Nash Equilibrium Research Articles

An Imitation Learning Based Algorithm Enabling Priori Knowledge Transfer in Modern Electricity Markets for Bayesian Nash Equilibrium Estimation

An Imitation Learning Based Algorithm Enabling Priori Knowledge Transfer in Modern Electricity Markets for Bayesian Nash Equilibrium Estimation

On adversarial robustness and the use of Wasserstein ascent-descent dynamics to enforce it

Abstract We propose iterative algorithms to solve adversarial training problems in a variety of supervised learning settings of interest. Our algorithms, which can be interpreted as suitable ascent-descent dynamics in Wasserstein spaces, take the form of a system of interacting particles. These interacting particle dynamics are shown to converge toward appropriate mean-field limit equations in certain large number of particles regimes. In turn, we prove that, under certain regularity assumptions, these mean-field equations converge, in the large time limit, toward approximate Nash equilibria of the original adversarial learning problems. We present results for non-convex non-concave settings, as well as for non-convex concave ones. Numerical experiments illustrate our results.

A Nash equilibrium against gun control

This work constructs a non-cooperative, static game of gun control between the citizen and a pacifistic society characterised by law enforcement imperfection, by which the retention of firearms and the certitude of punishment against all crimes emerge both as a strict Nash equilibrium, in pure strategies, and as a strict dominant strategy equilibrium. The reason is that ratified by the Second Amendment to the American Constitution, discerning the necessity of a militia to the individual and societal security of a free state, by which the right of the people to keep and bear arms cannot be infringed.

Neural Networks within Generative AI: A Review from a Marketing Research Perspective

Focusing on the role of neural networks within Generative Artificial Intelligence, this paper reviews their operating principles, recent developments, and implications for research in the marketing discipline. Special emphasis is placed on generative networks that produce synthetic data with a high degree of similarity to original data – such as realistic images, textual, or audio content – thereby expanding the potential for applied marketing practices. Besides significant opportunities opened up by Generative Artificial Intelligence, the review also elaborates on challenges, including technical obstacles like achieving an adequate Nash equilibrium between competing network components, and application-related considerations such as finding reliable metrics to evaluate their business performance. Broader implications are also analysed from recent publications, including ethical dilemmas related to data authenticity. As a result, this study provides a distinct perspective within the intersecting fields of marketing and computer science in the discourse surrounding Generative Artificial Intelligence, underscoring the research innovations arising from neural network models.

Order or Collaborate? Manufacturers Utilize 3D-Printed Parts to Sustainably Facilitate Increased Product Variety

3D printing (3DP) has garnered significant attention from industries, prompting traditional manufacturers to adopt 3DP to sustainably facilitate increased product variety. Observing manufacturers’ two adoption strategies, ordering parts and collaboratively printing 3DP parts, in a real-world setting, we utilize a wholesale price contract and a Nash Bargaining contract to describe these two strategies and then develop a supply-chain model including a 3DP supplier (Supplier) and a traditional manufacturer (Manufacturer). Further, we employ backward induction to solve the subgame-perfect Nash equilibrium for the model to reveal differences between these two strategies and the impact of 3DP’s improved resource efficiency. According to equilibrium outcomes, analytical results show that first, as long as the unit cost of each 3DP part is not overly high and 3DP’s resource efficiency is not extremely low, the Manufacturer is willing to implement 3DP to increase product variety. Second, a rise in the resource efficiency can create a “win-win” scenario for the Manufacturer and the Supplier. Third, supply-chain collaboration can be achieved when the Manufacturer’s and the Supplier’s bargaining powers approach equality. Interestingly, a Nash bargaining contract can incentivize the manufacturer to substitute a base product with a variety of products, a change facilitated by an increase in the retail price of this base product. The managerial implication of this research is that enhanced resource efficiency can lead to less environmental pollution in the collaboration model by resulting in the sale of lower quantities of the base product, which would otherwise consume more resources and generate greater environmental pollution.

Relief item inventory planning under centralized and decentralized bilateral cooperation and uncertain transshipment quantities

Pre-positioning relief inventory ensures timely delivery of in-kind aid after a catastrophe. Tragic disasters like major earthquakes are rare and unpredictable; therefore, stockpiled items may not be used. To avoid over-stocking and reduce shortage risk, the cooperation of two humanitarian agencies in supporting each other in case of shortages is suggested in the literature. In this study, we utilize newsvendor-based quantitative models to optimize the pre-disaster stocking decisions of agencies under centralized and decentralized cooperation mechanisms. In the former, both agencies jointly determine their inventory levels to maximize their combined benefits of relief operations, whereas, in the latter, each agency establishes its stocking level in isolation via a game theoretic approach. In both systems, the two agencies agree to transship their excessive items to the other party if needed. In this regard, we investigate the situation where only a portion of the transshipped items, denoted as the reliability factor, can be received and effectively utilized at the destination due to the chaotic nature of the disaster. Considering a deterministic reliability factor, we obtain the singular optimal inventory levels in the centralized system and identify the unique Nash Equilibrium in the decentralized system. Subsequently, we formulate a two-stage stochastic program, considering a random reliability factor for both cooperation systems. The study concludes by offering a range of managerial insights. Our analyses quantify the sub-optimality resulting from decentralized decision-making across diverse parameter settings using the concept of the price of anarchy. The findings highlight that centralized cooperation becomes particularly advisable when the average demand within either agency is high, the transshipment process is secure (i.e., the reliability factor is high), and transshipment costs remain low.

Time-optimal surveillance between two differential drive robots with a limited field of view

Keeping an intelligent agent under surveillance with an autonomous robot as it travels in the environment is one of the essential tasks in robotics. This work addresses a pursuit-evasion surveillance problem between two Differential Drive Robots moving on a plane without obstacles. One of them, the pursuer, is equipped with a limited field-of-view sensor and aims to maintain the other robot (evader) inside its detection region for as much time as possible. On the contrary, the evader wants to escape as soon as possible. Unlike prior studies that address the same problem, based on heuristic approaches, we frame it as a zero-sum differential game, and we use differential game theory to find a solution with theoretical guarantees. In particular, we compute the players' time-optimal motion strategies to achieve their goals near the end of the game and provide analytical expressions describing them. These strategies are in Nash equilibrium, meaning that any unilateral deviation by a player from these strategies does not provide such player benefit toward its goal. Our analysis exhibits the existence of a Transition Surface in which the evader switches its controls. We also determine the game's winner based on the players' initial configurations and velocities.

Distributed generalized Nash equilibrium seeking: event-triggered coding-decoding-based secure communication

Distributed generalized Nash equilibrium seeking: event-triggered coding-decoding-based secure communication

A two-level game theoretic approach for task offloading in mobile edge computing

In the mobile edge computing system subject to wireless interference, the Edge Server Provider (ESP) aims to offer profitable computing resources to Device Managers (DMs), who make optimal strategies based on the provided prices. However, the existence of mixed variables typically constitutes an NP-hard problem, posing a significant challenge for optimization. In response to address this issue, we formulate a bi-level optimization problem, where the upper level is devoted to optimizing the pricing of computing resources. The lower level optimizes DM migration strategies and resource allocation at specified prices. Leveraging game theory, we achieve distributed and efficient computation offloading by formulating the distributed computing offloading strategy among lower-level DMs as a task offloading game. Our analysis identifies Nash equilibrium and finite improvement characteristics within the game. Based on these insights, we present a bi-level distributed computation offloading algorithm capable of reaching Nash equilibrium, thus optimizing the profit for both DMs and ESP. The experiments have demonstrated the algorithm’s effectiveness in reducing system costs and maximizing the profits of ESP with DMs across diverse scenarios.

Edge computing collaborative offloading strategy for space‐air‐ground integrated networks

SummaryDue to geographical factors, it is impossible to build large‐scale communication network infrastructure in remote areas, which leads to poor network communication quality in these areas and a series of delay‐sensitive tasks cannot be timely processed and responded. Aiming at the problem of limited coverage in remote areas, the space‐air‐ground integrated networks (SAGIN) combined with mobile edge computing (MEC) can provide low latency and high reliability transmission for offloading delay‐sensitive tasks for users in remote areas. Considering the strong limitation of satellite resources in the space‐ground integrated network and insufficient energy of local user equipment, firstly, a satellite‐UAV cluster‐ground three‐layer edge computing network architecture is proposed in this paper. Under the condition that the delay requirements of various ground tasks are met, the task offloading problem is transformed into a Stackelberg game between ground user equipment and edge servers. In addition, it is proved that the existence of Nash equilibrium in non‐cooperative game between ground user equipment by using potential game. Finally, a Nash equilibrium iterative offloading algorithm based on Stackelberg game (NEIO‐SG) is proposed to find the optimal offloading strategy for tasks to minimize the system offloading cost and the optimal forwarding percentage strategy for offloading tasks to maximize the utility function of the edge server. Simulation results show that compared to other baseline algorithms, NEIO‐SG reduces the total system latency during task offloading by about 13 and the energy consumption of the edge server by about 35.

Location and Price Competition on a Uniform Path with Different Pricing Policies

AbstractThis paper models duopolistic competition between an online retailer and a physical store retailer with the online retailer modelled as a firm with uniform delivered pricing policy and the physical store as a firm with a mill pricing policy. Both firms seek to maximize their respective profits through an appropriate choice of location and price. The market is assumed to be given by a “uniform path” - a tree whose node weights and arc lengths are equal. Modelling reality, we consider two alternate types of transportation costs faced by the online retailer: either dependent on the relative location of the firm and a customer or independent of it. Beginning with the framework of a Stackelberg, i.e., sequential game, optimal location and price strategies are analytically derived for both sequences of market entry by the two competitors. Cases in which the leader faces the first entry paradox or can become a monopolist by strategically deterring entry by the follower are delineated. Thereafter, Nash Equilibrium solutions to the simultaneous game are identified. Salient insights from the results include: (a) the competitive pressure faced by the physical store in the presence of online competition (b) the inability of an online retailer to compete in “large” markets under the first type of transportation cost and (c) the advantage to the physical retailer of being a market leader.

Bifurcation and Chaos in a Fractional-Order Cournot Duopoly Game Model on Scale-Free Networks

In this study, a Cournot duopoly model describing Caputo fractional-order differential equations with piecewise constant arguments is discussed. We have obtained two-dimensional discrete dynamical system as a result of applying the discretization process to the model. By using the center manifold theory and the bifurcation theory, it is shown that the discrete dynamical system undergoes flip bifurcation about the Nash equilibrium point. Phase portraits, bifurcation diagrams, and Lyapunov exponents show the existence of many complex dynamical behaviors in the model such as the stable equilibrium point, period-2 orbit, period-4 orbit, period-8 orbit, period-16 orbit, and chaos according to changing the speed of the adjustment parameter [Formula: see text]. The discrete Cournot duopoly game model is also considered on two scale-free networks with different numbers of nodes. It is observed that the complex dynamical networks exhibit similar dynamical behaviors such as the stable equilibrium point, flip bifurcation, and chaos depending on changing the coupling strength parameter [Formula: see text]. Moreover, flip bifurcation and transition chaos take place earlier in more heterogeneous networks. Calculating the largest Lyapunov exponents guarantees the transition from nonchaotic to chaotic states in complex dynamical networks.

Non-cooperative games to control learned inverter dynamics of distributed energy resources

We propose a control scheme via a non-cooperative linear quadratic differential game to coordinate the inverter dynamics of Distributed Energy Resources (DERs) in a microgrid (MG). The MG can provide regulation services in support to the upper-level grid, in addition to serving its own load. The control scheme is designed for the MG to track a power reference, while each DER seeks to minimize its individual cost function subject to learned inverter dynamics and load perturbations. We use a nonlinear high-fidelity model developed by Sandia National Laboratories to learn inverter dynamics. We determine a Nash strategy for the DERs that uses state estimation of a Loop Transfer Recovery. Results show that the control scheme enables savings up to 9.3 to 208 times in the DERs objective cost functions and a time-domain response with no oscillations with up to 3 times faster settling times relative to using droop and PI control.

Robust distributed Nash equilibrium solution for multi‐agent differential graphical games

AbstractThis paper studies the differential graphical games for linear multi‐agent systems with modelling uncertainties. A robust optimal control policy that seeks the distributed Nash equilibrium solution and guarantees the leader‐following consensus is designed. The weighting matrices rely on modelling uncertainties, leading to the Nash equilibrium solution, and the solution can be obtained by solving a decoupled algebraic Riccati equation. Simulation studies are finally reported to illustrate the effectiveness of proposed policy.

The Feasibility of Coordinating International Monetary Policy Strategies in the Context of Asymmetric Demand Shocks

In the context of the increasing interdependence of countries due to the development of international trade, a relevant question arises as to whether it is necessary to conduct independent monetary policies for each country or whether it is advisable to coordinate these policies. This question becomes a key in the debate on optimal monetary policy strategies in open economies. The aim of this study is to analyze the impact of asymmetric aggregate demand shocks on the appropriateness of monetary policy coordination in a simple stochastic model of two interacting countries. The analysis of equilibrium states of the monetary authorities’ interaction strategies under study was carried out analytically by minimizing the loss function and solving one-period static optimization problems. The equilibrium states of macroeconomics of interacting countries under coordination of monetary policy and in cases of lack of coordination (Nash and Stackelberg equilibrium) in the presence of asymmetric, serially uncorrelated demand shocks have been analyzed. It is proven that the response of inflation to asymmetric demand shocks is smaller in the case of coordinated policy than in the case of non-cooperative policy. The loss function analysis shows that the compensation of demand shocks is found to be more costly in Nash equilibrium than in the case of monetary authority coordination policy. The analysis of the monetary authorities’ interaction strategies showed that the real exchange rate plays an important role in balancing supply and demand in the two economies.

Distributed model predictive control of fan coil system

To address the issues of large overshoot, long system stabilization time, and slow response associated with traditional PID-based and centralized model predictive control (MPC) of fan coil systems, this study proposes a distributed model predictive control (DMPC) method suitable for multi-zone building temperature regulation. Specifically, based on the thermal dynamic model of different zones, and aiming to constrain indoor temperature within set limits and minimize water system pressure drop and fan coil speed, a distributed MPC architecture for fan coil systems is developed. To solve the distributed optimization problem, the Nash equilibrium is introduced to find the global balance point within the distributed structure, and the Beetle Antennae Search-Particle Swarm Optimization (BAS-PSO) hybrid algorithm is used for online optimization of local MPCs. Experimental results show that compared to traditional PID control, the distributed MPC achieves coordinated multi-zone indoor temperature regulation with better dynamic performance, with the average absolute temperature error in each zone below 5 % and an energy savings rate of 16.23 %. Through semi-physical simulation, it is demonstrated that the proposed distributed MPC method has better applicability when the number of fan coils exceeds 10, compared to centralized MPC.

Nash equilibria in greenhouse gas offset credit markets

One approach to reducing greenhouse gas (GHG) emissions is to incentivise carbon capturing and carbon reducing projects while simultaneously penalising excess GHG output. In this work, we present a novel market framework and characterise the optimal behaviour of GHG offset credit (OC) market participants in both single-player and two-player settings. The single player setting is posed as an optimal stopping and control problem, while the two-player setting is posed as optimal stopping and mixed-Nash equilibria problem. We demonstrate the importance of acting optimally using numerical solutions and Monte Carlo simulations and explore the differences between the homogeneous and heterogeneous players. In both settings, we find that market participants benefit from optimal OC trading and OC generation.

Optimal decision-making and coordination of the shipping logistics service supply chain cooperation mode under the carbon quota and trading mechanism

Carbon cap-and-trade policy based on market mechanism becomes an important means to restrain shipping logistics enterprises' carbon emission reduction. This paper studies the new requirements of shipping enterprises under the pressure of carbon emission reduction. Considering the logistics service supply chain composed of two competing providers and one integrator under the constraint of carbon cap-and-trade policy, this paper explores the optimal pricing and revenue decision of shipping logistics service supply chain through vertical cooperation, horizontal cooperation between providers and revenue sharing cooperation among integrators. This paper obtains feedback strategies under different cooperation modes by constructing a game model. In the vertical game, the shipping logistics supplier is the Stackelberg leader, and the shipping logistics integrator is the follower; there is a Nash equilibrium in the emission reduction decisions among suppliers in the horizontal game. On this basis, the results of different cooperation modes are compared, and the influence of competitive strategies on the optimal results is discussed. We found that the vertical cooperation of the shipping logistics service supply chain has a higher carbon emission reduction rate and a lower sales price, and the horizontal cooperation of shipping logistics suppliers can improve their own profits but reduce the income of the shipping logistics integrators and consumer welfare. When the revenue sharing contract provides the shipping logistics integrator with a share proportion in a certain range, the revenue sharing contract can generate higher supply chain profits than the integration of two chains, which can urge shipping logistics suppliers to forfeit the horizontal cooperation and help the shipping logistics service supply chain achieve win-win results.

The Partial Solution of First Price Sealed Bid Auction in the Scope of Mechanism Design Theory and With Uniformly Distributed Types

In the article the first price sealed bid auction has been analysed within the scope of mechanism design theory and with uniformly distributed types. The sealed bid auction consisting of two of agents has been observed finding the partial solution to the auction. Bayesian Nash equilibrium strategies, the equilibrium state, and the implemented social choice function for the auction have been evaluated. The mechanism has been designed to truthfully implement the social choice function for the auction consisting of two agents. The variables such as the probability of an agent to win, the expected utility of an agent and the expected revenue of the seller have been evaluated.

A game-theoretic approach to mitigate charging anxiety for electric vehicle users through multi-parameter dynamic pricing and real-time traffic flow

While price-based demand response is universally recognized as crucial for managing electric vehicle charging load, the academic literature has explored diverse mechanisms for its implementation. Prior research has revealed that applying load management schemes based on price-based demand response programs results in higher scheduling costs for low or constant-energy consumers. In addition, the inherent uncertainties involved in arrival, service requirements, market pricing and user behaviours have posed serious challenges in managing real-time charging operations. To handle these challenges, this work has addressed the charging problem at the scheduling level by analysing arrival, waiting, service and departure requests. This work proposed a mathematical model to coordinate charging to minimize the total charging cost and time for a given number of vehicles. We have developed an advanced charging algorithm and introduced a multi-leader multi-follower Stackelberg game. This strategic model ensures a Nash equilibrium, aligning the interests of consumers (vehicles) and providers (charging stations), ensuring a fair and balanced charging system. Where, charging load demand, real-time pricing, charging location, and vehicle types are used as input parameters. In the first stage, the real-time pricing obtained from the Spanish Electricity network is used to schedule the charging load, whereas the second stage is dedicated to using the proposed multi-parameter pricing for customer satisfaction and reduced cost. The results demonstrate the superior performance of our proposed scheme compared to existing approaches. Finally, we present a real-life case study to illustrate the practical effectiveness of the proposed techniques. The study underscores the potential of our approach in real-world scenarios, offering a promising avenue for enhancing efficiency and user experience in charging systems.