Game Theory Concepts Research Articles

A comprehensive review of hybrid game theory techniques and multi-criteria decision-making methods

More studies trend to hybrid the game theory technique with the multi-criteria decision-making (MCDM) method to aid real-life problems. This paper provides a comprehensive review of the hybrid game theory technique and MCDM method. The fundamentals of game theory concepts and models are explained to make game theory principles clear to the readers. Moreover, the definitions and models are elaborated and classified to the static game, dynamic game, cooperative game and evolutionary game. Therefore, the hybrid game theory technique and MCDM method are reviewed and numerous applications studied from the past works of literature are highlighted. The result of the previous studies shows that the fundamental elements for both frameworks were studied in various ways with most of the past studies tend to integrate the static game with AHP and TOPSIS methods. Also, the integration of game theory techniques and MCDM methods was studied in various applications such as politics, economy, supply chain, engineering, water management problem, allocation problem and telecommunication network selection. The main contribution of the recent studies of employment between game theory technique and MCDM method are analyzed and discussed in detail which includes static and dynamic games in the non-cooperative game, cooperative game, both non-cooperative and cooperative games and evolutionary game.

Metric Routing Protocol for Detecting Untrustworthy Nodes for Packet Transmission

IoT objects that have a resource constrained nature resulting in a number of attacks in the routing protocol for lossy networks and low-power networks. RPL is very vulnerable to selfish behaviours and internal attacks though they are built with encryption protection to secure messages. To address this vulnerability, in this paper, we propose a novel trustworthiness methodology based on metric for incorporating trust evaluation, enhancing the robustness of security mechanism. Simulation results indicate that the proposed work is efficient in terms of throughput, nodes’ rank changes, energy consumption and packet delivery ratio. Moreover, using mathematical modelling, it has been observed that this methodology meets the demands of loop-freeness, optimality and consistency. This shows that this metic has both monotonicity and isotonicity requirements to enable the routing protocol. Incorporating the concepts of game theory, we can use this technique as a strategy to iterate Prisoner’s Dilemma. Both evolutionary simulation and mathematical analysis indicate that the proposed metric-based routing protocol is an efficient technique in promoting evolution and stability of the IoT network.

Rewards and penalties in an evolutionary game theoretic model of international environmental agreements

The UNFCC on climate change specifies that all nations must follow the rule of ‘common’ with differentiation regarding their responsibilities for the protection of the global environmental system. Recently, the formulation and stability of the IEA have been increased in the literature by applying the concept of game theory to make the climate agreements successful at the national and the international level. This study provides a novel evolutionary game theoretic model of self-enforcing IEA to overcome the free rider problem. The fundamental difference between our paper and existing literature is that we examine enforcement within a model as IEA has a governing authority while the typical model of enforcement involves a government enforcing a rule that it has imposed. For this purpose, we assign countries into different grades according to their pollution levels, consider a combination of rewards and penalties, use replicator dynamics to derive the conditions for the population steady state, and examine how the proposed regulatory mechanism fares in this steady state. This framework enables us to avoid the free rider and renegotiation problems as well as the rationality assumption. We establish the condition for evolutionary stability. The global environmental problem is managed effectively as a reward-punishment scheme and the monitoring frequency of IEA fulfills this condition. Our results provide an allocation principal with stable conditions under which countries get more benefits by monitoring the IEA and stability of the grand coalition holds.

Complexity and Algorithms for Exploiting Quantal Opponents in Large Two-Player Games

Solution concepts of traditional game theory assume entirely rational players; therefore, their ability to exploit subrational opponents is limited. One type of subrationality that describes human behavior well is the quantal response. While there exist algorithms for computing solutions against quantal opponents, they either do not scale or may provide strategies that are even worse than the entirely-rational Nash strategies. This paper aims to analyze and propose scalable algorithms for computing effective and robust strategies against a quantal opponent in normal-form and extensive-form games. Our contributions are: (1) we define two different solution concepts related to exploiting quantal opponents and analyze their properties; (2) we prove that computing these solutions is computationally hard; (3) therefore, we evaluate several heuristic approximations based on scalable counterfactual regret minimization (CFR); and (4) we identify a CFR variant that exploits the bounded opponents better than the previously used variants while being less exploitable by the worst-case perfectly-rational opponent.

Automated Explainable Multidimensional Deep Learning Platform of Retinal Images for Retinopathy of Prematurity Screening

A retinopathy of prematurity (ROP) diagnosis currently relies on indirect ophthalmoscopy assessed by experienced ophthalmologists. A deep learning algorithm based on retinal images may facilitate early detection and timely treatment of ROP to improve visual outcomes. To develop a retinal image-based, multidimensional, automated, deep learning platform for ROP screening and validate its performance accuracy. A total of 14 108 eyes of 8652 preterm infants who received ROP screening from 4 centers from November 4, 2010, to November 14, 2019, were included, and a total of 52 249 retinal images were randomly split into training, validation, and test sets. Four main dimensional independent classifiers were developed, including image quality, any stage of ROP, intraocular hemorrhage, and preplus/plus disease. Referral-warranted ROP was automatically generated by integrating the results of 4 classifiers at the image, eye, and patient levels. DeepSHAP, a method based on DeepLIFT and Shapley values (solution concepts in cooperative game theory), was adopted as the heat map technology to explain the predictions. The performance of the platform was further validated as compared with that of the experienced ROP experts. Data were analyzed from February 12, 2020, to June 24, 2020. A deep learning algorithm. The performance of each classifier included true negative, false positive, false negative, true positive, F1 score, sensitivity, specificity, receiver operating characteristic, area under curve (AUC), and Cohen unweighted κ. A total of 14 108 eyes of 8652 preterm infants (mean [SD] gestational age, 32.9 [3.1] weeks; 4818 boys [60.4%] of 7973 with known sex) received ROP screening. The performance of all classifiers achieved an F1 score of 0.718 to 0.981, a sensitivity of 0.918 to 0.982, a specificity of 0.949 to 0.992, and an AUC of 0.983 to 0.998, whereas that of the referral system achieved an F1 score of 0.898 to 0.956, a sensitivity of 0.981 to 0.986, a specificity of 0.939 to 0.974, and an AUC of 0.9901 to 0.9956. Fine-grained and class-discriminative heat maps were generated by DeepSHAP in real time. The platform achieved a Cohen unweighted κ of 0.86 to 0.98 compared with a Cohen κ of 0.93 to 0.98 by the ROP experts. In this diagnostic study, an automated ROP screening platform was able to identify and classify multidimensional pathologic lesions in the retinal images. This platform may be able to assist routine ROP screening in general and children hospitals.

Fair shares? Advancing land economics through cooperative game theory

Site consolidation is a perennial issue in the study of land economics. The emergence in many contexts of policies that follow variations on ‘land readjustment’ represent a common way for policy makers to overcome the barriers to wholesale redevelopment. In several important respects the nature of the problems that land readjustment seeks to confront are best thought of as questions in cooperative game theory. In this contribution we seek to explore the underpinning logic of land-readjustment using fundamental concepts in cooperative game theory: the Shapley value and the Core. In addition, we present results of an experiment on coalition and value distribution in four European countries. Our results shed light on a range of important practical issues for the policy ranging from the conditions under which development might be self-initiated to coalition stability, and to the value of an animating agency such as urban planning.

Improved Intrusion Detection System using Quantal Response Equilibrium-based Game Model and Rule-based Classification

Wireless sensor network has large number of low-cost tiny nodes with sensing capability. These provide low cost solutions to many real world problems such as such as defence, Internet of things, healthcare, environment monitoring and so on. The sensor nodes of these networks are placed in vulnerable environment. Hence, the security of these networks is very important. Intrusion Detection System (IDS) plays an important role in providing a security to such type of networks. The sensor nodes of the network have limited power and, traditional security mechanisms such as key-management, encryption decryption and authentication techniques cannot be installed on the nodes. Hence, there is a need of special security mechanism to handle the intrusions. In this paper, intrusion detection system is designed and implemented using game theory and machine learning to identify multiple attacks. Game theory is designed and used to apply the IDS optimally in WSN. The game model is designed by defining the players and the corresponding strategies. Quantal Response Equilibrium (QRE) concept of game theory is used to select the strategies in optimal way for the intrusion’s detection. Further, these intrusions are classified as denial of service attack, rank attack or selective forwarding attacks using supervised machine learning technique based on different parameters and rules. Results show that all the attacks are detected with good detection rate and the proposed approach provides optimal usage of IDS

On the Retrial-Queuing Model for Strategic Access and Equilibrium-Joining Strategies of Cognitive Users in Cognitive-Radio Networks with Energy Harvesting

This article studies the strategic access of single-server retrial queue with two types of customers, where priority is given according to their category. On the basis of this concept, a cognitive-radio network was developed as retrial queue with energy harvesting. Cognitive radio allows for a secondary user to opportunistically access the idle spectrum of a primary user (PU). Upon arrival of a primary user, the service given to the secondary user by the cognitive radio is interrupted, and the PU band is available for the primary user. After completion of service for the primary user, the PU band is again available to secondary users. Performance metrics are derived to study the equilibrium strategies of secondary users. A Stackelberg game was formulated and Nash equilibrium was derived for the noncooperative strategy of the secondary user. Game-theory concepts are incorporated with queuing theory ideas to obtain the net benefit for the noncooperative strategy and social benefit for cooperative strategy. Lastly, analytical results are verified with numerical examples, and the effects of energy-harvesting rate are discussed.

Possibilistic cooperative advertising and pricing games for a two-echelon supply chain

This paper addresses coordination of pricing and cooperative advertising policies in a two-echelon supply chain under fuzziness of demand function’s parameters and manufacturing costs. Three different decentralized scenarios are introduced with regard to the players’ market power: (1) manufacturer-Stackelberg game where the manufacturer has the dominant power in the channel, (2) retailer-Stackelberg game where the manufacturer follows the strategies taken by a dominant retailer, and (3) Nash game where the manufacture and the retailer with the same market power make the decisions simultaneously. The equilibrium wholesale and retail prices, national and local advertising expenditures, and participation rate are determined using the concepts of possibilistic game theory, and the results are compared with the centralized channel scenario. A numerical example is presented to illustrate the effectiveness of the proposed modeling approach, and sensitivity analyses are carried out to measure the impact of the demand function’s parameters as well as the levels of uncertainty.

Efficient parallel computing on the game theory-aware robust influence maximization problem

Influence maximization (IM) is a problem of finding the most influential nodes with limited budgets under the given propagation model, which finally maximizes the spread of influence into the network. This work considers the robustness assumption in the IM problem, named the robust influence maximization (RIM) problem, which focuses on the uncertainty factors among the influence propagation models and algorithms, so as to find nodes that can achieve robust performance with different diffusion functions in networks. For modeling the uncertainty, we generate parameter space by adding noises into the independent cascade (IC) propagation model, in which each edge has an interval to deposit its all possible activation probabilities. Then, a novel robust optimal objective function is proposed for the RIM problem, which based on the calculation of the Shapley value, one classical and crucial concept in cooperative game theory. Particularly, to face the computing time explosion for traversing various uncertainty scenarios, we first give a complete parallel computing based framework to improve the proposed algorithm’s efficiency, which will definitely motivate the research that how to fully use the computing resources to speed up the RIM problem solving. Through extensive experiments with nine real-world/synthetic networks and four centrality-based IC models, we find one exciting rule that the worst case on the perturbation interval model occurs when edge probability is equal to the endpoint of the interval, and the influence spread effect is positively correlated with the difference of probabilities between two directions over an edge. The seed nodes selected by the proposed robust algorithm outperforms other state-of-the-art methods under the worst diffusion case.

Game theory approach for optimum design of an aged structure with multiple objectives

A mathematical procedure based on the concept of game theory is described for evaluating an optimal strategy for increasing the residual life of an aged structure subject to cyclic loading. To increase the residual life of the structure, it is proposed to attach additional sections with the critical members. A computational procedure for estimating residual life of structure based on Paris equation for crack growth propagation with number of cycle is described. The decision making problem is formulated as constrained optimization problem having two objectives of conflicting nature. The design variables are taken as the cross-sectional area of attached sections in the structure. Geometric constraints in the form of lower and upper bounds on the design variables and constraint on stress developed are considered in the formulation. Two objectives considered in the present investigation are: minimization of the mass of attached sections and maximization of the extra residual life of structure due to mass attachment. The design problem is formulated as a two-person game and the Nash non-cooperative solution is evaluated for irrational play to determine the starting point of the game. For the cooperative game, a supercriterion is formulated for the overall benefit of the players. The game is terminated when an optimal trade-off between the objectives is reached with the maximization of the supercriterion. Two different optimization methods, namely interior penalty function method and grid search method have been used for supercriterion maximization. The methodology is demonstrated by solving a problem of practical interest.

Modelling the redistribution of benefits from joint investments in community energy projects

Given the widespread adoption of renewable generation, storage and new loads like electric vehicle charging, there has been a growing effort to enhance local energy resilience, particularly at the community level. This has led to increasing interest in the development of local or community energy projects, in which individual prosumers are able to generate, store and trade energy within the community — enabling a shift in market power from large utility companies to individual prosumers. Such schemes often involve a group of consumers investing in community-owned asset such as community-owned wind turbines or shared battery storage. Yet, developing methods to enable efficient control and fair sharing of jointly-owned assets is a key open question, of both research and practical importance. In this paper, we provide a method inspired from game theory concepts to fairly redistribute the benefits from community owned energy-assets such as community wind turbines and storage. We propose a heuristic-based battery control algorithm for maximization of behind-the-meter self-consumption, which considers the effect of battery life degradation. Using real consumption and production data to model a community of two hundred households, we assess and compare technical and economic benefits of investment in individually-owned or community-owned assets such as chemical storage. We show that battery storage simple pay-back period can be considerably reduced by sharing the asset within a community. Finally, we compare several redistribution and benefit allocation schemes for community-owned assets, and show that the proposed scheme based on principles from cooperative game theory achieves the fairest redistribution.

Game Theory and the Three-Body Problem

Game theory is used to analyze a variety of social situations with competing players and interests, such as competition between businesses and elections. However, the concept of game theory is rarely employed to examine literature work. This paper applies game theory to analyze decisions made in a renowned science fiction series, the Three-Body Problem. How is deterrence established between two entities that want to conquer each other? What about changing the context to many entities? In the context of a science fiction, this paper offers a new perspective that allows readers to understand the rationale behind decisions and consequent outcomes in international relations and deterrence. Additionally, this research employs a simple computer program to help test equilibria in various conditions.

Stackelberg Game Theory Based Energy Management Systems in the Presence of Renewable Energy Sources

The game theory concept has been adapted for energy management between energy producers and consumers in the presence of renewable energy sources (RES) and electric vehicles (EVs). The objective of the paper is to increase the penetration of renewable energy sources and EVs by the Stackelberg game theory model with real-time pricing. RES are the energy generation sources located near load centers to manage the demand of consumers. The primary objective of EV is transportation, but for managing the energy demand, EV participate in grid operations as a back up source of energy. EV are charged during off-peak hours and discharged to the grid during peak hours. Consumers benefited in terms of higher payoffs to supply energy during peak hours. To increase the payoffs, consumers can shift their appliance operation from high price duration to low price duration and create a new peak energy consumption. To maintain the balance between consumers and utility, an optimization tool is essential. The Stackelberg game theory model is a one leader and N followers’ game, the leader first declares the energy price and the follower respond by selecting their best response for energy consumption. The leader can update its strategy again by considering the follower best response to obtain maximum benefits. The process to achieve the best response of the follower and leader is called the Stackelberg nash equilibrium. Objective of energy producers is to supply maximum energy through renewable energy sources and the use of EVs as storage units. The prime objective of consumers is to minimize energy tariff by scheduling the appliances.

Intelligent Resource Allocation Method for Wireless Communication Networks Based on Deep Learning Techniques

In this paper, a deep learning approach is used to conduct an in‐depth study and analysis of intelligent resource allocation in wireless communication networks. Firstly, the concepts related to CSCN architecture are discussed and the throughput of small base stations (SBS) in CSCN architecture is analyzed; then, the long short‐term memory network (LSTM) model is used to predict the mobile location of users, and the transmission conditions of users are scored based on two conditions, namely, the mobile location of users and whether the small base stations to which users are connected have their desired cache states, and the small base stations select the transmission. The small base station selects several users with optimal transmission conditions based on the scores; then, the concept of game theory is introduced to model the problem of maximizing network throughput as a multi‐intelligent noncooperative game problem; finally, a deep augmented learning‐based wireless resource allocation algorithm is proposed to enable the small base station to learn autonomously and select channel resources based on the network environment to maximize the network throughput. Simulation results show that the algorithm proposed in this paper leads to a significant improvement in network throughput compared to the traditional random‐access algorithm and the algorithm proposed in the literature. In this paper, we apply it to the fine‐grained resource control problem of user traffic allocation and find that the resource control technique based on the AC framework can obtain a performance very close to the local optimal solution of a matching‐based proportional fair user dual connection algorithm with polynomial‐level computational complexity. The resource allocation and task unloading decision policy optimization is implemented, and at the end of the training process, each intelligent body independently performs resource allocation and task unloading according to the current system state and policy. Finally, the simulation results show that the algorithm can effectively improve the quality of user experience and reduce latency and energy consumption.

ВИКОРИСТАННЯ ТЕОРІЇ ІГОР ДЛЯ МОДЕЛЮВАННЯ ЕКОНОМІЧНОЇ ПОВЕДІНКИ НА ФІНАНСОВИХ РИНКАХ

The article analyzes simulation methods using game theory of the influence of information that runs inside and outside the market on exchange rates and prices through the strategic behavior of people directly involved in financial transactions. The purpose of the research conducted in the article is to simulate an investor's economic behavior to make an investment decision using a game theory methodology. To select the types of games that are suitable for the financial markets, the classification of game theory is generalized. A variety of factors and all kinds of behavioral strategies make up an event space that is measured by behaviors. It is determined that exchange players are building different strategies that lead to the required results only in specific game conditions, without using the standard theory of general equilibrium. The financial market can be considered a non-cooperative, continuous and parallel zero-sum game whose participants possess perfect information. There are several sequential actions of financial market participants based on the concepts of game theory: the player in the financial market must choose his style of trading or investing; the player must clearly understand who the other players are in the game; there is a limited rationality in the actions of participants in the financial market; analytical work that excludes the emotional component of decision making is important; the financial market participant must formulate its own strategy. It is justified that if people behaved more predictably (would be much slower in responding to different situations, making minor adjustments to the intended strategy or not changing it at all), and if the probability of success did not depend on the actions of other participants, market development would be extremely slow. But financial behavior is driven by motives, information, reputation, assumptions, hopes, willingness to take risks, incentives and other non-statistical indicators. The author has developed a method of using game theory in the practice of making investment decisions, provided that the investor wants to buy securities on the stock exchange for 10,000 UAH. and examines the shares of one of two companies: either A or B. The sequential actions of financial market participants based on game theory concepts are revealed.

Pareto optimality and game theory for pile design having conflicting objectives

ased on concept of Pareto-optimal solution and game theory associated with Nash non-cooperative and cooperative solution, a mathematical procedure is presented for optimum design of axially loaded pile structure. The decision making situation is formulated as a constrained optimization problem with two objectives of contradictory in nature. The factor of safety is taken as the design variable. Geometric constraints are considered by imposing a lower and upper bound on the design variable. Two objectives considered are: maximization of ultimate load carrying capacity of pile and minimization of associated cost. The generation of Pareto-optimal solution and methodology based on game theory concept is described. The design problem is mathematically formulated as two-person game. To obtain the starting point of game, Nash non-cooperative solution or Nash equilibrium solution is evaluated for an irrational play. For cooperative game, a negotiation model is developed for overall benefit of all players. Game is terminated when the optimal trade-off between two objectives is reached with maximization of supercriterion. Two numerical examples of practical interest are solved to demonstrate the methodology.

Polarized Population Under Imitation Dynamics in Complex Networks

Evolutionary game theory is applied in a variety of settings, ranging from economics to socio-technical networks. The core concept in evolutionary game theory is evolutionary dynamics, which determines the composition of strategies in the population at steady state. Most evolutionary dynamics are modeled to descriptively showcase the utility derived from interactions between random pairs of players in well-mixed populations, or random pairs of neighbors in structured populations. In real-life social and socio-technical networks, it is more appropriate to evaluate a player’s utility as a collection of interactions with its neighbors. To understand this; in practice, people form opinions by means of observation and imitation, by not just one friend, but a collection of friends. This paper displays a variation of the pairwise imitation dynamics where players imitate the most well-off neighbor. This process is memory-less i.e., players only use the outcome of the current game to determine their strategies in subsequent games. Empirical results demonstrate that in real-life social networks, this imitation dynamic leads to a polarized population with games that have multiple pure strategy Nash equilibria such as the Stag-Hunt game and anti-coordination games like Hawk-Dove, where an "undecided" population indefinitely swings between two strategies.

Efficient Computation and Estimation of the Shapley Value for Traveling Salesman Games

The traveling salesman game (TSG) consists of dividing the cost of a round trip among several customers. One of the most significant solution concepts in cooperative game theory is the Shapley value, which provides a fair division of the costs for a variety of games including the TSG, based on the marginal costs attributed with each customer. In this paper, we consider efficient methods for computing the Shapley value for the TSG. There exist two major variants of the TSG. In the first variant, there exists a fixed order in which the customers are serviced. We show a method for efficient computation of the Shapley value in this setting. Our result is also applicable for efficient computation of the Shapley value in ride-sharing settings, when a number of passengers would like to fairly split their ride cost. In the second variant, there is no predetermined fixed order. We show that the Shapley value cannot be efficiently computed in this setting. However, extensive simulations reveal that our approach for the first variant can serve as an excellent proxy for the second variant, outperforming the state-of-the-art methods.

Technical debt reduction using epsilon-Nash equilibrium for the perturbed software refactor game model

Technical debt (TD) is a metaphor that is one of the reasons for software to become obsolete. The process of refactoring can be effectively applied to reduce the technical debt and the improvement of other vital quality attributes such as abstraction, inheritance and coupling. This paper discusses a refactoring model that can be applied for an object oriented software system for improved quality by applying the concepts of game theory. A multi-player perturbed software refactor game model is developed, that models inheritance, abstraction, coupling and the technical debt, as multiple players of the game. An optimal strategy for refactoring the source code is arrived by calculating the ε-Nash equilibrium of the perturbed game. The results attained are compared against the popular genetic algorithm (GA), artificial bee colony (ABC) and simulated annealing (SA) optimisation algorithms, taking three open source Java project samples.