Search Results (8)

Many engineering problems must account for the non-cooperative decisions and actions of multiple players. These problems can be modeled within a game-theoretic framework. The approach herein is to model such problems as mathematical games, convert them to semi-infinite programs, and utilize a semi-infinite program solver whose output is provably an $ϵ$-optimal Nash equilibrium. The approach is successfully benchmarked on two low-dimensional problems. Two types of higher-dimensional linear quadratic dynamic games are then investigated: ones where each player’s problem is convex and ones where at least one player’s problem is nonconvex. Within each type, variations based on information structure, control constraints, number of players, and semi-infinite objective are considered. The algorithm is tested with different internal solvers, and it successfully solves all test problems using MATLAB’s fmincon. The numerical solutions approximate analytical solutions (when they are known) within approximately one percent. For a three-player game with input saturation constraints, hundreds of variables, and no analytical solution, the computational time is approximately five minutes. Full article

Behavioral authentication (BA) systems verify user identity claims based on unique behavioral characteristics using machine learning (ML)-based classifiers trained on user behavioral profiles. Although effective, ML-based BA systems face serious privacy threats, including profile inference and reconstruction attacks. This paper presents RUIP-BA (Renewable, Unlinkable, and Irreversible Privacy-Preserving Behavioral Authentication), a non-cryptographic framework designed for settings where computational resources may be limited. Random Projection (RP) maps behavioral profiles into lower-dimensional protected templates while approximately preserving utility-relevant geometry, and local Differential Privacy (DP) injects calibrated stochastic perturbations to provide formal privacy protection. The proposed design jointly targets the ISO/IEC 24745 requirements of renewability, unlinkability, and irreversibility. We provide complete algorithmic realizations for enrollment, verification, template renewal, unlinkability testing, and GAN-based adversarial privacy evaluation. We also introduce rigorous formal privacy derivations and proofs under explicit assumptions, including formal security games, information-theoretic theorem-level guarantees, Cramér–Rao lower bounds for irreversibility, full Jensen–Shannon divergence derivations for unlinkability, and a GAN Nash-equilibrium attack bound. Comprehensive dimensionality ablation across all three modalities confirms robust utility at compact template sizes, and an expanded analysis of the privacy–utility trade-off under varying $ϵ$ values is provided. Experiments on voice, swipe, and drawing datasets show authentication accuracy above $96\%$ while sharply limiting feature recoverability under strong GAN-based attacks. All reported FAR/FRR figures are single-session best-case estimates; cross-session longitudinal evaluation remains future work. RUIP-BA provides a scalable, mathematically grounded, and deployment-ready privacy-preserving BA solution. Full article

This paper investigates Mean Field Game methods to solve missile interception strategies in three-dimensional space, with a focus on analyzing the pursuit–evasion problem in many-to-many scenarios. By extending traditional missile interception models, an efficient solution is proposed to avoid dimensional explosion and communication burdens, particularly for large-scale, multi-missile systems. The paper presents a system of stochastic differential equations with control constraints, describing the motion dynamics between the missile (pursuer) and the target (evader), and defines the associated cost function, considering proximity group distributions with other missiles and targets. Next, Hamilton–Jacobi–Bellman equations for the pursuers and evaders are derived, and the uniqueness of the distributional solution is proved. Furthermore, using the $ϵ$-Nash equilibrium framework, it is demonstrated that, under the MFG model, participants can deviate from the optimal strategy within a certain tolerance, while still minimizing the cost. Finally, the paper summarizes the derivation process of the optimal strategy and proves that, under reasonable assumptions, the system can achieve a uniquely stable equilibrium, ensuring the stability of the strategies and distributions of both the pursuers and evaders. The research provides a scalable solution to high-risk, multi-agent control problems, with significant practical applications, particularly in fields such as missile defense systems. Full article

In this paper, we focus on developing self-organizing algorithms aimed at solving, in a distributed way, the coverage problem in Wireless Sensor Networks (WSNs). For this purpose, we apply a game-theoretical framework based on an application of a variant of the Spatial Prisoner’s Dilemma game. The framework is used to build a multi-agent system, where agent-players in the process of iterated games tend to achieve a Nash equilibrium, providing them the possible maximal values of payoffs. A reached equilibrium corresponds to a global solution for the coverage problem represented by the following two objectives: coverage and the corresponding number of sensors that need to be turned on. A multi-agent system using the game-theoretic framework assumes the creation of a graph model of WSNs and the further interpretation of nodes of the WSN graph as agents participating in iterated games. We use the following two types of reinforcement learning machines as agents: Learning Automata (LA) and Cellular Automata (CA). The main novelty of the paper is the development of a specialized reinforcement learning machine based on the application of ($ϵ,h$)-learning automata. As the second model of an agent, we use the adaptive CA that we recently proposed. While both agent models operate in discrete time, they differ in the way they store and use available information. LA-based agents store in their memories the current information obtained in the last h-time steps and only use this information to make a decision in the next time step. CA-based agents only retain information from the last time step. To make a decision in the next time step, they participate in local evolutionary competitions that determine their subsequent actions. We show that agent-players reaching the Nash equilibria corresponds to the system achieving a global optimization criterion related to the coverage problem, in a fully distributed way, without the agents’ knowledge of the global optimization criterion and without any central coordinator. We perform an extensive experimental study of both models and show that the proposed learning automata-based model significantly outperforms the cellular automata-based model. Full article

This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each player has knowledge of the reward realizations of different subsets of the resources. If both players choose the same resource, the reward is divided equally between them, whereas if they choose different resources, each player gains the full reward of the resource. We first implement the iterative best response algorithm to find an $ϵ$-approximate Nash equilibrium for this game. This method of finding a Nash equilibrium may not be desirable when players do not trust each other and place no assumptions on the incentives of the opponent. To handle this case, we solve the problem of maximizing the worst-case expected utility of the first player. The solution leads to counter-intuitive insights in certain special cases. To solve the general version of the problem, we develop an efficient algorithmic solution that combines online convex optimization and the drift-plus penalty technique. Full article

In this paper, we study the properties of Germeier’s scalarization applied for solving multicriteria games. The equilibria and the equilibrium values of such games, as a rule, make sets, and the problems of parametrizing and approximating these sets arise. Shapley proved that Nash equilibrium of multicriteria matrix game can be found by solving a two-parametric family of scalar games obtained with the help of linear scalarization of the criteria vector. We show that Germeier’s scalarization parametrizes the equilibria of the multicriteria game by using one-parametric family of scalar games. Germeier’s scalarization has certain advantages over the linear one, and we suggest it for approximating the multicriteria game equilibria with a finite set. For two-criteria games with $2\times 2$ matrices, we show by examples that there is no continuity of the values of scalar games in the scalarizing parameters. We prove one-sided (from the left or from the right) continuity for the game values. As a result, we come to convergence in Hausdorff metric for the set of equilibrium values obtained for $ϵ$-net on the simplex of scalarizing parameters to the value of the multicriteria game as $ϵ\to 0$. The constructed finite approximation may be helpful in practical applications, where players try to find a compromise in an iterative negotiating procedure under multiple criteria. Full article

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an $ϵ$-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem. Full article

The problem of distributed power allocation in wireless sensor network (WSN) localization systems is investigated in this paper, using the game theoretic approach. Existing research focuses on the minimization of the localization errors of individual agent nodes over all anchor nodes subject to power budgets. When the service area and the distribution of target nodes are considered, finding the optimal trade-off between localization accuracy and power consumption is a new critical task. To cope with this issue, we propose a power allocation game where each anchor node minimizes the square position error bound (SPEB) of the service area penalized by its individual power. Meanwhile, it is proven that the power allocation game is an exact potential game which has one pure Nash equilibrium (NE) at least. In addition, we also prove the existence of an $ϵ$ -equilibrium point, which is a refinement of NE and the better response dynamic approach can reach the end solution. Analytical and simulation results demonstrate that: (i) when prior distribution information is available, the proposed strategies have better localization accuracy than the uniform strategies; (ii) when prior distribution information is unknown, the performance of the proposed strategies outperforms power management strategies based on the second-order cone program (SOCP) for particular agent nodes after obtaining the estimated distribution of agent nodes. In addition, proposed strategies also provide an instructional trade-off between power consumption and localization accuracy. Full article