Strategy Nash Equilibrium Research Articles

A Novel Particle Swarm Optimization Approach to Support Decision-Making in the Multi-Round of an Auction by Game Theory

In this paper, game-theoretic optimization by particle swarm optimization (PSO) is used to determine the Nash equilibrium value, in order to resolve the confusion in choosing appropriate bidders in multi-round procurement. To this end, we introduce an approach that proposes (i) a game-theoretic model of the multi-round procurement problem; (ii) a Nash equilibrium strategy corresponding to the multi-round strategy bid; and (iii) an application of PSO for the determination of the global Nash equilibrium point. The balance point in Nash equilibrium can help to maintain a sustainable structure, not only in terms of project management but also in terms of future cooperation. As an alternative to procuring entities subjectively, a methodology using Nash equilibrium to support decision-making is developed to create a balance point that benefits procurement in which buyers and suppliers need multiple rounds of bidding. To solve complex optimization problems like this, PSO has been found to be one of the most effective meta-heuristic algorithms. These results propose a sustainable optimization procedure for the question of how to choose bidders and ensure a win-win relationship for all participants involved in the multi-round procurement process.

Nash equilibrium strategies and survival portfolio rules in evolutionary models of asset markets

We consider a stochastic model of a financial market with one-period assets and endogenous asset prices. The model was initially developed and analyzed in the context of Evolutionary Finance with the main focus on questions of “survival and extinction” of investment strategies (portfolio rules). In this paper we view the model from a different, game-theoretic, perspective and analyze Nash equilibrium properties of survival portfolio rules.

Sion's minimax theorem and Nash equilibrium of symmetric three-players zero-sum game

About a symmetric three-players zero-sum game we will show the following results. 1. A modified version of Sion's minimax theorem with the coincidence of the maximin strategy and the minimax strategy are proved by the existence of a symmetric Nash equilibrium. 2. The existence of a symmetric Nash equilibrium is proved by the modified version of Sion's minimax theorem with the coincidence of the maximin strategy and the minimax strategy. Thus, they are equivalent. If a zero-sum game is asymmetric, maximin strategies and minimax strategies of players do not correspond to Nash equilibrium strategies. If it is symmetric, the maximin strategies and the minimax strategies constitute a Nash equilibrium. However, without the coincidence of the maximin strategy and the minimax strategy there may exist an asymmetric equilibrium in a symmetric three-players zero-sum game.

Coordination on Networks with Farsighted and Myopic Agents

We study a coordination game on a fixed connected network where players have to choose between two projects. Some players are moderate (i.e. they are ex-ante indifferent between both project) while others are stubborn (i.e. They always choose the same project). Benefits for moderaote players are increasing in the number of neighbors who choose the same project. In addition, players are either farsighted or myopic. Farsighted players anticipate the reactions of others while myopic players do not. We show that, when all players are farsighted, full coordination among the moderate players is reached except if there are stubborn players for both projects. When the population is mixed, the set of stable strategy profiles is a refinement of the set of Nash equilibrium strategy profiles. In fact, turning myopic players into farsighted ones eliminates little by little in the inefficient Nash equilibria. Finally, we consider a social planner who can improve coordination by means of two policy instruments: Adding links to the network (socialization) and/or turning myopic players into farsighted ones (education).

Game Theoretical Defense Mechanism Against Reputation Based Sybil Attacks

Reputation mechanisms of a network or p2p applications can be compromised by a large number of fake or stolen identities recommending higher trust values of a malicious node. A high trust value classify such malicious or selfish nodes as legitimate nodes and help them to gain more access to network resource. It is detrimental to network security and makes a network vulnerable to Sybil attacks. In this paper, a game theoretical defense strategy based on zero sum and imperfect information game is proposed to discourage sybil attacks which exploit underlying reputation mechanism of a network. An attacker tries to maintain an optimum level of trusts of its sybil identities in the network in an intention to launch a successful sybil attack and obtain an attack benefit. Simultaneously, the attacker has to incur some cost to maintain trustworthiness of its identities. A rational attacker analyses associated costs and benefits prior to launch an attack. The proposed mechanism uses this idea and makes the attack costly by setting a global trust threshold for nodes or identities to remain trustworthy and active in network. In this work, utility functions of attacker and defender are defined. Nash Equilibrium strategies of the game are discussed and experiments are carried out which suggest the effectiveness of proposed mechanism to enhance network security against sybil attacks.

Optimizing Bidders Selection of Multi-Round Procurement Problem in Software Project Management Using Parallel Max-Min Ant System Algorithm

This paper presents a Game-theoretic optimization via Parallel MinMax Ant System (PMMAS) algorithm is used in practice to determine the Nash equilibrium value to resolve the confusion in choosing appropriate bidders of multi-round procurement problem in software project management. To this end, we introduce an approach that proposes: (i) A Game-theoretic model of multiround procurement problem (ii) A Nash equilibrium strategy corresponds to multi-round strategy bid (iii) An application of PSO for the determination of global Nash equilibrium. The balance point in Nash Equilibrium can help to maintain a sustainable structure not only in terms of project management but also in terms of future cooperation. As an alternative of procuring entities subjectively, a methodology to support decision making has been studied using Nash equilibrium to create a balance point on benefit in procurement where buyers and suppliers need multiple rounds of bidding. Our goal focus on the balance point in Nash Equilibrium to optimizing bidder selection in multi-round procurement which is the most beneficial for both investors and selected tenderers. Our PMMAS algorithm is implemented based on MPI (message passing interface) to find the approximate optimal solution for the question of how to choose bidders and ensure a path for a win-win relationship of all participants in the procurement process. We also evaluate the speedup ratio and parallel efficiency between our algorithm and other proposed algorithms. As the experiment results, the high feasibility and effectiveness of the PMMAS algorithm are verified.

Nash Equilibrium Strategy of Port Construction Considering Seawater Erosion

Lu, Q.; Wang, Z., and Wang, R., 2019. Nash equilibrium strategy of port construction considering seawater erosion. In: Li, L.; Wan, X.; and Huang, X. (eds.), Recent Developments in Practices and Research on Coastal Regions: Transportation, Environment and Economy. Journal of Coastal Research Journal of Coastal Research, Special Issue No. 98, pp. 330–334. Coconut Creek (Florida), ISSN 0749-0208.The main construction approaches to ports are based on government investment and contractor construction. This method faces a particular drawback for the implementation of construction: the contractor fails to carry out the work in strict accordance with the plan. By considering the problems of government supervision and contractors' strict adherence to construction plans, as well as to seawater erosion after port construction, this paper uses Nash equilibrium to solve the optimal mixed strategy for both parties. The main influencing factors of the strategy are analyzed. Then this paper finds that the high probability of erosion can stimulate the government and contractor to do their best, and the sum of gains and losses also influence the best strategy. Based on analysis results, the corresponding suggestions are put forward.

Nonlocal correlations and noise in different settings of a two-player game

Nonlocal correlations in a quantum mechanical system hold an indispensable place in understanding the foundational aspects of theory, and for exploring efficient theoretical and experimental proposals in the regime of quantum computation and information which are otherwise not possible using classical resources. One of the possible ways to understand the nuances of nonlocal correlations is to put it in the framework of game theory. For this purpose, we address the issue of decoherence and protection of nonlocal correlations from local noise from the perspective of a game, considering the two players as noise and weak measurement reversal operations, respectively. In order to effectively understand the moves of players, we study maximum payoff and Nash equilibrium strategies for different noisy channels. Our results compare two different situations where payoffs of players are defined using the Bell inequality and discord, respectively. The analysis shows a contrasting description of payoffs and strategies in two different cases. We believe that the results obtained here will help one to understand the intricacies involved in the process of entanglement distribution through noisy channels, evaluating optimal parameters to obtain maximum payoff in the designed game, and Nash equilibrium strategies of players to win the desired game.

A Game Approach to Distributed Robust Optimal Filtering With Consensus Through Multiple Sensors: Theory and Application

This article addresses the problem of distributed state estimation on the infinite-time horizon for discrete-time systems with multiple sensors. The desired filter, referred to as distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> Gaussian filter, reaching a tradeoff between optimality and robustness, constructs a local estimate based on its own observation and on those collected from its neighbors. A Nash game approach is used to deal with such a multiobjective distributed filtering problem, and causal bounded Nash equilibrium strategies, consisting of the optimal filter gains and the corresponding worst-case disturbance signals, are analytically conducted based on solutions to a set of cross-coupled algebraic Riccati equations. Moreover, to further improve the cohesiveness among local estimates, additional consensus objective is taken into consideration by exchanging prior estimates among neighboring nodes. A choice of the consensus term, with which the error dynamics are shown to be internally stable, is derived via a numerically tractable and efficient method. Finally, an application to speed monitoring through wireless sensor network is included to show the validity of the presented results.

How does the Quantity of Disclosed Information Provided by Insurers Affect Entity Behaviors in Internet Insurance Market?: A Study Based on Tripartite Evolutionary Game Analysis between Government, Insurance Companies and Consumers

The emergence of internet insurance provides a new consumption pattern for insurance consumers in the e-commerce era. However, without insurers fulfilling duty of disclosure, consumers’ interests cannot be guaranteed. This paper will analyze the costs and benefits of three parties (i.e. government, insurance companies and consumers) and their strategies regarding information disclosure of insurance products on the internet. Using an evolutionary game model under bounded rationality assumptions, the Nash Equilibrium (NE) and evolutionary stability strategy (ESS) of the system are explored. The results show that (Disclosing, not Regulating, not Complain) is the best ESS and it is consumers’ buying decision not regulation that ultimately compels insurers to disclose enough information. The different current situations in China and Japan are discussed in light of the model, and some measures are suggested to promote the development of internet insurance markets in both countries.

Stochastic Asymmetric Blotto Game Approach for Wireless Resource Allocation Strategies

The development of modellings and analytical tools to structurise and study the allocation of resources through noble user competitions become essential, especially considering the increased degree of heterogeneity in application and service demands that will be cornerstone in future communication systems. Stochastic asymmetric Blotto games appear promising to modelling such problems, and devising their Nash equilibrium (NE) strategies by anticipating the potential outcomes of user competitions. In this regard, this paper approaches the generic energy efficiency problem with a new stochastic asymmetric Blotto game paradigm to enable the derivation of joint optimal bandwidth and transmit power allocations by setting multiple users to compete in multiple auction-like contests for their individual resource demands. The proposed modelling innovates by abstracting the notion of fairness from centrally-imposed to distributed-competitive, where each user’s pay-off probability is expressed as quantitative bidding metric, so as, all users’ actions can be interdependent, i.e., each user attains its utility given the allocations of other users, which eliminates the chance of low-valued carriers not being claimed by any user, and, in principle, enables the full utilisation of wireless resources. We also contribute by resolving the allocation problem with low complexity using new mathematical techniques based on Charnes-Cooper transformation, which eliminate the additional coefficients and multipliers that typically appear during optimisation analysis, and derive the joint optimal strategy as a set of linear single-variable functions for each user. We prove that our strategy converges towards a unique, monotonous and scalable NE, and examine its optimality, positivity and feasibility properties in detail. Simulation comparisons with relevant studies confirm the superiority of our approach in terms of higher energy efficiency performance, fairness index and quality-of-service provision.

The game mechanism of stakeholders in comprehensive marine environmental governance

In the process of marine resource development and marine environmental protection, the government supervises the production behavior of enterprises; enterprises accept government supervision; and non-profit organizations supervise the process. On this basis, a conceptual model of the relationship between government, enterprises, and non-profit organizations is established, and the internal mechanism governing their interactions is analyzed. Using game theory, a simulation model of government, enterprises, and non-profit organizations is constructed, and a Nash equilibrium solution and strategy selection analysis are carried out. The correlation between the game participants and strategy selection is simulated and analyzed with MATLAB 7 software. Lastly, relevant countermeasures and suggestions are put forward to engender effective supervision by government departments, continuous environmental development and effective environmental protection of enterprises, and effective supervision by non-profit organizations. Studying the regulatory strategies of the government, enterprises, and non-profit organizations can provide a foundation for marine resource development and marine environmental protection policy in accordance with the current situation.

Nash Equilibrium Strategy for Bi-matrix Games with L-R Fuzzy Payoffs

In this paper, bi-matrix games are investigated based on L-R fuzzy variables. Also, based on the fuzzy max order several models in non-symmetrical L-R fuzzy environment is constructed and the existence condition of Nash equilibrium strategies of the fuzzy bi-matrix games is proposed. At last, based on the Nash equilibrium of crisp parametric bi-matrix games, we obtain the Pareto and weak Pareto Nash equilibrium strategies of the fuzzy bi-matrix games.

Research on Radar Waveform Design Strategy under Game Condition

In order to improve missile-borne radar detection performance in modern electronic warfare, a radar waveform design method based on Nash equilibrium is proposed. Firstly, the radar and jammer game signal models are established in electronic warfare. Based on maximum Signal-to-Interference-plus-Noise Ratio (SINR), waveform strategies of radar and jammer are designed respectively. Secondly, the existence of Nash equilibrium solution is demonstrated by mathematical derivation and verified in experimental simulation. A multiple iterative water-filling method which repeatedly eliminates strict disadvantages is designed to achieve Nash equilibrium. The maxmin scheme of disequilibrium game is deduced by two-step water-filling method. Finally, the radar detection performance of optimization strategies is tested by simulation experiments. Simulation results reveal that the radar waveform design based on Nash equilibrium is beneficial to improve the radar detection performance under game conditions. Compared with no-game and maxmin strategies, the radar detection probability of Nash equilibrium strategy can be increased by 12.02% and 3.82%, respectively. It is proved that the Nash equilibrium strategy of this paper is closer to the Pareto optimality.

Stochastic linear quadratic differential games in a state feedback setting with sampled measurements

The problem of sampled-data Nash equilibrium strategy in a state feedback setting for a stochastic linear quadratic differential game is addressed. It is assumed that the admissible strategies are constant on the interval between two measurements. The original problem is converted into an equivalent one for a linear stochastic system with finite jumps. This new formulation of the problem allows us to derive necessary and sufficient conditions for the existence of a sampled-data Nash equilibrium strategy in a state feedback form. These conditions are expressed in terms of solvability of a system of interconnected matrix linear differential equations with finite jumps and subject to some algebraic constraints. We provide explicit formulae of the gain matrices of the Nash equilibrium strategy in the class of piece-wise constant strategies in a state feedback form. The gain matrices of the feedback Nash equilibrium strategy are computed based on the solution of the considered system of matrix linear differential equations with finite jumps. For the implementation of these strategies only measurements at discrete-time instances of the states of the dynamical system are required. Finally, we show that under some additional assumptions regarding the sign of the weights matrices in the performance criteria of the two players, there exists a unique piecewise Nash equilibrium strategy in a state feedback form if the maximal length of the sampling period is sufficiently small.

THE VALUE OF COMMUNICATION AND COOPERATION WHEN SERVERS ARE STRATEGIC

In 2015, Guglielmi and Badia discussed optimal strategies in a particular type of service system with two strategic servers. In their setup, each server can be either active or inactive and an active server can be requested to transmit a sequence of packets. The servers have varying probabilities of successfully transmitting when they are active, and both servers receive a unit reward if the sequence of packets is transmitted successfully. Guglielmi and Badia provided an analysis of optimal strategies in four scenarios: where each server does not know the other’s successful transmission probability; one of the two servers is always inactive; each server knows the other’s successful transmission probability and they are willing to cooperate.Unfortunately, the analysis by Guglielmi and Badia contained some errors. In this paper we correct these errors. We discuss three cases where both servers (I) communicate and cooperate; (II) neither communicate nor cooperate; (III) communicate but do not cooperate. In particular, we obtain the unique Nash equilibrium strategy in Case II through a Bayesian game formulation, and demonstrate that there is a region in the parameter space where there are multiple Nash equilibria in Case III. We also quantify the value of communication or cooperation by comparing the social welfare in the three cases, and propose possible regulations to make the Nash equilibrium strategy the socially optimal strategy for both Cases II and III.

Allocating Marketing Resources Over Social Networks: A Long-Term Analysis

In this letter, we consider a network of consumers who are under the combined influence of their neighbors and external influencing entities (the marketers). The consumers' opinion follows a hybrid dynamics whose opinion jumps are due to the marketing campaigns. By using the relevant static game model proposed in previous works, we prove that although the marketers are in competition and therefore create tension in the network, the network reaches a consensus. Exploiting this key result, we propose a coopetition marketing strategy which combines the one-shot Nash equilibrium actions and a policy of no advertising. Under reasonable sufficient conditions, it is proved that the proposed coopetition strategy profile Pareto-dominates the one-shot Nash equilibrium strategy. This is a very encouraging result to tackle the much more challenging problem of designing Pareto-optimal and equilibrium strategies for the considered dynamical marketing game.

GAME WITH FUZZY PAYOFFS AND CRISP GAME

In this paper we consider a bi-matrix game with fuzzy payoffs. To compare a fuzzy numbers, some different ordering operators can be used. We define Nash equilibrium in fuzzy game using the ordering op erator. The game with crisp payoffs is associated with the original game. Here, crisp payoffs are the operator’s value on a fuzzy payoff. We propose the following statement: if the ordering operator is linear, then the game with payoffs has same Nash equilibrium strategy profile as the crisp game. We present an algorithm for constructing a Nash equilibrium in a bi-matrix game with fuzzy payoffs and we are using this fact. We use such ordering operators, and construct the Nash equilibrium in examples of bi-matrix games. Key Word: Fuzzy set, bi-matrix, membership function, cooperative game

Robust Optimal Filtering Over Lossy Networks

This paper addresses the robust optimal filtering design over unreliable networks, where the data packet dropouts occur during the signal transmission from the sensor side to the filter. The designed filter is expected, under communication data loss, to provide a guaranteed robustness against disturbance/model uncertainty while achieving the minimized variance of the estimation error under Gaussian white noises and the worst case of the disturbance. The Nash game approach is adopted to deal with such a multiobjective filtering problem. Based on the concept of the mean-square stability, Nash equilibrium strategies are analytically applied in terms of two cross-coupled modified algebraic Riccati equations. The presented design method provides a systematic way to achieve a tradeoff of the estimation performance in the $\mathcal {H}_2$ and $\mathcal {H}_\infty$ senses in the presence of data loss.

Non-Cooperative Spectrum Access Strategy Based on Impatient Behavior of Secondary Users in Cognitive Radio Networks

In the cognitive radio network (CRN), secondary users (SUs) compete for limited spectrum resources, so the spectrum access process of SUs can be regarded as a non-cooperative game. With enough artificial intelligence (AI), SUs can adopt certain spectrum access strategies through their learning ability, so as to improve their own benefit. Taking into account the impatience of the SUs with the waiting time to access the spectrum and the fact that the primary users (PUs) have preemptive priority to use the licensed spectrum in the CRN, this paper proposed the repairable queueing model with balking and reneging to investigate the spectrum access. Based on the utility function from an economic perspective, the relationship between the Nash equilibrium and the socially optimal spectrum access strategy of SUs was studied through the analysis of the system model. Then a reasonable spectrum pricing scheme was proposed to maximize the social benefits. Simulation results show that the proposed access mechanism can realize the consistency of Nash equilibrium strategy and social optimal strategy to maximize the benefits of the whole cognitive system.