Nash Equilibrium Conditions Research Articles

Defensive resource allocation in terrorism conflict management based on graph model with relative preferences

In real-world counterterrorism activities, it is usually difficult for the defender and the attacker to accurately know the private information of the each other such as valuations of targets. Instead, players may only know the relative preference on the target valuations from the adversary. In the conflict analysis, graph model is a powerful tool for dealing with relative preferences. This paper studies the defensive resource allocation in terrorism conflict management with incomplete information by establishing a graph model. To solve the model, we divide the conflict states into two types and discuss the conditions under which these two types of states are at equilibrium. Furthermore, we study how the defender should optimally allocate the resource to achieve two goals: (i) achieving a certain Nash equilibrium state desired by the defender; and (ii) minimizing the total loss from an attack in equilibrium. Subsequently, we conduct several numerical analyses: (i) analyzing the effects of both players' investment effectiveness on the optimal defense loss; (ii) comparing our model's results with those obtained using three classical decision methods, revealing that the defense loss in our model is lower; and (iii) presenting a case study to illustrate the applicability of the proposed model. This paper provides novel insights on how to efficiently allocate defensive resource when the defender and attacker know only the relative preference of the adversary on target valuations.

Tullock contest with reference‐dependent preferences

AbstractWe study the Tullock contest model with loss aversion and endogenously formed reference points. In a contest with n possibly heterogeneous players and convex effort costs, we establish sufficient conditions for a unique Nash equilibrium in pure strategies. Subsequently, we analyze the impact of loss aversion on players' spending behavior, probability of winning, and rent dissipation.

AgriGAN: unpaired image dehazing via a cycle-consistent generative adversarial network for the agricultural plant phenotype

Artificially extracted agricultural phenotype information exhibits high subjectivity and low accuracy, while the utilization of image extraction information is susceptible to interference from haze. Furthermore, the effectiveness of the agricultural image dehazing method used for extracting such information is limited due to unclear texture details and color representation in the images. To address these limitations, we propose AgriGAN (unpaired image dehazing via a cycle-consistent generative adversarial network) for enhancing the dehazing performance in agricultural plant phenotyping. The algorithm incorporates an atmospheric scattering model to improve the discriminator model and employs a whole-detail consistent discrimination approach to enhance discriminator efficiency, thereby accelerating convergence towards Nash equilibrium state within the adversarial network. Finally, by training with network adversarial loss + cycle consistent loss, clear images are obtained after dehazing process. Experimental evaluations and comparative analysis were conducted to assess this algorithm's performance, demonstrating improved accuracy in dehazing agricultural images while preserving detailed texture information and mitigating color deviation issues.

An Adaptive Dual-Mode Task-Oriented Resource Management Strategy for GEO Relay Systems

With the fierce global competition on satellite networks, the building of satellite constellations grows explosively. Sharply increasing on-orbit data will face the challenge of satellite-ground data transmission. GEO satellites become the top choice for satellite data relay due to their stable satellite-ground link. Most existing spectrum resource management for GEO relays is equipment-oriented and benefit priority, which may lead to a waste of spectrum resources. In this paper, we propose a real-time task-oriented resource allocation strategy for GEO relay systems. We model the spectrum allocation problem as a distributed non-cooperative Stackelberg game process. We prove that when both sides of the game pursue the maximization of personal revenue, the system will enter a Nash equilibrium state, whereas spectrum resources are not fully used. Based on the maximization of individual utilities (U-prior) and spectrum utilization (S-prior) methods, we design an adaptive dual-mode pricing mode to maximize the spectrum resources within a certain loss of revenue. The simulation results show that the S-prior and U-prior have better performance than the baseline method and existing optimization methods. Our proposed dual-mode strategy is making more throughputs and has less delay with little loss of utility values than that of individual utility maximization.

Learning Stationary Nash Equilibrium Policies in \(n\)-Player Stochastic Games with Independent Chains

Learning Stationary Nash Equilibrium Policies in \(n\)-Player Stochastic Games with Independent Chains

Approaching the Global Nash Equilibrium of Non-convex Multi-player Games.

Many machine learning problems can be formulated as non-convex multi-player games. Due to non-convexity, it is challenging to obtain the existence condition of the global Nash equilibrium (NE) and design theoretically guaranteed algorithms. This paper studies a class of non-convex multi-player games, where players' payoff functions consist of canonical functions and quadratic operators. We leverage conjugate properties to transform the complementary problem into a variational inequality (VI) problem using a continuous pseudo-gradient mapping. We prove the existence condition of the global NE as the solution to the VI problem satisfies a duality relation. We then design an ordinary differential equationto approach the global NE with an exponential convergence rate. For practical implementation, we derive a discretized algorithm and apply it to two scenarios: multi-player games with generalized monotonicity and multi-player potential games. In the two settings, step sizes are required to be O(1/k) and O(1/√k) to yield the convergence rates of O(1/ k) and O(1/√k), respectively. Extensive experiments on robust neural network training and sensor network localization validate our theory. Our code is available at https://github.com/GuanpuChen/Global-NE.

Generalized Hyperbolic Discounting in Security Games of Timing

In recent years, several high-profile incidents have spurred research into games of timing. A framework emanating from the FlipIt model features two covert agents competing to control a single contested resource. In its basic form, the resource exists forever while generating value at a constant rate. As this research area evolves, attempts to introduce more economically realistic models have led to the application of various forms of economic discounting to the contested resource. This paper investigates the application of a two-parameter economic discounting method, called generalized hyperbolic discounting, and characterizes the game’s Nash equilibrium conditions. We prove that for agents discounting such that accumulated value generated by the resource diverges, equilibrium conditions are identical to those of non-discounting agents. The methodology presented in this paper generalizes the findings of several other studies and may be of independent interest when applying economic discounting to other models.

Asymmetries in banking conduct: A Cournot - Bertrand model

This paper presents a Cournot – Bertrand model with differentiated loans and deposits. In this context, banks compete in different strategic variables, with bank 1 competing in quantities and bank 2 in interest rates. It is shown that loan and deposit differentiation are necessary conditions for a unique Nash equilibrium. The analysis constitutes a simple framework for the introduction of asymmetries in the behavior of oligopolistic banks, providing possible policy and bank ownership extensions.

Rent dissipation and streamlined costs: Laboratory experiments

The effect of group size and effort cost on rent dissipation in the standard Tullock rent seeking model is examined using a laboratory experiment. Data support qualitative comparative static Nash equilibrium predictions as reductions in both group size and effort cost increase effort levels. However, effort and dissipation rates are above Nash predictions for all treatments. In addition, while cutting per-unit effort costs in half increases individual effort levels, they do not fully double as predicted and therefore lower rent dissipation, creating a policy-relevant “streamlining effect”. A quantal response equilibrium, which adds stochastic elements into the game structure, predicts the observed higher effort levels and dissipation but is proven to be unable to explain the streamlining effect. A modification of quantal response that incorporates implementation error noise and loss aversion outperforms other estimated models and tracks the observed all data patterns more closely, including the streamlining effect.

A data-driven game theoretic multi-objective hybrid algorithm for the Dial-A-Ride Problem with multiple time windows

The Dial-A-Ride Problem (DARP) designs pick-up and delivery routes for a set of customers. It arises in door-to-door transport services tailored to elderly and impaired people. It minimizes operational costs while accommodating as many drivers’ and customers’ constraints as possible; e.g., constraints on transit time and time windows on pick up and drop off.This paper develops a two-layer and a three-layer artificial neural network (ANN) to predict DARP parameters. The ANN is trained with real data provided by a transit agency from the Canadian city/region of Vancouver. Experimental results show that a three-layer ANN with rectified linear activation functions in conjunction with a stochastic gradient descent optimizer provides the most accurate output forecasts.Utilizing the predictions as parameter estimates for a deterministic mean DARP with multiple time windows (DARPMTW), this paper models the problem as a Company-Drivers-Customers’ theoretic game that minimizes the total route duration and maximizes the minimal satisfaction of the drivers and the customers. It shows that non-dominated Pareto feasible solutions satisfy the Nash equilibrium conditions of the game-theoretic model. It then creates a multi-objective hybrid adaptive large neighborhood search (DD-HALNS) to estimate the Pareto front. The multi-objective DD-HALNS algorithm confines its search to feasible solutions that satisfy the Nash equilibrium conditions and employs local search operators based on their success rates. The operators are controlled by a learning mechanism that utilizes previous successful moves, cost savings, and utility maximization. Four hybridization operators are applied, namely Simulated Annealing, Tabu Lists, Genetic Crossover, and Restarts. The results of experiments conducted on real-world DARPMTW instances demonstrate the ability of the multi-objective DD-HALNS to enhance the best-known routing solutions, as well as its implementability.

Learning to Mitigate Epidemic Risks: A Dynamic Population Game Approach

We present a dynamic population game model to capture the behavior of a large population of individuals in presence of an infectious disease or epidemic. Individuals can be in one of five possible infection states at any given time: susceptible, asymptomatic, symptomatic, recovered and unknowingly recovered, and choose whether to opt for vaccination, testing or social activity with a certain degree. We define the evolution of the proportion of agents in each epidemic state, and the notion of best response for agents that maximize long-run discounted expected reward as a function of the current state and policy. We further show the existence of a stationary Nash equilibrium and explore the transient evolution of the disease states and individual behavior under a class of evolutionary learning dynamics. Our results provide compelling insights into how individuals evaluate the trade-off among vaccination, testing and social activity under different parameter regimes, and the impact of different intervention strategies (such as restrictions on social activity) on vaccination and infection prevalence.

2D brain MRI image synthesis based on lightweight denoising diffusion probabilistic model

In recent years, brain health has received increasing attention, but conventional acquisition of brain MRI (magnetic resonance imaging) images still suffer from issues such as missing data, artifacts, and high costs, which hinders research and diagnosis. With the application of deep learning in medical image synthesis, low-cost, efficient, and high-quality medical MRI synthesis techniques have become a prominent research focus and have gradually matured. However, traditional methods for synthesizing magnetic resonance imaging (MRI) mostly rely on generative adversarial networks, which require fine-tuning of parameters and learning rates to achieve stringent Nash equilibrium conditions, leading to problems such as gradient explosions and mode collapse. Building upon the latest research in synthetic models DDPM (denoising diffusion probabilistic model), we propose a novel approach for 2D brain MRI image synthesis based on a lightweight denoising diffusion probabilistic model. This method improves the attention module in the denoising diffusion probabilistic model to make it more lightweight. Additionally, we adopt the smooth L1 loss function as a replacement for the traditional mean absolute error (L1 loss) by comparing the error between the 2D brain MRI images with added noise and the real noise for training the model. Finally, we validate the proposed model on the MRI Brain Tumor Classification dataset, demonstrating that it achieves high-quality synthesis results while significantly reducing the parameter count of the DDPM model.

A Self-Contained Karma Economy for the Dynamic Allocation of Common Resources

This paper presents karma mechanisms, a novel approach to the repeated allocation of a scarce resource among competing agents over an infinite time. Examples include deciding which ride hailing trip requests to serve during peak demand, granting the right of way in intersections or lane mergers, or admitting internet content to a regulated fast channel. We study a simplified yet insightful formulation of these problems where at every instant two agents from a large population get randomly matched to compete over the resource. The intuitive interpretation of a karma mechanism is “If I give in now, I will be rewarded in the future.” Agents compete in an auction-like setting where they bid units of karma, which circulates directly among them and is self-contained in the system. We demonstrate that this allows a society of self-interested agents to achieve high levels of efficiency without resorting to a (possibly problematic) monetary pricing of the resource. We model karma mechanisms as dynamic population games and guarantee the existence of a stationary Nash equilibrium. We then analyze the performance at the stationary Nash equilibrium numerically. For the case of homogeneous agents, we compare different mechanism design choices, showing that it is possible to achieve an efficient and ex-post fair allocation when the agents are future aware. Finally, we test the robustness against agent heterogeneity and propose remedies to some of the observed phenomena via karma redistribution.

Linear-quadratic and norm-bounded differential game combined guidance strategy against active defense aircraft in three-player engagement

A new type of guidance strategy, combining linear quadratic and norm-bounded game theory, is proposed for the scenario of an attacker against active defense aircraft in three-player engagement. The problem involves three players, an attacker, a defender and a target. The differential game theory and the solution of Hamiltonian equation are utilized to obtain the combined guidance strategy for each player with arbitrary-order dynamics. The game process is divided into 4 phases, C1-C4, according to the switching time. The linear quadratic differential game guidance scheme is employed to reduce the fuel cost in the game parts of C1 and C3. The norm-bounded game guidance strategy is adopted to satisfy the constraint of control input in the game stages C2 and C4. Furthermore, zero-effort miss distance is introduced to meet the constraints of game space and defender’s killing radius in the guidance strategy, which guarantees that the attacker is able to avoid the interception of the defender and hit the target with lower fuel cost and maximum acceleration. And it is proved that the proposed guidance strategy satisfies the Nash equilibrium condition. Finally, the feasibility and superiority of combined guidance strategy are respectively illustrated by nonlinear numerical simulation and verified by comparing with linear quadratic and norm-bounded differential game guidance strategies.

Developing an integrated land allocation model based on linear programming and game theory.

Land use configuration in any given landscape is the result of a multi-objective optimization process, which takes into account different ecological, economic, and social factors. In this process, coordinating stakeholders is a key factor to successful spatial land use optimization. Stakeholders need to be modeled as players who have the ability to interact with each other towards their best solution, while considering multiple goals and constraints at the same time. Game theory provides a tool for land use planners to model and analyze such interactions. In order to apply the spatial allocation model and address stakeholder conflicts, an integrated model based on linear programming and game theory was designed in this study. For implementing such model, we conducted an optimal land use allocation process through multi-objective land allocation (MOLA) and linear programming methods. Then, two groups of environmental and land development players were considered to implement the optimization model. The game algorithm was used to select the appropriate constraint so that the result would be acceptable to all stakeholders. The results showed that during the third round of the game, the decision-making process and the optimization of land uses reached the desired Nash Equilibrium state and the conflict between stakeholders was resolved. Ultimately, in order to localize the results, a suitable solution was presented in a GIS environment.

Evolutionary dynamics of hyperbolic language.

Models of evolution of simple languages have typically assumed full alignment of the speaker and listeners interests, with perfect understanding representing the optimal outcome for both parties. In more realistic settings, communicating individuals will often desire different outcomes from one another. Previous work has shown that misalignment of speaker-listener interests reduces the maximum informativeness among Nash-equilibrium languages, and that multiple equilibrium languages (with different degrees of informativeness) are supported. We study the stochastic evolutionary dynamics of signaling games in which the alignment of speaker-listener interests can vary. We find that increased misalignment of speaker-listener interests is associated with a decrease in information transmission. Moreover, the most common languages to evolve are typically the most informative languages supportable as static Nash equilibria, suggesting a solution to the 'equilibrium selection problem'. In addition, our dynamics reveal the mechanism by which less informative languages evolve: words that previously signaled intense states come to be used hyperbolically for less intense states, with listeners' interpretation of these newly-ambiguous words evolving downward in response. We ground our results in linguistic data on intensifiers such as so and very, words which have unique dynamics-with constant recycling and innovation that match our theoretical results well.

Online Distributed Seeking for First-Order Nash Equilibria of Nonconvex Noncooperative Games With Multiple Clusters

In this brief, we study the problem of online distributed seeking for first-order Nash equilibria of nonconvex noncooperative games with multiple clusters. In this game, each cluster is composed of multiple players, whose goals are to cooperatively minimize the sum of time-varying cost functions in their own cluster. Each player can only have access to its own cost function and action set, and can only communicate with its immediate neighbors in the same cluster through a time-varying graph. Moreover, cost functions cannot be known by players in advance. Unlike existing studies on noncooperative games, the cost function we consider is nonconvex. To address this challenge, an online distributed dual averaging algorithm is proposed. Interestingly enough, the performance of the algorithm is measured by regrets involving the first-order Nash equilibrium condition, and the sublinearity of the regrets is achieved under the proposed algorithm. The validity of the results is illustrated by a numerical example.

Research on Queue Equilibrium Control Algorithm of Urban Traffic Based on Game Theory

The intersection traffic signal control is an essential means of urban traffic. To solve the problem of urban congestion, it is necessary to consider the optimal signal control strategy for intersections. Using the store-and-forward method of traffic control modeling, the in-queue vehicle number of the key signal phase as the payoff index, this paper designs an optimal intersection signal-timing strategy based on the game theory method. In this strategy, each key phase is regarded as a game player, and each player competes for the release time to maximize their own payoff and minimize the queue. To optimize the intersection efficiency, a game strategy is designed to achieve the Nash equilibrium state, which is the queueing equilibrium of each key phase. Finally, by VISSIM simulation, the total number of stops can be decreased by 5% to 10% compared with the MA-DD-DACC method.

On Approximate and Weak Correlated Equilibria in Constrained Discounted Stochastic Games

In this paper, we consider constrained discounted stochastic games with a countably generated state space and norm continuous transition probability having a density function. We prove existence of approximate stationary equilibria and stationary weak correlated equilibria. Our results imply the existence of stationary Nash equilibrium in ARAT stochastic games.

Convergence of output dynamics in duopoly co-opetition model with incomplete information

This paper explores the role of gradient learning on the convergence of output dynamics in duopoly competition model under incomplete information. For this purpose, we develop two scenarios dynamic co-opetition duopoly models under incomplete information. To this end, the gradient learning is adopted to update the strategy output. We propose dynamic co-opetition duopoly model with homogeneous gradient learning to analyze whether gradient learning enables two firm approach to the Cournot–Nash equilibrium state, when the output dynamics converges to interior stable point meaning the coexistence of two firms. It deduces that gradient learning decreases the profit difference between two firms. Furthermore, we highlight that the dynamics of output converges to the Cournot–Nash equilibrium. We mention dynamic co-opetition duopoly model with heterogeneous gradient learning to explore the survival of the firm that leaves the market, when output dynamics converges to the boundary stable point indicating one firm leaves the market while the other monopolies it. Our conclusion identifies that gradient learning can make the firm that leaves the market enter the market again. Finally, the numerical simulations are presented to verify our results.