On Dynamics and Nash Equilibriums of Networked Games

Networked noncooperative games are investigated,where each player(or agent) plays with all other players in its neighborhood. Assume the evolution is based on the fact that each player uses its neighbors current information to decide its next strategy. By using sub-neighborhood, the dynamics of the evolution is obtained. Then a method for calculating Nash equilibriums from mixed strategies of multi-players is proposed.The relationship between local Nash equilibriums based on individual neighborhoods and global Nash equilibriums of overall network is revealed. Then a technique is proposed to construct Nash equilibriums of an evolutionary game from its one step static Nash equilibriums. The basic tool of this approach is the semi-tensor product of matrices, which converts strategies into logical matrices and payoffs into pseudo-Boolean functions, then networked evolutionary games become discrete time dynamic systems.

Resource Allocation for Network Security Risk Assessment：A Non-Cooperative Differential Game Based Approach

In this paper, we propose a non-cooperative differential game theory based resource allocation approach for the network security risk assessment. For the risk assessment, the resource will be used for risk assess, including response cost and response negative cost. The whole assessment process is considered as a differential game for optimal resource control. The proposed scheme can be obtained through the Nash Equilibrium. It is proved that the game theory based algorithm is applicable and the optimal resource level can be achieved based on the proposed algorithm.

MADRL-based UAV swarm non-cooperative game under incomplete information

Unmanned Aerial Vehicles(UAVs)play increasing important role in modern battlefield.In this paper,considering the incomplete observation information of individual UAV in complex combat environment,we put forward an UAV swarm non-cooperative game model based on Multi-Agent Deep Reinforcement Learning(MADRL),where the state space and action space are constructed to adapt the real features of UAV swarm air-to-air combat.The multi-agent particle environment is employed to generate an UAV combat scene with continuous observation space.Some recently popular MADRL methods are compared extensively in the UAV swarm noncooperative game model,the results indicate that the performance of Multi-Agent Soft Actor-Critic(MASAC)is better than that of other MADRL methods by a large margin.UAV swarm employing MASAC can learn more effective policies,and obtain much higher hit rate and win rate.Simulations under different swarm sizes and UAV physical parameters are also performed,which implies that MASAC owns a well generalization effect.Furthermore,the practicability and convergence of MASAC are addressed by investigating the loss value of Q-value networks with respect to individual UAV,the results demonstrate that MASAC is of good practicability and the Nash equilibrium of the UAV swarm non-cooperative game under incomplete information can be reached.

Differential Game Based Link Resource Management for Next Generation Optical Network

In this paper, we investigate the link resource management problem for optical networks, to achieve the resource cost during the information transmission. We use the differential game to formulate the cost control problem for the link resource management, to minimize the resource allocation cost functions, which dynamic behaviours are described by differential equations. Each link controls its transmission bandwidth based on the Nash equilibriums of the differential game. The effectiveness of the proposed model is given through numerical simulations.

Nash equilibrium seeking with prescribed performance

In this work,we study a Nash equilibrium(NE)seeking problem for strongly monotone non-cooperative games with prescribed performance.Unlike general NE seeking algorithms,the proposed prescribed-performance NE seeking laws ensure that the convergence error evolves within a predefined region.Thus,the settling time,convergence rate,and maximum overshoot of the algorithm can be guaranteed.First,we develop a second-order Newton-like algorithm that can guarantee prescribed performance and asymptotically converge to the NE of the game.Then,we develop a first-order gradient-based algorithm.To remove some restrictions on this first-order algorithm,we propose two discontinuous dynamical system-based algorithms using tools from non-smooth analysis and adaptive control.We study the special case in optimization problems.Then,we investigate the robustness of the algorithms.It can be proven that the proposed algorithms can guarantee asymptotic convergence to the Nash equilibrium with prescribed performance in the presence of bounded disturbances.Furthermore,we consider a second-order dynamical system solution.The simulation results verify the effectiveness and efficiency of the algorithms,in terms of their convergence rate and disturbance rejection ability.

No-cooperative games for multiple emergency locations in resource scheduling

When an emergency happens, the scheduling of relief resources to multiple emergency locations is a realistic and intricate problem, especially when the available resources are limited. A non-cooperative games model and an algorithm for scheduling of relief resources are presented. In the model, the players correspond to the multiple emergency locations, strategies correspond to all resources scheduling and the payoff of each emergency location corresponds to the reciprocal of its scheduling cost. Thus, the optimal results are determined by the Nash equilibrium point of this game. Then the iterative algorithm is introduced to seek the Nash equilibrium point. Simulation and analysis are given to demonstrate the feasibility and availability of the model.

Coverage and capacity optimization in LTE network based on non-cooperative games

expenditures and operational expenditures （OPEX） （CAPEX） for operator, the coverage and capacity optimization （CCO） is one of the key use cases in long term evolution （LTE） self-organization network （SON）. In LTE system, some factors （e.g. load, traffic type, user distribution, uplink power setting, inter-cell interference, etc.） limit the coverage and capacity performance. From the view of single cell, it always pursuits maximize performance of coverage and capacity by optimizing the uplink power setting and intra-cell resource allocation, but it may result in decreasing the performance of its neighbor cells. Therefore, the benefit of every cell conflicts each other. In order to tradeoff the benefit of every cell and maximize the performance of the whole network, this paper proposes a multi-cell uplink power allocation scheme based on non-cooperative games. The scheme aims to make the performance of coverage and capacity balanced by the negotiation of the uplink power parameters among multi-cells. So the performance of every cell can reach the Nash equilibrium, making it feasible to reduce the inter-cell interference by setting an appropriate uplink power parameter. Finally, the simulation result shows the proposed algorithm can effectively enhance the performance of coverage and capacity in LTE network.

A game-theory approach against Byzantine attack in cooperative spectrum sensing

In order to solve the Byzantine attack problem in cooperative spectrum sensing,a non-cooperative game-theory approach is proposed to realize an effective Byzantine defense.First,under the framework of the proposed non-cooperative game theory,the pure Byzantine attack strategy and defense strategy in cooperative spectrum sensing are analyzed from the perspective of the Byzantine attacker and network administrator.The cost and benefit of the pure strategy on both sides are defined. Secondly,the mixed attack and defense strategy are also derived. The closed form Nash equilibrium is obtained by the Lemke-Howson algorithm. Furthermore,the impact of the benefit ratio and penalty rate on the dynamic process of the noncooperative game is analyzed. Numerical simulation results show that the proposed game-theory approach can effectively defend against the Byzantine attack and save the defensive cost.

Modeling and game strategy analysis of suppressing IADS for multiple fighters' cooperation

This paper addresses the problem of suppression of the integrated air defense system(IADS) by multiple fighters’ cooperation. Considering the dynamic changing of the number of the nodes in the operational process, a profit model for the influence of the mission’s cost for the whole system is developed for both offense and defensive sides. The scenario analysis is given for the process of suppressing the IADS by multiple fighters. Based on this scenario analysis, the modeling method and the specific expression for the payoff function are proposed in four cases for each node. Moreover, a distributed virtual learning algorithm is designed for the n-person and n-strategy game, and the mixed strategy Nash equilibrium(MSNE) of this game can be solved from the n × m × 3-dimensional profit space. Finally, the simulation examples are provided to demonstrate the effectiveness of the proposed model and the game algorithm.

A Tree Formulation for Signaling Games with Noise

The paper provides an analysis of a sender-receiver sequential signaling game. The private information of the sender is transmitted with noise by a Machine, i.e. does not always correctly reflect the state of nature. Hence, a truthful revelation by the sender of his information does not necessarily imply that the signal he sends is correct. Also, the receiver can take a correct action even if the sender transmits an incorrect signal. The payoffs of the two players depend on their combined actions. Perfect Bayesian Equilibria which can result from different degrees of noise is analysed. The Bayesian updating of probabilities is explained. The fixed point theorem which makes the connection with the idea of rational expectations in economics is calculated. Given a number of equilibria, we comment on the most credible one on the basis of the implied payoffs for both players. The equilibrium signals are an example of the formation of a language convention discussed by D. Lewis.

Game Theory Application and Strategic Bidding in Electricity Supply Market

This paper introduced the application of game theory in electricity power market. Moreover, the electricity pool model and the merit order dispatch method was introduced. In pool mode, participants are trying to maximize their benefit via competition with each other. Hence the market can be regarded as a non-cooperative game, especially, the electrical supply competition. Players (generators) could use strategic bidding to occupy advantages in competition. The bidding strategies of generators in electricity pool model were researched via build a 3-generator competition model. Moreover, Nash Equilibrium idea was used to explore generator’s optimal bidding strategy. The results show when players are in Nash Equilibrium;thestrategy is their optimal bidding strategy.

Multi-cell uplink power allocation game for user minimum performance guarantee in OFDMA systems

The multi-cell uplink power allocation problem for orthogonal frequency division multiplexing access （OFDMA） cellular networks is investigated with the uplink transmission power allocation on each co-frequency subchannel being defined as a multi-cell non-cooperative power allocation game （MNPG）.The principle of the design of the utility function is given and a novel utility function is proposed for MNPG.By using this utility function,the minimum signal to interference plus noise ratio （SINR） requirement of a user can be guaranteed.It can be shown that MNPG will converge to the Nash equilibrium and that this Nash equilibrium is unique.In considering the simulation results,the effect of the algorithm parameters on the system performance is discussed,and the convergence of the MNPG is verified.The performance of MNPG is compared with that of traditional power allocation schemes,the simulation results showing that the proposed algorithm increases the cell-edge user throughput greatly with only a small decrease in cell total throughput; this gives a good tradeoff between the throughput of cell-edge users and the system spectrum efficiency.

A projected gradient based game theoretic approach for multi-user power control in cognitive radio network

The fifth generation （5G） networks have been envisioned to support the explosive growth of data demand caused by the increasing traditional high-rate mobile users and the expected rise of interconnections between human and things. To accommodate the ever-growing data traffic with scarce spectrum resources, cognitive radio （CR） is considered a promising technology to improve spectrum utilization. We study the power control problem for secondary users in an underlay CR network. Unlike most existing studies which simplify the problem by considering only a single primary user or channel, we investigate a more realistic scenario where multiple primary users share multiple channels with secondary users. We formulate the power control problem as a non-cooperative game with coupled constraints, where the Pareto optimality and achievable total throughput can be obtained by a Nash equilibrium （NE） solution. To achieve NE of the game, we first propose a projected gradient based dynamic model whose equilibrium points are equivalent to the NE of the original game, and then derive a centralized algorithm to solve the problem. Simulation results show that the convergence and effectiveness of our proposed solution, emphasizing the proposed algorithm, are competitive. Moreover, we demonstrate the robustness of our proposed solution as the network size increases.

Game-theoretic energy management with storage capacity optimization in smart grids

With the development of smart grids, a renewable energy generation system has been introduced into a smart house. The generation system usually supplies a storage system with the capability to store the produced energy for satisfying a user's future demand. In this paper,the main objective is to determine the best strategies of energy consumption and optimal storage capacities for residential users, which are both closely related to the energy cost of the users. Energy management with storage capacity optimization is studied by considering the cost of renewable energy generation, depreciation cost of storage and bidirectional energy trading. To minimize the cost to residential users, the non-cooperative game-theoretic method is employed to formulate the model that combines energy consumption and storage capacity optimization.The distributed algorithm is presented to understand the Nash equilibrium which can guarantee Pareto optimality in terms of minimizing the energy cost. Simulation results show that the proposed game approach can significantly benefit residential users. Furthermore, it also contributes toreducing the peak-to-average ratio(PAR) of overall energy demand.

Bid Strategies of Primary Users in Double Spectrum Auctions

Extensive research in recent years has shown that dynamic spectrum sharing is a promising ap- proach to＇address the artificial spectrum scarcity problem by improving spectrum utilization. This new communication paradigm, however, requires a well-designed spectrum allocation mechanism. This paper designs a double spectrum auction framework that allows unlicensed secondary users to obtain selected idle spectra assigned to licensed primary users. This is a win-win game because primary users can earn extra revenue and secondary users can obtain spectra they desperately need. The competition among primary users in the auction framework is studied combining game theory with a double spectrum auction in a non-cooperative game with the Nash Equilibrium （NE） as the best solution. Primary users use the prices obtained from the NE as their bid strategies to participate in the auction. In this auction sellers and buyers bid privately and confidentially, which means that the secondary users do not actually know the price and the spectrum size offered by the primary users, then a new net utility function was developed for the primary users with an iterative algorithm to find the Nash equilibrium point. Simulations demonstrate that this design effectively improves spectrum utilization.