Game theory is a central tool in many disciplines: in economics, biology, business and finance, road transport, marketing, political and social sciences, ecology and the environment, operational research, and many others. It also plays a role in military research in control theory, in telecommunication networks and computer networks  . But game theory research is not limited to the applications mentioned above. Indeed, the very foundations of game theory is a mathematical field still very active, which uses a lot of mathematical tools that often seem more sophisticated than the problem at hand. This is the case of algebraic logic, algebraic geometry, and the approach of viscosity solutions for differential equations appearing in dynamic games in continuous time. Game theory is probably the best known in the context of economics, especially since 1994, when the Nobel Prize in economics was attributed to researchers for their contribution to the analysis of equilibrium and non-cooperativegame theory. Recall that before this, K. Arrow and J. HICS (1972) and Debreu (1983) received the Nobel Prize on their contribution to the theory of equilibrium, related to game theory  . In this paper, we present some facets of non- cooperativegame theory that provide a framework for modeling and analysis for competitive situations in telecommunication networks.
Wireless data demands keep rising at a fast rate. In 2016, Cisco measured a global mobile data traffic volume of 7.2 Exabytes per month and projected a growth to 49 Exabytes per month in 2021. Wi-Fi plays an important role in this as well. Up to 60% of the total mobile traffic was off-loaded via Wi-Fi (and femtocells) in 2016. This is further expected to increase to 63% in 2021. In this publication, we look into the roll-out of public Wi-Fi networks, public meaning in a public or semi-public place (pubs, restaurants, sport stadiums, etc.). More concretely we look into the collaboration between two parties, a technical party and a venue owner, for the roll-out of a new Wi-Fi network. The technical party is interested in reducing load on its mobile network and generating additional direct revenues, while the venue owner wants to improve the attractiveness of the venue and consequentially generate additional indirect revenues. Three Wi-Fi pricing models are considered: entirely free, slow access with ads or fast access via paid access (freemium), and paid access only (premium). The technical party prefers a premium model with high direct revenues, the venue owner a free/freemium model which is attractive to its customers, meaning both parties have conflicting interests. This conflict has been modeled using non-cooperativegame theory incorporating detailed cost and revenue models for all three Wi-Fi pricing models. The initial outcome of the game is a premium Wi-Fi network, which is not the optimal solution from an outsider ’ s perspective as a freemium network yields highest total payoffs. By introducing an additional compensation scheme which corresponds with negotiation in real life, the outcome of the game is steered toward a freemium solution.
This article concentrates on call center prompt information reliability decision and customer behavioral decision and establishes a non-cooperativegame model of the master-slave. Through numerical experiments analysis found several conclusions: Prompt information reliability is positively related to the customer service rate, and is negatively correlated with the average waiting time, As call center load is larger, the prompt information reliability sensitivity is greater; Customers patient size is positively related to the average waiting time; On the basis of meeting customer service rate, when the gain coefficient and opportunity coefficient ratio are high, call centers should take high reliability prompt information, otherwise, should take low reliability prompt information; and the customer should take a low value of patience. The variation plays a reference role of prompting information with a call center queue management and customer coordination.
In addition, its decisions are also affected by other servers strategies indirectly. During the whole iteration process, each server tries to optimize its own unit power efficiency, and make the resource proportion match with its task proportion. Similarly, the resource allocation proportion of the three servers converge after 26 iterations, and the proportion of resource proportion varies due to the difference in performance parameters between heterogeneous servers. Figure 5 shows the variation of the unit power efficiency of the three servers. It can be seen from the figure 5, in the initial state, the three servers of the unit power efficiency are very low, this is mainly caused by the mismatch of computing resources and the task amount, then the three servers change their strategies. When the total task is constant, the unit power efficiency of a single server will not increase or decrease unlimitedly due to the selfishness of each server in the non-cooperativegame, the strategy constraint among the servers and the limitation of its own performance parameters. As can be seen from the figure, after 26 iterations, the unit power efficiency of the three servers achieves a constant value, it is determined by p* ij and Φ* ij together, then the strategies of the
discussed in any paper on EM-WNSNs. In our opinion, an NPCG could be a potential scheme for enhancing the energy efficiency of nanosensors in EM-WNSNs. Accordingly, we apply an NPCG to EM-WNSNs for the power control of nanosensors, and the game is on the emission power of the nanosensors. The NPCG is based on a novel utility function, with consideration on the properties of the THz channel. This study is different from the communication mode control game for GBAN  and the molecular emission control game for molecular nanonetworks . In this study, we define the new NPCG and its Nash equilibrium (NE), and present the existence and uniqueness of the NE, as well as a power control algorithm based on the proposed NPCG.
Efficient energy usage is a major design challenge in wireless sensor networks. In this paper, an efficient power control scheme that mitigates interference and reduces the energy usage of the sensor nodes in a wireless sensor network is presented using the game theory. A non-cooperativegame was formulated among the sensor nodes in the modeled network by setting a transmission power limit at the receiving nodes which ensured that the transmitting nodes transmits at the optimal power level. The utility of the sensor nodes and the interference proportion within the network was evaluated at the optimal and discrete transmit powers. The Nash equilibrium of the proposed game was studied and it corresponds to a stability point where the network performance was optimized. Simulation results showed that the proposed scheme is effective for optimization of network resource utilization, reduction in the energy consumption of the nodes, increasing the transmission sum rate, reduction of interference within the network, and improving the network capacity.
In non-cooperativegame theory, the usual solution method is to look for a Nash equilibrium . In a Nash equilibrium, no player can unilaterally change his or her strategy to receive a better payoff, given that the strategies of the other players remain unchanged. This will be the basis for the solution method of the industrial symbiosis bargaining game in Section 4.2. For this bargaining game, the same player set and the same characteristic function as for the industrial symbiosis game of Chapter 3 can be used. The player set consists of all the companies that want to bargain for an industrial symbiosis network. The characteristic function represents, per possible industrial symbiosis network, the obtainable benefit by cooperating. But, to be able to solve this bargaining game later on, some assumptions need to be made about the characteristic function v. Remember, v(S) of coalition S ⊆ N is expressed as v(S) = T (S) − O(S), where T (S) denotes the traditional operating costs of coalition S and O(S) denotes the costs of maintaining an industrial symbiosis network among coalition S.
The coalitions in game are with optimal allocations. However, as part of the “stakeholder governance” of listed companies, the multiplicity and the complexity of the relations and the vague and short-lived character of coalitions can give place only to satisfactory allowances not necessarily quite pecuniary. The very nature of the “stakeholder governance” is subject to policy changes notably because the existence of individual and/or small groups’ with non- cooperative behavior. The game of compromise which characterizes the “stakeholder governance” may tend to a non-cooperativegame. In both cases, the measurement attempt reflecting the “True Value Company” is impossible to perform.
game. Therefore, for each stage of the game, the total cost of a given player can be measured as the number of gains or losses. Game theory categorizes games under several categories, including Cooperative vs. Non-cooperative, Static vs. Dynamic, Strategic-form vs. Extensive-form, Perfect vs. Imperfect, and Complete Game theory categorizes games under several categories, including Cooperative vs. No-cooperative, Static vs. Dynamic, Strategic-form vs. Extensive-form, Perfect vs. Imperfect, and Complete vs. Incomplete information. The selection of one of these criteria depends in particular on the procedure and conditions of the game itself.Basically, two main game families exist cooperative games and non-cooperative games. The cooperative games require mutual agreements between users; external signals are also required. In a highly mobile, heterogeneous system like VANET, it may be harder to achieve this conclusion. In a non-cooperativegame, decision- makers are the players themselves, but without the necessity of any cooperation, everyone decides for themselves. Therefore, the most important contribution of the paper is to provide a modern formalism based on non-cooperativegame theory to refuse the DoS attack in VANETs.The following paper is structured as follows. In section 2 we start with the related work. Chapter 3 explains the proposed security-game algorithms. In Section 4 we describes the simulation environment, parameters of simulation, matrices, and performance evaluation results. The article finishes with the conclusion in Section 5.
Because the utility of the base station (BS) is a non-convex function, it is difficult to find the optimal pricing scheme. Therefore, a novel price-based power control algorithm was presented in  to find the optimal price for each SU. In , a novel non-cooperativegame power control model was given to verify the sub-optimality, fairness, and efficiency of the proposed pricing scheme. Joint pricing and power allocation for Dynamic Spectrum Access (DSA) networks with Stackelberg game was developed in . In , the authors considered a wireless amplify-and-forward relay network with one relay node and multiple source-destination pairs and proposed a pricing framework that enabled the relay to set prices to maximize either its revenue or any desirable system utility. However, those research studies didn’t take the energy-efficiency into account, and the minimum SINR requirement among each SU was ignored either. While these schemes offer some remedies to the non-cooperativegame approach, they still leave room for improvement toward the global optimum.
The main objective of CoMP is to reduce the inter-cell interference, improv- ing the user’s receiving SINR and the spectrum efficiency. Therefore, maximiz- ing spectral efficiency has become the main consideration for CoMP cluster de- sign. The distributed interference management is studied in  in a multi-cell multiple-input multiple-output time-division duplex network downlink. Us- er-centric clusters are built, where users are connected to multiple base stations. These base stations serve users through CoMP-JT. The goal of this paper is to allocate appropriate serving base stations and precoding matrices for each user. Then, the interference and base station transmit power are controlled to max- imize the system’s spectral efficiency. Because the same frequency spectrum is reused among the same user clusters in the UDN, there may be strong interfe- rence between them. For the downlink transmission of UDN in , an interfe- rence graph is first created based on large-scale fading according to the interfe- rence strength between user clusters. Then, the user clusters with strong interfe- rence are merged to form a new user cluster, and the intra-cluster interference is eliminated through the CoMP-JT, which can improve the average spectrum effi- ciency of the user, especially the spectrum efficiency of the edge user. However, the small base stations use same power to transmit signals for users in the me- thod, and power allocation and resource scheduling are not considered. A re- source allocation scheme based on interference coordination is proposed in  for solving the inter-cell interference problem in UDN. First, small cells with strong interference are grouped into the same cluster based on the interference strength among the small cells, and the small cells in the same cluster share fre- quency band resources. Then based on the max-min fairness criteria in power, optimal power allocation is performed and resources are dynamically allocated. In order to mitigate the severe interference among dense small cells and improve the performance of cell edge users, hybrid clustering based on non-cooperativegame theory is proposed in , where SINR measurement mechanism are in- troduced, Non-cooperativegame is used to help users select the best serving cell through considering the load of the cell, so as to achieve the purpose of improv- ing spectrum efficiency. For CoMP can only eliminate intra-cluster interference but cannot mitigate inter-cluster interference, a dynamic joint processing scheme is proposed in . Through the joint consideration of network-centric clustering methods and sub-band allocation, a single sub-band cluster is con- structed. It can eliminate users at the edge of the cluster, which can reduce in- ter-cluster interference and improve system spectral efficiency.
The performance and efficiency of a cooperative diversity scheme depend, largely on proper allocation of resources like power and bandwidth. Another important factor to consider is the selection of a proper partner by the source node to help in forwarding information to the destination. In this letter, we look at the concept of relay selection for a distributed communication networks, rather than the more common centralized system where precise channel state information data has to be available at the base station. Also coded cooperation is used as the cooperative scheme rather than the more common amplify- and-forward or decode-and-forward system. A type of game known as non-cooperativegame is employed in this analysis so as to jointly consider the utilities of the source and relay nodes, where in this case, the source is the buyer while the relay is the seller. The approach enables the source to maximize its benefit (or utility) by selecting to buy power from the relay that would enable it do so. Results show that at a low price, the source node buys more power from the relay, which also increases the utility of the relay itself. It also shows that among a set of relays competing for the attention of a source node, the source will only select a partner (relay) that gives it the highest utility in terms of the resource, i.e power. In this paper, partner and relay are used interchangeably.
In the proposed attack model, a noncooperativegame theory approach for handling security issues in WSNs is proposed. The game is defined between the intruder (player 1) and the IDS (player 2) where each one tries to maximize its own payoff. For example, if we consider the cooperation of neighboring nodes, the reputation of node for packet transfer and the appropriate security by IDS, the following payoff function to transfer a packet from node i to node j at any time t is given by 
weights, in contrast to 2N numbers which are usually required to represent a cooperative and non- cooperativegame. Basic idea is to allocate more measurements to nodes that contribute more to the localization process. The allocation algorithm has been integrated into a Bayesian estimator. In (Ghassemi F. & Krishnamurthy V., 2008b), utility is defined as information gain from a node, i.e. the mutual information between the prior density of target position and the measurement. Additionally, a price for transmission is included to account for the current energy level in the nodes, and the energy needed for data transmission. The algorithm proposed in (Moragrega A., 2011) assumes a number of static anchor nodes, strategically placed to guarantee coverage to all unknown nodes. Anchors transmitting with lower energy can provide coverage to a smaller number of nodes; aim is to minimize power consumption at the anchor nodes, while assuring desired localization accuracy. The metric for positioning quality is the GDOP. The problem has been formulated as a cooperative and non-cooperativegame, using Nash equilibrium as solution concept
Abstract. The paper proposes a coopetitive model for the Green Economy. It addresses the issue of the climate change policy and the creation and diffusion of low-carbon technologies. In the present paper the complex construct of coopetiton is applied at macroeconomic level. The model, based on Game Theory, enables us to offer a set of possible solutions in a coopetitive context, allowing to find a Pareto solution in a win-win scenario. The model, which is based on the assumption that each country produces a level of output which is determined in a non-cooperativegame of Cournot-type and that considers at the same time a coopetitive strategy regarding the low technologies, will suggest a solution that shows the convenience for each country to participate actively to a program of low carbon technologies within a coopetitive framework to address a policy of climate change, thus aiming at balancing the environmental imbalances.
As the number of connected vehicles on a road network in- crease so does the number of transmitted messages which leads to congestion in the wireless communication channel. This degrades the network performance and the QoS parameters. In this paper, congestion control in the communication channel has been formulated as a non-cooperativegame. Each vehicle acts as a player in the game and requests a high data rate in a selfish way. Simulation results show that the GTACC has a better performance as compared to the Carrier-Sense Multiple Access with Collision Avoidance mechanism of the Wireless Access for Vehicular Environment protocol. As reported from the highway street scenario, it is shown that the proposed approach improves the QoS parameters such as throughput, average delay, number of lost packets and total channel busy time by an overall average of 50.40%, 49.37%, 58.39% and 36.66% respectively, as compared to Carrier-Sense Multiple Access with Collision Avoidance mechanism.
Abstract: Establishing effective interaction between the manufacturer and the retailer as participants of supply chain implies the construction of an effective mechanism for the implementation of the main strategies of their business behavior, in particular price strategies, as well as strategies for generating costs for joint promotion of the product. This provides the manufacturer and the retailer with the ability to make independent management decisions regarding the selection of the most appropriate business game scenarios that maximize their profits in the short and long term, and is therefore a topical question in the practice of operating distribution networks. The purpose of the study is to determine the optimal values of the parameters of the advertising cost response function, under which the maximization of manufacturer and the retailer profits can be achieved in the process of their independent decision-making on determining pricing strategies, as well as strategies for generating joint costs for product promotion. The paper presents a numerical experiment on the possible values of the parameters of the advertising cost response function, calculated on the basis of effectively selected range and step change. Nash game solution is mathematically substantiated and defined as a variant of interaction between participants of the supply chain, in which neither of them can maximize their own profit without affecting the profit of the other. A numerical experiment was carried out on the possibilities of maximizing the profit functions of the manufacturer, the retailer and the channel from the standpoint of pricing strategies, as well as joint costs strategies of both channel members for product advertising. The results obtained can be the initial information base for providing recommendations on the possibilities of using non-cooperativegame in comparison with other types of game-theoretic models of enterprises’ interactions in supply chains, in particular in the study of activities of enterprises – participants of oligopoly (duopoly).
Non-cooperativegame theory studies strategies between interactions among competing players. In the game, a player is called an agent and his goal is to maximize its utility by choosing its strategy individually, in other words, each player is selfish but rational in a non-cooperativegame. Non-cooperativegame theory uses a utility function to find the NE. Non- cooperativegame theory is mainly applied in distributed resource allocation, congestion control, power control, spectrum sharing in cognitive radio and many others. With the concepts from economics and game theory, Wu and Wei proposed a mechanism design to handle incentives of strategic agents. A power control model based on non-cooperativegame theory. Gharehshiran and Krishnamurthy used cooperativegame theory as a tool to devise a distributed dynamic coalition formation algorithm in which nodes autonomously decide which coalition to join while maximizing their feasible sleep times. The sleep time allocation problem is formulated as a non-convex cooperativegame and the concept of the core is exploited to solve this problem. They solved two problems: (1) what are the optimal coalition structures for localizing multiple targets with a pre-specified accuracy? (2) How can nodes dynamically form optimal coalitions to ensure that the average sleep time allocated to the nodes is maximized? The two questions are solved nicely within the framework of coalition formation in a cooperativegame.
In this paper, a cooperativegame theoretic approach, namely the Nucleolus game is utilized to equitably allocate the total cost reduction to dischargers and calculate side payments. The share of each discharger from the total cost reduction, final treatment cost after cost reallocation, and side payments are summarized in Table IV. In this table, a positive value for the side payment of discharger 6 shows that this discharger should sell discharge permit and gain money equal to its side payment. Similarly, negative values for the side payments of dischargers 2 and 7 show that these dischargers should buy discharge permits and pay money to discharger 6 equal to their side payments.
It is very well known fact that real world problem can be modeled as a mathematical equation. The existence of a solution of such problems has been investigated in several branches of mathematics, such as diﬀerential equations, integral equations, functional equations, partial diﬀerential equations, random diﬀerential equations, etc. and one has proposed solutions for such problems via ﬁxed point theory. But the application area of ﬁxed point theory is not only limited to mathematics, but also occurs in other quantita- tive sciences, such as, computer science, economics, biology, physics, etc. Game theory, a branch of economics, has used ﬁxed point theory techniques and approaches to solve its own problems.