, we review papers that analyze dynamic retail-wholesale pricing strategies, joint slotting and pricing decisions to launch an innovative durable product, and investment in supply chain infrastructure. We consider Stackelberg equilibria as the solution concept for the games under consideration. We shall begin our review with an introduction to the basics of the Stackelberg DGs. We then summarize the important managerial insights obtained in each of the studies being reviewed. Finally, we point out future research avenues for applications of DGs in supply chain management.

Consumers' environmental protection awareness promotes the quality of green products produced by remanufacturers, which requires higher input cost and more efforts but wins environmental reputation in return. In order to encourage remanufacturers to produce products with less pollution, government enacts environmental policy to subsidy the production of remanufacturing. This paper aims to analyze the impact of subsidy on remanufacturing decision and identify the optimal decisions under the effect of green network using a differential game model. First, both government and remanufacturer's cost functions are established with their own environmental effort, respectively. Then, their benefit functions are built to represent their own reward, in which multiple factors are taken into account including but not limited to the environmental reputation of remanufacturer and consumers' demand for remanufactured products. Using the models of Nash-non cooperative game, Stackelberg master-slave game and cooperative game, their benefits are calculated and compared. The equilibrium results show that the improvement level of products' environmental quality is equal to the level of subsidies, and subsidies will increase with the improvement of products' environmental quality. In addition, with the support of the government, remanufactures are able to produce the most environmentally friendly products with the most benefit. Finally, a case study is given to prove the theorems obtained in this paper.

Aiming at actual traffic travel guidance demand, the common information for gaming was analysed. The strategies of traffic management and road users were studied, and a differential Stackelberg game model which could describe the guidance strategies was constructed based on the established fuzzy model of road users. After two phases game character of traffic travel guidance were summarized, converse induction method to solving game process was brought out. The calculating method by Genetic Arithmetic (GA) to solve Stackelberg game model was devised. And the travel guidance scheme solved would achieve the aim of the individual user optimum based on system optimum. The analysis result for the example road-net shows that the game model and calculating method brought out in the paper would importantly conduce to produce the traffic guidance scheme for traffic guidance system from the aspect of theory and technology.

A differential game (DG) model for a developing and a developed country is considered. Each player makes decisions about how much resource to be used to restrict the opponent's development so as to maximize his weighted sum of current consumption and final output. Current consumption is assumed to be preferred to final output for both players. The developing country is assumed to have a higher economic growth rate and a higher preference to final output, whereas the developed country is assumed to have a higher initial income and a higher efficiency in restricting his opponent. This problem is investigated under three kinds of information structures, i.e., a zerosum, a nonzero-sum, and a Stackelberg game. Open-loop equilibrium solutions are obtained for all the three cases. Economic implications of the result are provided.

This paper is devoted to the application of a class of differential games with continuous updating in low-carbon chain. It is performed that the optimal control (cooperative strategies) and feedback Nash equilibrium strategies uniformly converge to the corresponding strategies in the game model with continuous updating as the number of updating instants converges to infinity. With respect to the traditional model, this method gives the chances for players to adjust their strategies according to the information in the near future. The key point is that players could adjust their strategies corresponding to the current time information. In this paper we for the first time study the low-carbon chain differential game model with continuous updating.