Dynamic Game Theory Research Articles

Choice of Government’s Mechanism in Closed-loop Supply Chain by Considering Customer’s Awareness of Environmental Protection Under Asymmetric Information

Environmental consciousness has become very important in theory and practice, the recycling and reusing of waste electrical and electronic equipment (WEEE) can effectively improve the efficiency of resource utilization. In the paper, based on the customer’s awareness of environmental protection, we compare the impact of different government mechanisms on reducing the carbon emission and improving the effectiveness of the recovery quantity under asymmetric information. We build three different decision-making models by using the dynamic game theory. We analyze the optimal decision in four decision-making models and explain the feature of different government mechanisms. Lastly, we analyze the impact of the customer’s awareness of environmental protection on the optimal decision making models. The result shows that (1) The government’s carbon emission reward-penalty mechanism can improve the wholesale price for new product and improve the buy-back price for the WEEE in manufacturer. (2) The government’s unit carbon tax for manufacturer is larger than the degree of the carbon emission reward-penalty for manufacturer, the manufacturer’s cost of production can increase. The unit sale price of retailer can improve with the increasing of the manufacturer’s wholesale price for new product. (3) The government’s unit carbon tax for manufacturer is larger than the degree of the carbon emission reward-penalty for manufacturer, the manufacturer’s cost of production can increase.

<inline-formula> <tex-math notation="LaTeX">$\mathcal{L}_2$</tex-math> </inline-formula>-Gain for Hybrid Linear Systems With Periodic Jumps: A Game Theoretic Approach for Analysis and Design

In this paper, the disturbance attenuation problem is formulated and solved for a class of linear hybrid systems in the presence of periodic jumps. The results are achieved, both in the finite and infinite horizon cases, by borrowing ideas from the theory of dynamic games. In the considered formulation, independent disturbances affecting the continuous-time and the discrete-time components of the hybrid system are allowed. Moreover, the analysis is carried out by introducing easily verifiable conditions, involving the definition of a Monodromy Riccati Equation , i.e., a classical Riccati equation defined for the one-period discrete-time equivalent model. Interestingly, as a by-product, the main statements essentially characterize the solution of zero-sum noncooperative dynamic games for periodic linear hybrid systems, which is of interest per se .

Interactive Control Paradigm-Based Robust Lateral Stability Controller Design for Autonomous Automobile Path Tracking With Uncertain Disturbance: A Dynamic Game Approach

Stability as well as robustness is the major concerns in the design of a trajectory tracking controller for an autonomous vehicle. In this paper, a novel lateral stability controller design for vehicle path tracking is developed. First, using dynamic game theory as a general framework, vehicle lateral stability can be viewed as a dynamic difference game so that its two players, namely, the active front steering (AFS) system and active rear steering (ARS) system can work together to provide more stability for vehicle path tracking control. The interactive steering control strategies between AFS and ARS are obtained by noncooperative closed-loop feedback Stackelberg game theory to ensure optimal performance for vehicle path tracking. Then, based on the proposed path-following shared control paradigm, by applying the method of zero-sum game theory, a finite-time robust regulator is developed to make the interaction model more robust to uncertain lateral disturbances. Finally, double-lane change and serpentine driving condition with and without uncertain time-varying lateral disturbance are used to evaluate the proposed control algorithm. Simulation and hardware-in-loop implementation results show that the proposed shared control paradigm based robust path-tracking controller can robustly provide better lateral stability when time-varying lateral disturbances are bounded.

New results on the existence of open loop Nash equilibria in discrete time dynamic games via generalized Nash games

We address the problem of finding conditions which guarantee the existence of open-loop Nash equilibria in discrete time dynamic games (DTDGs). A classical approach to DTDGs involves analyzing the problem using optimal control theory. Sufficient conditions for the existence of open-loop Nash equilibria obtained from this approach are mainly limited to linear-quadratic games (Basar and Olsder in Dynamic noncooperative game theory, 2nd edn, SIAM, Philadelphia, 1999). Another approach of analysis is to substitute the dynamics and transform the game into a static game. But the substitution of state dynamics makes the objective functions of the resulting static problems extremely hard to analyze. We introduce a third approach in which the dynamics are not substituted, but retained as constraints in the optimization problem of each player, resulting thereby in a generalized Nash game. Using this, we give sufficient conditions for the existence of open-loop Nash equilibria for a class of DTDGs where the cost functions of players admit a quasi-potential function. Our results apply with nonlinear dynamics and without stage additive cost functions, and allow constraints on state and actions spaces, and in some cases, yield a generalization of similar results from linear-quadratic games.

Slow treatment promotes control of harmful species by multiple agents

AbstractThe management of harmful species, including invasive species, pests, parasites, and diseases, is a major, global challenge. Harmful species cause severe damage to ecosystems, biodiversity, agriculture, and human health. The control of harmful species is challenging and often requires cooperation among multiple agents, such as land‐owners, agencies, and countries. Agents may have incentives to contribute less, leaving more work for other agents, which can result in inefficient treatment. Here we present a dynamic game theory model and we show that slow treatment may promote a stable solution (Markovian Nash equilibrium) where all agents cooperate to remove the harmful species. The efficiency of this solution depends critically on the life history of the harmful species that determines the speed of optimal treatment. Furthermore, this cooperative equilibrium may coexist with other Nash equilibria, including one dictating no treatment of the harmful species, which implies that coordination among agents is critical for successful control.

Tree Construction and Backward Induction: A Mobile Experiment

Dynamic game theory has two fundamental goals: modeling how decision-makers perceive the interaction they participate in (tree construction) and identifying the strategies they select (backward induction). In our experiment, subjects often violate the theory (i.e., they do not construct a tree or backward induct), which is because either their skills are too low or the interaction is too complex. We use response times to measure skills and complexity. We find that complexity of interaction increases with its length and width; however, the length has a relatively bigger impact. Improving skills or decreasing complexity increases the likelihood of subjects behaving according to the theory; however, improving skills has a bigger impact. To collect the data, we developed a mobile application, Blues and Reds, comprising of 58 dynamic games. Our samples include 4,582 (analysis of tree construction) and 6,677 (analysis of backward induction) subjects coming from over 100 countries.

Stress-Testing U.S. Macroeconomic Policy: A Computational Approach Using Stochastic and Robust Designs in a Wavelet-Based Optimal Control Framework

This paper analyzes fiscal and monetary policy in a wavelet-based model under stochastic and mixed minimax robust optimal control. A state-space model is constructed after applying the Maximal Overlap Discrete Wavelet Transform to U.S. quarterly real GDP data. We derive the theoretical framework for the linear–quadratic Gaussian (LQG) design and the mixed design where the disturbances in a subset of frequency ranges are stochastic, and the other disturbances are modeled by a multiple-parameter minimax worst-case robust design. We then use the model to jointly simulate optimal fiscal and monetary policy to “stress test” the policies under the worst-case design. The results show that, compared to a deterministic design, the LQG framework introduces considerable variability into aggregate investment. Under active fiscal stabilization with restricted monetary policy, the minimax structure induces more aggressive fiscal spending, slightly larger aggregate consumption, and substantially lower aggregate investment compared to the LQG design. Thus, pursuing a minimax worst-case model induces larger government deficits and stifles long-term capital accumulation. Under active monetary stabilization with restricted fiscal policy, the simulations predict that both consumption and investment will be far less in the minimax design than in the stochastic design. This research is the first to integrate robust control and dynamic game theory with wavelet decomposition.

A game-theoretic strategic mechanism to control brand counterfeiting

PurposeThe purpose of this paper is to design a game theory based model that not only provide theoretical basis to control brand counterfeiting, but it also provide a mechanism to enhance brand revenue.Design/methodology/approachThis study used the dynamic game theory of incomplete information to understand and encounter the brand counterfeiting issues. The study analyzed the economic relationship of legitimate brand, counterfeiter and consumers using mixed strategy of the dynamic game theory of incomplete information.FindingsThe results have indicated that brands those take countermeasures to reduce counterfeiting earn maximum revenue, even when the legitimate brands and consumers are unaware from the actions of counterfeiting firms, the legitimate brands should take countermeasures to reduce counterfeiting to earn maximum revenue, and there exists optimal anti-counterfeiting cost for the legitimate brand. Further, this study provides theoretical basis where brand managers can decide to adopt or not to adopt anti-counterfeiting strategy, and also indicate the consequences of each decision.Practical implicationsBased upon the findings, the study put forward valuable managerial implications. The study revealed that the legitimate brand must emphasize on the significance of taking countermeasures against counterfeiter and also, brand managers should focus on making product traceable, empowering the consumer and ensuring coordination with government officials to control the counterfeiting issues.Originality/valueThis paper incorporates the role of legitimate brand, counterfeiter and a consumer to establish the dynamic game theory model using mixed strategy to understand and address the counterfeiting issues in the global market.

RETRACTED ARTICLE: Development trend of sharing economy in big data era based on duplication dynamic evolution game theory

Since the 1990s, with the perfection and infiltration of Internet infrastructure and the vigorous development of a new generation of information technology industry, the contemporary sharing economy supported by big data has emerged. On the surface, sharing economy has indeed formed a brand new economic model that is different from the past. However, when we analyze the contradictory vision of supply and demand determined by the inclusion of the sharing economy in the basic social system, we can see that the essence of the contemporary sharing economy is from two dimensions influence rather than change the development mode of this contradictory paradigm: one is the anarchy state of social production is improved through communication of big data based on the Internet; the other is the reduced demand for workers having ability to pay is alleviated through collaborative consumption. Therefore, the sharing economy as a commercial operation mode still can not escape the contradiction between production and consumption. From the perspective of social conflict resolution, the real sharing comes from the improvement of fairness and justice and from the reformation of the sharing system. Such reformation is from the reuse of private resource to the collaborative sharing of public resource, that is, the commonweal development of sharing economy. Through the duplication dynamic evolution game theory model of sharing economy, it can be found that the degree of public benefit of sharing economy depends on the degree of benefit of imitation object and the number of imitators. How countries can promote the development direction of sharing economy towards public sphere and public welfare through conscious policy guidance will be an important indicator for testing the government’s ability to respond to emerging policy issues.

Value-added service investment strategy of a two-sided platform with the negative intra-group network externality

PurposeConsidering the resource constraint, this paper aims to study how to make value-added service (VAS) investment strategy considering the negative intra-group network externality on the seller side from the perspective of a two-sided platform.Design/methodology/approachThe authors use the dynamic game theory, optimization, sensitive analysis and numerical study in this research. The authors model their research question from the perspective of the dynamic game theory, and through optimizing the platform’s profit function, the equilibrium results in terms of VAS investing and pricing strategies are derived. To explore the characteristics of the optimal strategies, sensitive analysis is used, and numerical studies are conducted to further illustrate the analytical results.FindingsIt is found that the intra-group network externality is not necessarily the determinant for VAS investment strategy, and its overall negative impact can be overtaken by the investment in certain conditions. The optimal VAS investment level decreases in the negative intra-group network externality. Though the VAS investment is on the seller side, it has either positive or negative impact on the pricing for buyers. Moreover, for a stronger intra-group network externality among sellers, the two-sided prices could either increase or decrease.Research limitations/implicationsThe authors implicate how the intra-group network externality reduces the investment benefit and impacts the other side users. The limitation of considering the intra-group network externalities on only one side needs further extension.Practical implicationsThe authors provide insights for platform operators in how to use recourse to improve users’ utility and how to price the two sides when competition exists on the seller side.Originality/valueThis study specifies the role of negative intra-group network externality in determining the investment and pricing strategy of a two-sided platform in addition to the positive inter-group network externality.

Let the games begin and go on

Real life is a bigger game in which what a player does early on can affect what others choose to do later on. In particular, we can strive to explain how cooperative behaviour can be established as a result of rational behaviour. When engaged in a repeated situation, players must consider not only their short-term gains but also their long-term payoffs. The general idea of repeated games is that players may be able to deter another player from exploiting his short-term advantage by threatening a punishment that reduces his long-term payoff. The aim of the paper that supports this abstract is to present and discuss dynamic game theory. There are three basic kinds of reasons, which are not mutually exclusive, to study what happens in repeated games. First, it provides a pleasant and a very interesting theory and it has the advantage of making us become more humble in our predictions. Second, many of the most interesting economic interactions repeated often can incorporate a phenomenon which we believe are important but which are not captured when we restrict our attention to static games. Finally, economics, and equilibrium-based theories more generally, do best when analysing routinised interactions.

A study of cooperative advertising in a one-manufacturer two-retailer supply chain based on the multi-stage dynamic game theory

In this paper, the coordination of cooperative advertising decisions is analysed in a supply chain with one manufacturer and two retailers. Suppose the manufacturer invests in national advertising and one retailer invests in local advertising, the manufacturer agrees to share part of the local advertising cost with the retailer. Meanwhile, the other retailer refuses to take part in cooperative advertising. The manufacturer and retailer who put investment in cooperative advertising could choose cooperative or non-cooperative attitude, but the other retailer always chooses non-cooperative attitude. We select four decision variables including local advertising effort, two retailers' marginal profits, and price of product to discuss seven three-stage dynamic game models according to the parties' attitudes being cooperative or not. Seven game models, including one non-cooperative model, five partial cooperative models and one cooperative model, are investigated in detail based on a whole mathematical analysis. By comparing the proposed seven models, several interesting propositions are obtained and the corresponding interesting results are also acquired via these propositions.

Let the games begin and go on

Real life is a bigger game in which what a player does early on can affect what others choose to do later on. In particular, we can strive to explain how cooperative behaviour can be established as a result of rational behaviour. When engaged in a repeated situation, players must consider not only their short-term gains but also their long-term payoffs. The general idea of repeated games is that players may be able to deter another player from exploiting his short-term advantage by threatening a punishment that reduces his long-term payoff. The aim of the paper that supports this abstract is to present and discuss dynamic game theory. There are three basic kinds of reasons, which are not mutually exclusive, to study what happens in repeated games. First, it provides a pleasant and a very interesting theory and it has the advantage of making us become more humble in our predictions. Second, many of the most interesting economic interactions repeated often can incorporate a phenomenon which we believe are important but which are not captured when we restrict our attention to static games. Finally, economics, and equilibrium-based theories more generally, do best when analysing routinised interactions.

Game‐Theoretic Social‐Aware Resource Allocation for Device‐to‐Device Communications Underlaying Cellular Network

Device‐to‐Device communication underlaying cellular network can increase the spectrum efficiency due to direct proximity communication and frequency reuse. However, such performance improvement is influenced by the power interference caused by spectrum sharing and social characteristics in each social community jointly. In this investigation, we present a dynamic game theory with complete information based D2D resource allocation scheme for D2D communication underlaying cellular network. In this resource allocation method, we quantify both the rate influence from the power interference caused by the D2D transmitter to cellular users and rate enhancement brought by the social relationships between mobile users. Then, the utility function maximization game is formulated to optimize the overall transmission rate performance of the network, which synthetically measures the final influence from both power interference and sociality enhancement. Simultaneously, we discuss the Nash Equilibrium of the proposed utility function maximization game from a theoretical point of view and further put forward a utility priority searching algorithm based resource allocation scheme. Simulation results show that our proposed scheme attains better performance compared with the other two advanced proposals.

A study of cooperative advertising in a one-manufacturer two-retailer supply chain based on the multi-stage dynamic game theory

In this paper, the coordination of cooperative advertising decisions is analysed in a supply chain with one manufacturer and two retailers. Suppose the manufacturer invests in national advertising and one retailer invests in local advertising, the manufacturer agrees to share part of the local advertising cost with the retailer. Meanwhile, the other retailer refuses to take part in cooperative advertising. The manufacturer and retailer who put investment in cooperative advertising could choose cooperative or non-cooperative attitude, but the other retailer always chooses non-cooperative attitude. We select four decision variables including local advertising effort, two retailers' marginal profits, and price of product to discuss seven three-stage dynamic game models according to the parties' attitudes being cooperative or not. Seven game models, including one non-cooperative model, five partial cooperative models and one cooperative model, are investigated in detail based on a whole mathematical analysis. By comparing the proposed seven models, several interesting propositions are obtained and the corresponding interesting results are also acquired via these propositions.

Game theoretic analysis for the mechanism of moving target defense

Moving target defense (MTD) is a novel way to alter the asymmetric situation of attacks and defenses, and a lot of MTD studies have been carried out recently. However, relevant analysis for the defense mechanism of the MTD technology is still absent. In this paper, we analyze the defense mechanism of MTD technology in two dimensions. First, we present a new defense model named MP2R to describe the proactivity and effect of MTD technology intuitively. Second, we use the incomplete information dynamic game theory to verify the proactivity and effect of MTD technology. Specifically, we model the interaction between a defender who equips a server with different types of MTD techniques and a visitor who can be a user or an attacker, and analyze the equilibria and their conditions for these models. Then, we take an existing incomplete information dynamic game model for traditional defense and its equilibrium result as baseline for comparison, to validate the proactivity and effect of MTD technology. We also identify the factors that will influence the proactivity and effectiveness of the MTD approaches. This work gives theoretical support for understanding the defense process and defense mechanism of MTD technology and provides suggestions to improve the effectiveness of MTD approaches.

Strategy selection of production technical standards in a manufacturing supply chain network: the role of partnership density

This paper presents the game of production technical standards between downstream and upstream suppliers on a manufacturing supply chain network when the two parties have different partnership densities, namely, the numbers of replaceable and mature manufacturing partners. We firstly constructed a manufacturing chain network and analyzed its three relationship structures among suppliers with the presence of different relationship densities, and found that all the three relationships brought about the game of production technical standards between partnership- rich and partnership-scanty suppliers. Then we built a two-party payoff matrix, and analyzed the two-party game and evolutionary stable strategy, based on replication dynamic equation and asymmetric evolutionary game theory. The evolutionary stable strategies of two parties under varying payoff parameters were validated through numerical simulation. Finally, we proposed some suggestions for both those manufacturers with more partners and fewer partners, respectively.

Distributed optimal integrated tracking control for separate kinematic and dynamic uncertain non‐holonomic mobile mechanical multi‐agent systems

This study addres,ses a distributed optimal integrated tracking control method with disturbance rejection for separate kinematic and dynamic uncertain non-holonomic mobile mechanical multi-agent ( N M 3 ) systems. Initially, based on the graph theory, the overall tracking systems of agents are defined and the distributed optimal tracking problem of separate kinematics and dynamics is transformed into an equivalent distributed optimal regulation problem of the integrated affine system. Then, neural network (NN)-based adaptive dynamic programming and cooperative differential game theory is utilised for control, in which only one NN is required for each agent. The NN weight-tuning law and the online algorithm is developed to approximate the value function, and synchronously update both optimal control and worst disturbance laws in only one iterative loop. The tracking errors and function approximation errors are proven to be uniformly ultimately bounded using Lyapunov theory. Finally, as applications of the proposed method, control of the wheeled mobile multi-robot system is discussed. The effectiveness of the method is demonstrated by the results of the comparative numerical simulation.

A dynamic parking charge optimal control model under perspective of commuters’ evolutionary game behavior

In this research we consider commuters’ dynamic learning effect by modeling the trip mode choice behavior from a new perspective of dynamic evolutionary game theory. We explore the behavior pattern of different types of commuters and study the evolution path and equilibrium properties under different traffic conditions. We further establish a dynamic parking charge optimal control (referred to as DPCOC) model to alter commuters’ trip mode choice while minimizing the total social cost. Numerical tests show. (1) Under fixed parking fee policy, the evolutionary results are completely decided by the travel time and the only method for public transit induction is to increase the parking charge price. (2) Compared with fixed parking fee policy, DPCOC policy proposed in this research has several advantages. Firstly, it can effectively turn the evolutionary path and evolutionary stable strategy to a better situation while minimizing the total social cost. Secondly, it can reduce the sensitivity of trip mode choice behavior to traffic congestion and improve the ability to resist interferences and emergencies. Thirdly, it is able to control the private car proportion to a stable state and make the trip behavior more predictable for the transportation management department. The research results can provide theoretical basis and decision-making references for commuters’ mode choice prediction, dynamic setting of urban parking charge prices and public transit induction.

Game theory based real-time multi-objective flexible job shop scheduling considering environmental impact

Production scheduling greatly contributes to optimising the allocation of processes, reducing resource and energy consumption, lowering production costs and alleviating environmental pollution. It is an effective way to progress towards green manufacturing. With the extensive use of the Internet of Things in the manufacturing shop floor, a huge amount of real-time data is created. A typical challenge is how to achieve the real-time data-driven optimisation for the manufacturing shop floor to improve energy efficiency and production efficiency. To address this problem, a dynamic game theory based two-layer scheduling method was developed to reduce makespan, the total workload of machines and energy consumption to achieve real-time multi-objective flexible job shop scheduling. To obtain an optimal solution, a sub-game perfect Nash equilibrium solution was designed. Then, a case study was employed to analyse the performance of the proposed method. The results showed that the makespan, the total workload of machines and energy consumption were reduced by 4.5%, 8.75%, and 9.3% respectively. These improvements can contribute to sustainable development and cleaner production of manufacturing industry.