Nash Equilibrium Analysis Research Articles

Strategic behavior in TSO-DSO coordinated flexibility markets: A Nash equilibrium and efficiency analysis

This paper investigates the way in which the design of a TSO-DSO coordinated flexibility market can enable strategic behavior by flexibility service providers (FSPs). Multiple flexibility market models are considered for the procurement of flexibility services by transmission and distribution system operators, namely: a common (joint) market, a fragmented market, and a sequential multi-level market. Considering these market models, three non-cooperative games are introduced to investigate the strategic bidding and interaction between FSPs therein. Detailed conclusions are then drawn on the existence and uniqueness of Nash Equilibria (NEs) in the developed games, including derivations of closed-form expressions of the resulting NEs and corresponding price-of-anarchy, capturing the FSPs’ strategic bidding impact on the markets’ efficiency. The analysis considers – first in a duopoly setting, then with multiple players – three different use cases representing when: (1) a sufficient flexible capacity exists (sufficient flexibility offered from the FSPs and adequate interconnection/grid capacity between systems); (2) participants have a scarce flexibility capacity; and (3) a restrictive interface capacity exists between the systems. A case study considering an interconnected transmission–distribution system and multiple FSPs corroborates the analytical findings. The obtained results show that market participants have incentives to set bid prices greater than their marginal costs, thus decreasing the markets’ efficiency. This aspect is shown to be more pronounced when the available flexible capacity is limited, a restrictive line limit is present, or when the market is fragmented, thus supporting the need for additional network investments and the creation of joint flexibility market formats.

Generalized Nash Equilibrium Analysis for Peer-to-Peer Transactive Energy Market Considering Coupling Distribution Network Constraints

Generalized Nash Equilibrium Analysis for Peer-to-Peer Transactive Energy Market Considering Coupling Distribution Network Constraints

Tale of two emergent games: Opinion dynamics in dynamical directed networks.

Unidirectional social interactions are ubiquitous in real social networks whereas undirected interactions are intensively studied. We establish a voter model in a dynamical directed network. We analytically obtain the degree distribution of the evolving network at any given time. Furthermore, we find that the average degree is captured by an emergent game. However, we find that the fate of opinions is captured by another emergent game. Beyond expectation, the two emergent games are typically different due to the unidirectionality of the evolving networks. The Nash equilibrium analysis of the two games facilitates us to give the criterion under which the minority opinion with few disciples initially takes over the population eventually for in-group bias. Our work fosters the understanding of opinion dynamics ranging from methodology to research content.

Using Game Theory to Analyze the Interaction between Teachers and Students in the Teaching of Civics in College Courses

Abstract In this paper, firstly, on the basis of Marx’s theory of intersubjectivity, we use the concept of teachers and students as the main body of each other to construct the interactive teaching mode and mechanism of teachers and students in Civics courses and actively explore the path and prospect of interactive teaching of Civics in courses in the new era. Then we use the pure strategy game in game theory to determine the performance production function, and then we use Nash equilibrium to obtain the teacher utility function and student utility function on the basis of the performance production function so as to further construct the game model of teacher-student behavior in the teaching process of Civics courses, and analyze the teacher-student interaction in the Civics of higher education courses by using the game model. The results show that in the pure strategy game analysis of teacher-student behavior, 0.3872 teachers will choose to reduce teaching inputs, while the other 0.6128 teachers will choose to reduce teaching inputs to “almost no” or “very little”, i.e., the optimal choice strategy is “no” or “very little”, i.e., the optimal choice strategy is “no” or “very little”. The optimal choice strategy is “no reduction in instructional inputs”. In the Nash equilibrium analysis of teacher-student behavior, the equilibrium value of the teacher-student behavior game is (42.22% and 64.59%), and teachers and students need to continuously improve their behavioral strategy choices in order to achieve the maximum utility value of each other. This study improves the quality of teaching and ultimately achieves the objective of Civic Education.

Nash Equilibrium Estimation and Analysis in Joint Peer-to-Peer Electricity and Carbon Emission Auction Market With Microgrid Prosumers

The joint Peer-to-Peer (P2P) electricity market (EM) and carbon emission auction market (CEAM) among prosumer microgrids (MGs) in the distribution network is a promising paradigm to facilitate the participation of distributed energy resources (DERs) and incentivize the decarbonization. In this market, MGs will modify their bidding strategies to be adaptive to other rival MGs' for profit maximization. Such modification will converge to the Nash Equilibrium Point (NEP), where each MG cannot obtain more profits by modifying its strategy subject to the fixed strategy of other rival MGs. In this paper, the NEP under such a joint market paradigm is investigated, in which MGs will trade electricity in the EM and purchase carbon emission quotas (CEQs) in the CEAM. In addition, MGs must adjust their bidding strategies considering penalties due to deviations between day-ahead (DA) scheduling and real-time (RT) procurement caused by uncertainties of net load, as well as the price fluctuation in the CEAM. The NEP is estimated by a novel Multi-agent Deep Deterministic Policy Gradient (MADDPG) algorithm, and the risk mitigation is achieved by incorporating the conditional value-at-risk (CVaR) constraint. The computational performance and effectiveness of risk mitigation of this proposed algorithm, and the obtained NEP in the joint EM and CEAM, are analyzed in the case studies.

Study of Education and Punishment Based on Game Theory

Punishment as a means to regulate students behavior has reached a consensus in Chinese education for thousands of years, but it does not play a sufficient role in guiding the specif-ic problems in todays social practice. Based on the idea of game theory, this paper con-structs a mixed strategy game model in which schools, teachers and students participate at the same time, and through the analysis of the mixed strategy Nash equilibrium of the game model, puts forward methods to reduce students mistakes and improve students moral level. The results show that the probability of teachers implementation of educa-tional discipline is mainly related to the degree of punishment for teachers failure to im-plement educational discipline, the income and cost of paying attention to students moral cultivation; Students wrong behaviors are influenced by the spiritual benefits, costs, pun-ishments, rewards and costs obtained by teachers implementation of educational punish-ments, punishments obtained by teachers non implementation of educational punish-ments, and the benefits and costs of schools emphasis on students moral cultivation; It will be more helpful to improve the efficiency of the standardized training of students by improving the punishment for teachers failure to implement education discipline and stu-dents wrong behavior and reducing the cost of paying attention to students moral training.

"Are we in this together?": embedding social identity detection in drones improves emergency coordination.

Autonomous systems, such as drones, are critical for emergency mitigation, management, and recovery. They provide situational awareness and deliver communication services which effectively guide emergency responders' decision making. This combination of technology and people comprises a socio-technical system. Yet, focusing on the use of drone technology as a solely operational tool, underplays its potential to enhance coordination between the different agents involved in mass emergencies, both human and non-human. This paper proposes a new methodological approach that capitalizes on social identity principles to enable this coordination in an evacuation operation. In the proposed approach, an adaptive drone uses sensor data to infer the group membership of the survivors it encounters during the operation. A corpus of 200 interactions of survivors' talk during real-life emergencies was computationally classified as being indicative of a shared identity or personal/no identity. This classification model, then, informed a game-theoretic model of human-robot interactions. Bayesian Nash Equilibrium analysis determined the predicted behavior for the human agent and the strategy that the drone needs to adopt to help with survivor evacuation. Using linguistic and synthetic data, we show that the identity-adaptive architecture outperformed two non-adaptive architectures in the number of successful evacuations. The identity-adaptive drone can infer which victims are likely to be helped by survivors and where help from emergency teams is needed. This facilitates effective coordination and adaptive performance. This study shows decision-making can be an emergent capacity that arises from the interactions of both human and non-human agents in a socio-technical system.

Social Sourcing: Incorporating Social Networks Into Crowdsourcing Contest Design

In a crowdsourcing contest, a principal holding a task posts it to a crowd. People in the crowd then compete with each other to win the rewards. Although in real life, a crowd is usually networked and people influence each other via social ties, existing crowdsourcing contest theories do not aim to answer how interpersonal relationships influence people's incentives and behaviors and thereby affect the crowdsourcing performance. In this work, we novelly take people's social ties as a key factor in the modeling and designing of agents' incentives in crowdsourcing contests. We establish two contest mechanisms by which the principal can impel the agents to invite their neighbors to contribute to the task. The first mechanism has a symmetric Bayesian Nash equilibrium, and it is very simple for agents to play and easy for the principal to predict the contest performance. The second mechanism has an asymmetric Bayesian Nash equilibrium, and agents' behaviors in equilibrium show a vast diversity which is strongly related to their social relations. The Bayesian Nash equilibrium analysis of these new mechanisms reveals that, besides agents' intrinsic abilities, the social relations among them also play a central role in decision-making. Moreover, we design an effective algorithm to automatically compute the Bayesian Nash equilibrium of the invitation crowdsourcing contest and further adapt it to a large graph dataset. Both theoretical and empirical results show that the new invitation crowdsourcing contests can substantially enlarge the number of participants, whereby the principal can obtain significantly better solutions without a large advertisement expenditure.

Non-cooperative differential game and feedback Nash equilibrium analysis for real-time electricity markets

Continuous liberalization of electricity markets makes a strong correlation between the economic behaviors of market participants and their profits. To guide the production of generators before the market reaches equilibrium, a new framework is proposed to model the real-time electricity market with help of optimal control theory. The market price is described as the dynamic state using a sticky price model. We establish an N-person non-cooperative differential game model, where all participants try to maximize their profits independently only by observing power prices. The existence of feedback Nash equilibrium and uniqueness of optimal price trajectory are proved in detail, which will help other scholars build an effective differential game model. To protect the privacy of all generators, a distributed algorithm is proposed based on neurodynamic and consensus theory, which only requires information exchange among neighboring participants. Furthermore, a special case of a duopoly power market is investigated in detail and we provide a feedback time-continuous solution for each generator. Compared with the commercial Cplex solver, the proposed distributed algorithm performs better in convergence speed.

On the Efficiency of Decentralized Epidemic Management and Application to Covid-19

In this letter, we introduce a game that allows one to assess the potential loss of efficiency induced by a decentralized control or local management of a global epidemic. Each player typically represents a region or a country which is assumed to choose its control action to implement a tradeoff between socio-economic aspects and the health aspect. We conduct the Nash equilibrium analysis of this game. Since the analysis is not trivial in general, sufficient conditions for existence and uniqueness are provided. Then we quantify through numerical results the loss induced by decentralization, measured in terms of price of anarchy (PoA) and price of connectedness (PoC). These results allow one to clearly identify scenarios where decentralization is acceptable or not regarding to the retained global efficiency measures.

Generalized Nash equilibrium analysis of transmission and distribution coordination in coexistence of centralized and local markets

The increasing scale of distributed energy resources connected to distribution networks can not only solve the operational problems in the distribution system, but it can also supply the transmission system with flexibility and ancillary services. Thus, the design of a market framework to suit this situation is required. This paper builds a generalized Nash game model with shared constraints for the joint day-ahead market where the centralized market coexists with the local market. In this model, the transmission system operator clears the centralized market assuming that resources of distribution systems are fixed, the distribution system operator clears the local market assuming that resources of the transmission system are fixed, and the clearing of the two markets are conducted simultaneously. Subsequently, the generalized Nash game model can be reformulated to a variational inequality problem that can be solved by the Goldstein–Levitin–Polyak projection method, and more than one generalized Nash equilibrium solution is obtained by the parametrized variational inequality approach. Finally, case studies on two systems, which consist of a 30-bus transmission system and 33-bus distribution system, and a practical 343-bus transmission system and 110-bus distribution system, respectively, are used to verify the effectiveness of the proposed method.

Matching-game approach for green technology investment strategies in a supply chain under environmental regulations

Facing increasingly severe environmental problems, green technology (GT) innovation has become an effective way to achieve the sustainable development of firms. Many manufacturers often choose and invest in appropriate GTs from GT-suppliers to improve the environmental impact of production. But others abandon GTs because they are too expensive to invest in. This paper thereby studies the dynamic investment strategy of GT in a manufacturer-supplier supply chain and explores the optimal government subsidy incentive and its impact on investment and sustainable production decisions. Firstly, an original two-sided matching game model (including two-sided matching analysis and Nash equilibrium analysis) is presented to study the matching process between a manufacturer with a limited investment budget and a GT-supplier with GTs and to determine the optimal GT investment-production strategy. Then, a government-manufacturer Stackelberg game model integrating differential game is constructed to determine the optimal government subsidy strategy and to investigate the effect of government subsidy on investment-production decisions. The results show that stable matching between the manufacturer and GT-supplier can be obtained. Numerical simulations verify the feasibility and rationality of the proposed matching game mechanism and demonstrate that GT investment profit is higher than non-investment profit, and subsidy profit is better than non-subsidy profit. The increase in the carbon price leads to an increase in the GT investment intensity. The increase in the carbon price can cause an increase in product greenness and green demand. The contributions of this paper are in providing an infrastructure for studying how managers can obtain the optimal GT investment-production strategy in the supply chain, and how the government formulates the optimal subsidy strategy to stimulate managers’ GT innovation behavior.

Stability Analysis of Nash Equilibrium for Two-Agent Loss-Aversion-Based Noncooperative Switched Systems

The stability property of the loss-aversion-based noncooperative switched systems with quadratic payoffs is investigated. In this system, each agent adopts the lower sensitivity parameter in the myopic pseudo-gradient dynamics for the case of losing utility than gaining utility, and both systems' dynamics and switching events (conditions) are depending on agents' payoff functions. Sufficient conditions under which agents' state converges towards the Nash equilibrium are derived in accordance with the location of the Nash equilibrium. In the analysis, the mode transition sequence and interesting phenomena which we call flash switching instants are characterized. Finally, we present several numerical examples to illustrate the properties of our results.

Level-k reasoning in school choice

Boston Mechanism (BM) and Deferred Acceptance (DA) are two competing algorithms in school choice. BM is manipulable whereas DA encourages truth-telling. Recognizing heterogeneous sophistication of students, we use the level-k model to analyze students' strategies under BM in a complete information environment with strict school priorities. Because students tend to manipulate first choice under BM, we characterize the first choice reported by students at all possible sophistication levels. In a general framework we show that BM is no less efficient than DA, and in two specific belief settings we further show that it is as if students run DA in their minds when they make level-k reasoning under BM. We compare the relation between sophistication and welfare under BM in the two belief settings to emphasize the role of high sophistication and correct belief. We also compare our results with Nash equilibrium analysis.

The Purity of Impure Public Goods

In this paper we demonstrate how the impure public good model can be converted into a pure public good model with satiation of private consumption, which can be handled more easily, by using a variation of the aggregative game approach as devised by Cornes and Hartley (2007). We point out the conditions for impure public good utility functions that allow for this conversion through which the analysis of Nash equilibria can be conducted in a unified way for the impure and the pure public good model and which facilitates comparative statics analysis for impure public goods. Our approach also offers new insights on the determinants for becoming a contributor to the public good in the impure case as well as on the non-neutral effects of income transfers on Nash equilibria when the public good is impure.

Real-Time Pricing Scheme in Smart Grid Considering Time Preference: Game Theoretic Approach

Unbalanced power demand across time slots causes overload in a specific time zone. Various studies have proved that this can be mitigated through smart grid and price policy, but research on time preference is insufficient. This study proposed a real-time pricing model on a smart grid through a two-stage Stackelberg game model based on a utility function that reflects the user’s time preference. In the first step, the suppliers determine the profit-maximizing price, and then, the users decide the electricity usage schedule according to the given price. Nash equilibrium and comparative analysis of the proposed game explain the relationship between time preference, price, and usage. Additionally, a Monte Carlo simulation demonstrated the effect of the change in time preference distribution. The experimental results confirmed that the proposed real-time pricing method lowers peak-to-average ratio (PAR) and increases overall social welfare. This study is meaningful in that it presents a pricing method that considers both users’ and suppliers’ strategies with time preference. It is expected that the proposed method would contribute to a reduction in the need for additional power generation facilities through efficient operation of the smart grid.

Conditional cooperator enhances institutional punishment in public goods game

The role of incentive institutions on promoting cooperation in public goods game (PGG) has attracted much attention. Theoretical studies based on Nash equilibrium analysis predict that the punishment effect is often stronger than the reward effect. Although this result is confirmed by empirical studies, subjects do not always play these rational strategies. Recent experiments indicate that most subjects in PGGs are conditional cooperators who tend to contribute the group average. In this paper, we consider PGGs with three types of subjects, namely, cooperators, defectors, and conditional cooperators. Evolutionary game method is applied to investigate how conditional cooperators affect the effectiveness of different types of incentives. Overall, having conditional cooperators cannot lead to a higher contribution level in the standard PGG or the PGG with institutional rewards. However, they can enhance the effectiveness of institutional punishment, where a high contribution level can be maintained even for small punishments. As a consequence, in PGGs with conditional cooperators, punishment always leads to a higher contribution rate than do rewards. Numerical analysis indicates that this result is robust to errors in decision making.

Competitive Data Trading Model With Privacy Valuation for Multiple Stakeholders in IoT Data Markets

With the widespread of Internet-of-Things (IoT) environment, a big data concept has emerged to handle a large number of data generated by IoT devices. Moreover, since data-driven approaches now become important for business, IoT data markets have emerged, and IoT big data are exploited by major stakeholders, such as data brokers and data service providers. Since many services and applications utilize data analytic methods with collected data from IoT devices, the conflict issues between privacy and data exploitation are raised, and the markets are mainly categorized as privacy protection markets and privacy valuation markets, respectively. Since these kinds of data value chains (which are mainly considered by business stakeholders) are revealed, data providers are interested in proper incentives in exchange for their privacy (i.e., privacy valuation) under their agreement. Therefore, this article proposes a competitive data trading model that consists of data providers who weigh the value between privacy protection and valuation as well as other business stakeholders. Each data broker considers the willingness-to-sell of data providers, and a single data service provider considers the willingness-to-pay of service consumers. At the same time, multiple data brokers compete to sell their data set to the data service provider as a noncooperative game model. Based on the Nash equilibrium analysis (NE) of the game, the feasibility is shown that the proposed model has the unique NE that maximizes the profits of business stakeholders while satisfying all market participants.

Multiagent Task Allocation in Complementary Teams: A Hunter-and-Gatherer Approach

Consider a dynamic task allocation problem, where tasks are unknowingly distributed over an environment. This paper considers each task comprising two sequential subtasks: detection and completion, where each subtask can only be carried out by a certain type of agent. We address this problem using a novel nature-inspired approach called “hunter and gatherer.” The proposed method employs two complementary teams of agents: one agile in detecting (hunters) and another skillful in completing (gatherers) the tasks. To minimize the collective cost of task accomplishments in a distributed manner, a game-theoretic solution is introduced to couple agents from complementary teams. We utilize market-based negotiation models to develop incentive-based decision-making algorithms relying on innovative notions of “certainty and uncertainty profit margins.” The simulation results demonstrate that employing two complementary teams of hunters and gatherers can effectually improve the number of tasks completed by agents compared to conventional methods, while the collective cost of accomplishments is minimized. In addition, the stability and efficacy of the proposed solutions are studied using Nash equilibrium analysis and statistical analysis, respectively. It is also numerically shown that the proposed solutions function fairly; that is, for each type of agent, the overall workload is distributed equally.

Adaptive Strategic Cyber Defense for Advanced Persistent Threats in Critical Infrastructure Networks

Advanced Persistent Threats (APTs) have created new security challenges for critical infrastructures due to their stealthy, dynamic, and adaptive natures. In this work, we aim to lay a game-theoretic foundation by establishing a multi-stage Bayesian game framework to capture incomplete information of deceptive APTs and their multistage multi-phase movement. The analysis of the perfect Bayesian Nash equilibrium (PBNE) enables a prediction of attacker's behaviors and a design of defensive strategies that can deter the adversaries and mitigate the security risks. A conjugate-prior method allows online computation of the belief and reduces Bayesian update into an iterative parameter update. The forwardly updated parameters are assimilated into the backward dynamic programming computation to characterize a computationally tractable and timeconsistent equilibrium solution based on the expanded state space. The Tennessee Eastman (TE) process control problem is used as a case study to demonstrate the dynamic game under the information asymmetry and show that APTs tend to be stealthy and deceptive during their transitions in the cyber layer and behave aggressively when reaching the targeted physical plant. The online update of the belief allows the defender to learn the behavior of the attacker and choose strategic defensive actions that can thwart adversarial behaviors and mitigate APTs. Numerical results illustrate the defender's tradeoff between the immediate reward and the future expectation as well as the attacker's goal to reach an advantageous system state while making the defender form a positive belief.