Matrix Game with Payoffs Represented by Triangular Dual Hesitant Fuzzy Numbers

Matrix Game with Payoffs RepresentedDue to the complexity of information or the inaccuracy of decision-makers’ cognition, it is difficult for experts to quantify the information accurately in the decision-making process. However, the integration of the fuzzy set and game theory provides a way to help decision makers solve the problem. This research aims to develop a methodology for solving matrix game with payoffs represented by triangular dual hesitant fuzzy numbers (TDHFNs). First, the definition of TDHFNs with their cut sets are presented. The inequality relations between two TDHFNs are also introduced. Second, the matrix game with payoffs represented by TDHFNs is investigated. Moreover, two TDHFNs programming models are transformed into two linear programming models to obtain the numerical solution of the proposed fuzzy matrix game. Furthermore, a case study is given to to illustrate the efficiency and applicability of the proposed methodology. Our results also demonstrate the advantage of the proposed concept of TDHFNs

Fuzzy decision making system and the dynamics of business games

Effective and efficient strategic decision making is the backbone for the success of a business organisation among its competitors in a particular industry. The results of these decision making processes determine whether the business will continue to survive or not. In this thesis, fuzzy logic (FL) concepts and game theory are being used to model strategic decision making processes in business organisations. We generally modelled competition by business organisations in industries as games where each business organization is a player. A player formulates his own decisions by making strategic moves based on uncertain information he has gained about the opponents. This information relates to prevailing market demand, cost of production, marketing, consolidation efforts and other business variables. This uncertain information is being modelled using the concept of fuzzy logic. In this thesis, simulation experiments were run and results obtained in six different settings. The first experiment addresses the payoff of the fuzzy player in a typical duopoly system. The second analyses payoff in an n-player game which was used to model a perfect market competition with many players. It is an extension of the two-player game of a duopoly market which we considered in the first experiment. The third experiment used and analysed real data of companies in a case study. Here, we chose the competition between Coca-cola and PepsiCo companies who are major players in the beverage industry. Data were extracted from their published financial statements to validate our experiment. In the fourth experiment, we modelled competition in business networks with uncertain information and varying level of connectivity. We varied the level of interconnections (connectivity) among business units in the business networks and investigated how missing links affect the payoffs of players on the networks. We used the fifth experiment to model business competition as games on boards with possible constraints or restrictions and varying level of connectivity on the boards. We also investigated this for games with uncertain information. We varied the level of interconnections (connectivity) among the nodes on the boards and investigated how these a ect the payoffs of players that played on the boards. We principally used these experiments to investigate how the level of availability of vital infrastructures (such as road networks) in a particular location or region affects profitability of businesses in that particular region. The sixth experiment contains simulations in which we introduced the fuzzy game approach to wage negotiation in managing employers and employees (unions) relationships. The scheme proposes how employers and employees (unions) can successfully manage the deadlocks that usually accompany wage negotiations. In all cases, fuzzy rules are constructed that symbolise various rules and strategic variables that firms take into consideration before taken decisions. The models also include learning procedures that enable the agents to optimize these fuzzy rules and their decision processes. This is the main contribution of the thesis: a set of fuzzy models that include learning, and can be used to improve decision making in business

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy

The Expressive Power of Adjudication

This article provides a causal explanation of adjudicative compliance that is distinct from both the court\u27s threat of sanctions and its institutional legitimacy. The new mechanism for compliance is the power of adjudicative expression. The theory of expressive adjudication arises from a previously neglected synergy among three expressive concepts in game theory -correlated equilibria, focal points, and signals. The article identifies the circumstances in which adjudicative expression can, by itself, influence the behavior of existing disputants and of future potential disputants. In each case, ambiguity in the relevant facts or the concepts underlying intentional and spontaneous order can cause a conflict that clarifying expression resolves. This expressive power explains otherwise puzzling instances of compliance with tribunals that lack the power of sanctions, and unifies theories of third-party norm enforcement with a theory of legal sanctions. Finally, the article examines certain normative implications of the expressive theory, including a novel function of adjudicative impartiality, a new justification for the system of public adjudication, and a trade-off between dispute resolution and dispute avoidance

Game Theoretic Model Predictive Control for Autonomous Driving

This study presents two closely-related solutions to autonomous vehicle control problems in highway driving scenario using game theory and model predictive control. We first develop a game theoretic four-stage model predictive controller (GT4SMPC). The controller is responsible for both longitudinal and lateral movements of Subject Vehicle (SV) . It includes a Stackelberg game as a high level controller and a model predictive controller (MPC) as a low level one. Specifically, GT4SMPC constantly establishes and solves games corresponding to multiple gaps in front of multiple-candidate vehicles (GCV) when SV is interacting with them by signaling a lane change intention through turning light or by a small lateral movement. SV’s payoff is the negative of the MPC’s cost function , which ensures strong connection between the game and that the solution of the game is more likely to be achieved by a hybrid MPC (HMPC). GCV’s payoff is a linear combination of the speed payoff, headway payoff and acceleration payoff. . We use decreasing acceleration model to generate our prediction of TV’s future motion, which is utilized in both defining TV’s payoffs over the prediction horizon in the game and as the reference of the MPC. Solving the games gives the optimal gap and the target vehicle (TV). In the low level , the lane change process are divided into four stages: traveling in the current lane, leaving current lane, crossing lane marking, traveling in the target lane. The division identifies the time that SV should initiate actual lateral movement for the lateral controller and specifies the constraints HMPC should deal at each step of the MPC prediction horizon. Then the four-stage HMPC controls SV’s actual longitudinal motion and execute the lane change at the right moment. Simulations showed the GT4SMPC is able to intelligently drive SV into the selected gap and accomplish both discretionary land change (DLC) and mandatory lane change (MLC) in a dynamic situation. Human-in-the-loop driving simulation indicated that GT4SMPC can decently control the SV to complete lane changes with the presence of human drivers. Second, we propose a differential game theoretic model predictive controller (DGTMPC) to address the drawbacks of GT4SMPC. In GT4SMPC, the games are defined as table game, which indicates each players only have limited amount of choices for a specific game and such choice remain fixed during the prediction horizon. In addition, we assume a known model for traffic vehicles but in reality drivers’ preference is partly unknown. In order to allow the TV to make multiple decisions within the prediction horizon and to measure TV’s driving style on-line, we propose a differential game theoretic model predictive controller (DGTMPC). The high level of the hierarchical DGTMPC is the two-player differential lane-change Stackelberg game. We assume each player uses a MPC to control its motion and the optimal solution of leaders’ MPC depends on the solution of the follower. Therefore, we convert this differential game problem into a bi-level optimization problem and solves the problem with the branch and bound algorithm. Besides the game, we propose an inverse model predictive control algorithm (IMPC) to estimate the MPC weights of other drivers on-line based on surrounding vehicle’s real-time behavior, assuming they are controlled by MPC as well. The estimation results contribute to a more appropriate solution to the game against driver of specific type. The solution of the algorithm indicates the future motion of the TV, which can be used as the reference for the low level controller. The low level HMPC controls both the longitudinal motion of SV and his real-time lane decision. Simulations showed that the DGTMPC can well identify the weights traffic vehicles’ MPC cost function and behave intelligently during the interaction. Comparison with level-k controller indicates DGTMPC’s Superior performance

Game Theory Meets Network Security and Privacy

This survey provides a structured and comprehensive overview of the research contributions that analyze and solve security and privacy problems in computer networks by game-theoretic approaches. A selected set of works are presented to highlight the application of game theory in order to address different forms of security and privacy problems in computer networks and mobile applications. The presented works are classified into six main categories based on their topics: security of the physical and MAC layers, application layer security in mobile networks, intrusion detection systems, anonymity and privacy, economics of network security, and cryptography. In each category, security problems, players, and game models are identified and the main results of selected works, such as equilibrium analysis and security mechanism designs are summarized. In addition, a discussion on advantages, drawbacks, and the future direction of using game theory in this field is provided. In this survey, we aim to provide a better understanding of the different research approaches for applying game theory to network security. This survey can also help researchers from various fields develop game-theoretic solutions to current and emerging security problems in computer networking

Modelling human fairness in cooperative games : a goal programming approach

The issues of rationality in human behavior and fairness in cooperation have gained interest in various economic studies. In many prescriptive models of games, rationality of human decision makers implicitly assumes exchange-ability. This means that real people are assumed to adopt the beliefs of a player as expressed in the game when placed in the shoes of that particular player. However, it is a well debated topic in the literature that this modeling assumption is not in accordance to what behavioral economists have observed in some games played with real human subjects. Even when assuming the role of the same player in the game, different people think differently about the fairness of a particular outcome. People also view fairness as an essential ingredient of their decision making processes in games on cooperation. The aim of this research is to develop a new modeling approach to decision making in games on cooperation in which fairness is an important consideration. The satisficing and egilitarian philosophies on which weighted and Chebyshev Goal Programming (GP) rely, seem to offer an adequate and natural way for modeling human decision processes in at least the single-shot games of coordination that are investigated in this work. The solutions returned by the proposed GP approach aim to strike the right balance on several dimensions of con icting goals that are set by players themselves and that arise in the mental models these players have of other relevant players.EThOS - Electronic Theses Online ServiceGBUnited Kingdo