Unique Nash Equilibrium Point Research Articles

Joint Channel and Power Assignment for Underwater Cognitive Acoustic Networks on Marine Mammal-Friendly

When marine animals and underwater acoustic sensor networks (UASNs) share spectrum resources, problems such as serious harm caused to marine animals by underwater acoustic systems and scarcity of underwater spectrum resources are encountered. To address these issues, a mammal-friendly underwater acoustic sensor network channel power allocation algorithm is proposed. Firstly, marine animals are treated as authorized users and sensor nodes as unauthorized users. Considering the interference level of sensor nodes on authorized users, this approach improves network service quality and achieves a mammal-friendly underwater communication mechanism. Secondly, to maximize the utility of unauthorized users, the algorithm incorporates a network interference level and node remaining energy into a game-theoretical framework. Using channel allocation and power control, a game model is constructed with a unique Nash equilibrium point. Finally, through simulation, it can be found that the proposed algorithm can obtain a stable optimal power value, and with the increase of network load, the system capacity of the proposed algorithm is significantly improved than that of the traditional cognitive radio technology and the common spectrum allocation algorithm, and the transmitted power of nodes can be controlled according to the size of the residual energy, so as to comprehensively improve the overall performance of the network.

On ambiguity-averse market equilibrium

We develop a Nash equilibrium problem representing a perfectly competitive market wherein all players are subject to the same source of uncertainty with an unknown probability distribution. Each player—depending on her individual access to and confidence over empirical data—builds an ambiguity set containing a family of potential probability distributions describing the uncertain event. The ambiguity set of different players is not necessarily identical, yielding a market with potentially heterogeneous ambiguity aversion. Built upon recent developments in the field of Wasserstein distributionally robust chance-constrained optimization, each ambiguity-averse player maximizes her own expected payoff under the worst-case probability distribution within her ambiguity set. Using an affine policy and a conditional value-at-risk approximation of chance constraints, we define a tractable Nash game. We prove that under certain conditions a unique Nash equilibrium point exists, which coincides with the solution of a single optimization problem. Numerical results indicate that players with comparatively lower consumption utility are highly exposed to rival ambiguity aversion.

Global Analysis, Multi-stability and Synchronization in a Competition Model of Public Enterprises with Consumer Surplus

We research global dynamic behaviors, multi-stability and synchronization in a dynamic duopoly Cournotian model with consumer surplus on the basis of nonlinear demand function and bounded rationality. This game generalizes the traditional dynamic duopoly Cournot game. The aim of enterprises is to optimize their own profits and the social welfare. This game is characterized by discrete difference equations incorporated in the competition model's optimization problem. The stability of equilibrium points and complicated dynamical phenomena are studied, such as flip bifurcation for unique Nash equilibrium point. The global bifurcation of non-invertible two-dimensional map is analyzed through critical curves, which is an important method to further study global properties. Multi-stability is observed due to the presence of multiple complex attractors. An inspection of the basins of attraction is provided for the situation of several attractors coexisting. Since this game has symmetry, it can be stated that a one-dimensional invariant sub-manifold is the diagonal of the system by analyzing the nonlinear map x(t+1)=μx(t)(1−x(t)). The properties of this nonlinear map is completely different from the logistic map although both of them have similar form. Along the invariant diagonal, the synchronization phenomenon of the game is discussed in the end.

Mean-field type forward-backward doubly stochastic differential equations and related stochastic differential games

We study a kind of partial information non-zero sum differential games of mean-field backward doubly stochastic differential equations, in which the coefficient contains not only the state process but also its marginal distribution, and the cost functional is also of mean-field type. It is required that the control is adapted to a sub-filtration of the filtration generated by the underlying Brownian motions. We establish a necessary condition in the form of maximum principle and a verification theorem, which is a sufficient condition for Nash equilibrium point. We use the theoretical results to deal with a partial information linear-quadratic (LQ) game, and obtain the unique Nash equilibrium point for our LQ game problem by virtue of the unique solvability of mean-field forward-backward doubly stochastic differential equation.

SYSTEMIC RISK: THE EFFECT OF MARKET CONFIDENCE

In a crisis, when faced with insolvency, banks can sell stock in a dilutive offering in the stock market and borrow money in order to raise funds. We propose a simple model to find the maximum amount of new funds the banks can raise in these ways. To do this, we incorporate market confidence of the bank together with market confidence of all the other banks in the system into the overnight borrowing rate. Additionally, for a given cash shortfall, we find the optimal mix of borrowing and stock selling strategy. We show the existence and uniqueness of Nash equilibrium point for all these problems. Finally, using this model we investigate if banks have become safer since the crisis. We calibrate this model with market data and conduct an empirical study to assess safety of the financial system before, during after the last financial crisis.

Systemic Risk: the Effect of Market Confidence

In a crisis, when faced with insolvency, banks can sell stock in a dilutive offering in the stock market and borrow money in order to raise funds. We propose a simple model to find the maximum amount of new funds the banks can raise in these ways. To do this, we incorporate market confidence of the bank together with market confidence of all the other banks in the system into the overnight borrowing rate. Additionally, for a given cash shortfall, we find the optimal mix of borrowing and stock selling strategy. We show the existence and uniqueness of Nash equilibrium point for all these problems. Finally, using this model we investigate if banks have become safer since the crisis. We calibrate this model with market data and conduct an empirical study to assess safety of the financial system before, during after the last financial crisis.

The Generic Uniqueness and Well-Posedness of Nash Equilibria for Stable Population Games

This paper aims at studying a new kind of stable population games introduced by J. Hofbauer and H. Sandholm in 2009. We first construct a complete distance space M consisting of stable population games and show that most of stable population games have unique Nash equilibrium point that according to Baire’s category theorem. It implies that every stable population game that possesses more than one Nash equilibrium can be approached arbitrarily by a sequence of the stable population game each of which has a unique Nash equilibrium. Then, we construct a bounded rationality function and deduce some results on the generic well-posedness implying Tikhonov well-posedness and Hadamard well-posedness for stable population games.

Mean Field Optimal Energy Management of Plug-In Hybrid Electric Vehicles

This paper addresses the problem of energy consumption management of a large population of plug-in hybrid electric vehicles (PHEVs). A PHEV can be derived either on its gasoline or the battery modes while traveling, and can be either charged from or discharged to the grid while parking at home, respectively. This feature is the main novel consideration in our system model, besides taking into account the constraints like traveling time and distance, and the bounds on the charging power and state of charge of the battery. On the basis of the proposed model of PHEV, the optimal battery-gasoline energy management strategy is obtained in order to minimize the cost of energy and battery degradation for each user. Such a strategy can also compensate the peak load. Since the strategy of each PHEV affects other users’ cost through the electricity price, we model such an interaction as a game problem and we prove that there exist a unique Nash equilibrium point of the game. Then, due to the fact that the effect of a single PHEV of a large population on the other users’ costs is negligible, the theory of mean filed (MF) game is utilized to develop a decentralized control strategy for PHEVs. The lightweight information exchange of the proposed MF algorithm ensures a low computational cost and communication overhead. The proof of convergence for the proposed algorithm is given and it is shown that as the number of PHEVs goes to infinity the MF optimal strategy of the players converges to the unique Nash equilibrium point of the game. In simulation results, the effectiveness of the proposed method in terms of demand side management, peak shaving, convergence rate, and robustness is studied.

Revenue sharing model in New Hong Kong’s warehousing business paradigm

The booming e-commerce and fierce regional competition pose challenges to Hong Kong’s warehousing industry, which needs transformation to keep its competitiveness. However, neither of the stakeholders (warehouse owner and user) has the motivation to upgrade, due to high facility investment and short terms of rental agreements. Thus it calls for new business paradigms and incentive mechanisms as a driving force. To address this problem, we first propose a new paradigm in which a third party-warehousing equipment supplier is introduced with their advanced facility and technical capability. The three parties can cooperate with different competences to gain more individual payoffs, via the improved warehousing service and operational efficiency. Then a coordination mechanism between the warehouse owner and warehousing equipment supplier is developed to resolve their conflictions on revenue sharing. Accordingly, we develop a stackelberg game to study stakeholders’ optimal strategies, through first establishing a revenue sharing stackelberg-game model and then finding a unique Nash Equilibrium point in analytical format. The properties and constraints about the revenue sharing model are analysed. Comparatively, we also model a centralized decision-making case when the two parties as a whole make decisions to maximize the overall profit. The two models can be used as references to guide the cooperation and competition of companies.

Interest-aware energy collection & resource management in machine to machine communications

The emerging paradigm of Machine to Machine (M2M)-driven Internet of Things (IoT), where physical objects are not disconnected from the virtual world but aim at collectively provide contextual services, calls for enhanced and more energy-efficient resource management approaches. In this paper, the problem is addressed through a joint interest, physical and energy-aware clustering and resource management framework, capitalizing on the wireless powered communication (WPC) technique. Within the proposed framework the numerous M2M devices initially form different clusters based on the low complexity Chinese Restaurant Process (CRP), properly adapted to account for interest, physical and energy related factors. Following that, a cluster-head is selected among the members of each cluster. The proposed approach enables the devices of a cluster with the support of the cluster-head to harvest and store energy in a stable manner through Radio Frequency (RF) signals adopting the WPC paradigm, thus prolonging the operation of the overall M2M network. Each M2M device is associated with a generic utility function, which appropriately represents its degree of satisfaction in relation to the consumed transmission power. Based on the distributed nature of the M2M network, a maximization problem of each device's utility function is formulated as a non-cooperative game and its unique Nash equilibrium point is determined, in terms of devices’ optimal transmission powers. Considering the devices’ equilibrium transmission powers, the optimal charging transmission powers of the cluster-heads are derived. The performance of the proposed approach is evaluated via modeling and simulation and under various topologies and scenarios, and its operational efficiency and effectiveness is demonstrated.

Research on Admission Control of Wireless Mesh Networks Based on Game Theory

We study the admission control of regional resource allocation in heterogeneous wireless network. The blocking rate and the efficiency of the system based on the regional resource allocation in the case of high access are analyzed in this paper. We proposed the admission control theory model of the regional resource allocation in heterogeneous wireless mesh networks which based on the non-cooperative game theory. The regional resource allocation is defined as the theoretical distribution model of the bandwidth and the number of connections of mesh network resources. By constructing the utility function of network connection number, the existence and uniqueness of Nash equilibrium point in mesh resource allocation of non-cooperative game are demonstrated. Meanwhile, we analyse the blocking rate and system efficiency of the high traffic situation and a reliable admission control algorithm is proposed.

Privacy Preservation for Context Sensing on Smartphone

The proliferation of sensor-equipped smartphones has enabled an increasing number of context-aware applications that provide personalized services based on users' contexts. However, most of these applications aggressively collect users' sensing data without providing clear statements on the usage and disclosure strategies of such sensitive information, which raises severe privacy concerns and leads to some initial investigation on privacy preservation mechanisms design. While most prior studies have assumed static adversary models, we investigate the context dynamics and call attention to the existence of intelligent adversaries. In this paper, we identify the context privacy problem with consideration of the context dynamics and malicious adversaries with capabilities of adjusting their attacking strategies. Then, we formulate the interactive competition between users and adversaries as a competitive Markov decision process (MDP), in which the users attempt to preserve the context-based service quality and their context privacy in the long-term defense against the strategic adversaries with the opposite interests. In addition, we propose an efficient minimax learning algorithm to obtain the optimal policy of the users and prove that the algorithm quickly converges to the unique Nash equilibrium point. Our evaluations on real smartphone context traces of 94 users demonstrate that the proposed algorithm largely improves the convergence speed by three orders of magnitude compared with traditional algorithm and the optimal policy obtained by our minimax learning algorithm outperforms the baseline algorithms.

Joint spectrum load balancing and handoff management in cognitive radio networks: a non-cooperative game approach

We propose a non-cooperative game theory based algorithm for spectrum management problem in cognitive radio networks taking into account the spectrum handoff effects. The objective is to minimize the spectrum access time of Secondary Users (SUs) which are competing for spectrum opportunities in heterogeneous environment. In this paper, the preemptive resume priority (PRP) M/G/1 queuing model is used to characterize the multiple handoff and data delivery time of SUs. Also an explicit solution for channels selection probabilities of each SU is extracted for PRP M/M/1 model specifically. The effect of handoffs is considered as the interrupted packets which return to the SUs' low priority queue when the high priority Primary User's packets are arrived to take service. The queuing delay of SUs' and the effect of these returned packets are considered in order to balance the load of SUs on channels so that the minimum spectrum access time is sensed by each SU. The non-cooperative spectrum load balancing with handoff management game is proposed to find a distributed solution for each SU. It is shown that this game has a unique Nash equilibrium point which can be achieved by SUs as decision makers. At this equilibrium, each SU incurs the minimum delay on all channels while the free spectrum holes of channels are utilized efficiently. Simulation results are provided to evaluate the performance of the proposed scheme in terms of spectrum access delay, fairness, and channels spectrum holes utilization.

Recursive stochastic linear-quadratic optimal control and nonzero-sum differential game problems with random jumps

This paper presents an existence and uniqueness result for a kind of forward-backward stochastic differential equations (FBSDEs for short) driven by Brownian motion and Poisson process under some monotonicity conditions. By virtue of the conclusion of FBSDEs, we solve a linear-quadratic stochastic optimal control problem for forward-backward stochastic systems with random jumps. Moreover, we also solve a linear-quadratic nonzero-sum stochastic differential game problem. We obtain explicit forms of the unique optimal control and the unique Nash equilibrium point, respectively.

Stackelberg Game on Space and Frequency Heterogeneity Analysis in an OFDMA-Based Cognitive Spectrum Leasing

With the development of cognitive radio technologies, dynamic spectrum access (DSA) techniques are being regarded as a promising approach to increase the efficiency of spectrum utilization and to solve spectrum scarcity problem. This comes as a greater challenge in a cellular network where there are multiple primary users (PUs) who communicate with their access point while the other secondary users (SUs) want to use PU's spectrum. On the other hand, heterogeneity in terms of space and frequency can affect the primary users' decision to release their spectrum to the SUs. In this respect, the present paper is intended to address this issue and thus propose a solution with regard to the reward and punishment policy and equivalent revenue per unit transmission parameter. It has to be noted that both PUs and SUs aim to maximize their utilities in terms of their transmission rate and revenue/payment. Therefore, the proposed model is formulated as a Stackelberg Game, and a unique Nash Equilibrium Point is achieved by analytical procedure. Based on the analyses, the paper presents the conditions under which cooperation will enhance the performance of the whole system. Both analytical and numerical results reveal that the cooperative cognitive radio framework is a promising framework under which the utility of both the primary and secondary systems is maximized.

Client–server games and their equilibria in peer-to-peer networks

In peer-to-peer networks, each peer acts simultaneously as client and server, by issuing and satisfying content requests respectively. In this work, we use concepts from non-cooperative game theory to model the interaction of autonomous peers. The client strategy set consists of feasible request load splits towards servers, while the server strategy set is formed out of possible service disciplines on received requests. The performance metric of interest is the average retrieval delay of content requests.First, we assume preassigned fixed server policies (FIFO and priority) and study the emerging client request load splitting game. Peers are either egotistic (i.e. interested only in optimizing their own delay) or altruistic ones that also take into account delay incurred to other peers. We consider best response updates to model iterative peer interaction. For egotistic peers, we show that the sequence of best responses always converges to the unique Nash Equilibrium Point (NEP). For altruistic peers best response updates converge to one of the multiple NEPs exist, with each one being a global optimum for the FIFO case and a local optimum for any other service strategy profile. We also consider mixed swarms consisting of both egotistic and (partially-) altruistic peers and show an interesting transition from one to multiple NEPs. Next, we include service strategies in the peer strategy set. Though with its service policy a peer cannot directly affect its delay, it can affect the resulting NEP. We devise two-level game models, where, at a first level, a peer selects its favorable service rule and then peers play a client load splitting game.

Linear Quadratic Nonzero Sum Differential Games with Asymmetric Information

This paper studies a linear quadratic nonzero sum differential game problem with asymmetric information. Compared with the existing literature, a distinct feature is that the information available to players is asymmetric. Nash equilibrium points are obtained for several classes of asymmetric information by stochastic maximum principle and technique of completion square. The systems of some Riccati equations and forward-backward stochastic filtering equations are introduced and the existence and uniqueness of the solutions are proved. Finally, the unique Nash equilibrium point for each class of asymmetric information is represented in a feedback form of the optimal filtering of the state, through the solutions of the Riccati equations.

Dynamic Pricing and Queue Stability in Wireless Random Access Games

We study the interaction among users of contention-based wireless networks, where the performance of the network is highly correlated with user transmission probabilities. Considering the underlying user incentives, we make use of the conceptual framework of noncooperative game theory to obtain a distributed control mechanism to limit the contention among wireless nodes by taking into account queue stability and injecting linear pricing to punish greedy behavior. We present a comprehensive analysis of the game including existence and uniqueness of Nash equilibrium point, convergence dynamics, and robustness properties. Utilizing linear pricing enables us to move the equilibrium point of the game to a desirable region. We obtain conditions on linear prices necessary to achieve stability of user queues in the asymmetric and symmetric cases. In addition, we propose dynamic pricing algorithms, in which wireless users play the game without cooperation while the base station adjusts the linear price of each user. Under limited knowledge of game parameters, we present a dynamic equal pricing algorithm that moves the Nash equilibrium to the aggregate throughput maximizing solution. The theoretical results are verified, and the convergence and efficiency of the proposed game are illustrated via simulations.

Distributed Uplink Power Control in Multiservice Wireless Networks via a Game Theoretic Approach with Convex Pricing

In this paper, the problem of efficient distributed power control via convex pricing of users' transmission power in the uplink of CDMA wireless networks supporting multiple services is addressed. Each user is associated with a nested utility function, which appropriately represents his degree of satisfaction in relation to the expected trade-off between his QoS-aware actual uplink throughput performance and the corresponding power consumption. Initially, a Multiservice Uplink Power Control game (MSUPC) is formulated, where each user aims selfishly at maximizing his utility-based performance under the imposed physical limitations and its unique Nash equilibrium point is determined. Then the inefficiency of MSUPC game's Nash equilibrium is proven and a usage-based convex pricing policy of the transmission power is introduced, which offers a more effective approach compared to the linear pricing schemes that have been adopted in the literature. Consequently, a Multiservice Uplink Power Control game with Convex Pricing (MSUPC-CP) is formulated and its unique Pareto optimal Nash equilibrium is determined. A distributed iterative algorithm for computing MSUPC-CP game's equilibrium is proposed, while the overall approach's efficiency is illustrated via modeling and simulation.

Bandwidth scheduling and optimization using non-cooperative game model-based shuffled frog leaping algorithm in a networked learning control system

In this paper, under a general framework of Networked two-layer Learning Control Systems (NLCSs), optimal and fair network scheduling is studied. Multi-networked feedback control loops called subsystems in an NLCS share a common communication media. Therefore, there is a competition for the available bandwidth. A non-cooperative game fairness model is first formulated, and then the utility function of subsystems is designed. This takes into account of a number of factors, namely transmission data rate, sampling, the feature of scheduling pattern adopted, and networked control. For the problem defined above, the existence and uniqueness of Nash equilibrium point are proved. Following this, an evolutionary algorithm appeared in the literature recently, shuffled frog leaping algorithm, is improved applying to obtain an optimal solution. The algorithm has a high convergence rate, and the comparison simulation results have demonstrated the effectiveness of the proposed theoretical approach and the algorithm applied.