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This paper investigates the nonsmooth noncooperative games (NGs) over unbalanced digraphs, where each player has a nondifferentiable payoff function. Meanwhile, these players are subject to local nonsmooth inequality constraints, local convex set constraints and coupled equality constraints. Due to the coexistence of nonsmooth payoff functions, unbalanced digraphs and constraints, existing generalized Nash equilibrium (GNE) seeking strategies are fail to address our problem. Based on subgradient descents, differential inclusions, projection and primal-dual methods, we develop a distributed seeking strategy. Besides, the convergence of the strategy is proved. Finally, the proposed method is applied to electricity market games (EMGs) of smart grids. [ABSTRACT FROM AUTHOR]

This paper proposes an incentive-based cooperative payoff design method to accommodate faults in weakly acyclic games, where the payoff functions of normal players are designed such that all players' optimal payoffs are recovered into an admissible level. Besides, the stochastically stable Nash equilibrium (SSNE) is regarded as the optimal state to avoid some inefficient Nash equilibria. Firstly, without cooperation among players, the effect of faults on SSNE and the optimal payoff is analyzed deeply. Further, the conditions of fault accommodation are discussed under the proposed cooperative fault tolerance method, based on which an algorithm is designed to calculate the feasible incentive. Secondly, with cooperation among players, the effect of faults is analyzed again in special weakly acyclic games, namely potential games, and the simpler conditions of fault accommodation are provided. Finally, two examples of frequency assignment in distributed systems and power management in sensor networks illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper studies the verification of multi-potential games with a given partition, and proposes a kind of multi-potential equation based on semi-tensor product of matrices. Firstly, the basis of each player's potential function is constructed, based on which, a new formula is established for the calculation of each player's potential function. Secondly, a new potential equation is proposed for the verification of potential games via each player's potential function. Using the new potential equation, a kind of multi-potential equation is constructed for the verification of multi-potential games with a given partition. It is proved that a finite game is a multi-potential game with a given partition if and only if the multi-potential equation has solution. In addition, all possible potential functions are obtained for each group of the partition. An illustrative example is worked out to show the effectiveness of the obtained new results. [ABSTRACT FROM AUTHOR]

Networked evolutionary games (NEGs) are a class of models that capture the interactions and evolution of strategies among rational agents in a network. In this paper, we study the problem of minimum cost control of NEGs with switched topologies and threshold, where the network structure can change over time and the agents have a minimum payoff requirement to survive. Using the semi-tensor product (STP) of matrices, we express the weighted networked evolutionary game in an algebraic form. Then, we propose an efficient algorithm to design the minimum cost control that ensures the survival of the agents. Finally, we demonstrate the validity of our theoretical results with an example and simulations. [ABSTRACT FROM AUTHOR]

An off-policy model-free reinforcement learning (RL) algorithm is proposed for a robust hierarchical game while considering incomplete information and input constraints. The robust hierarchical game exhibits characteristics of a Stackelberg–Nash (SN) game, where equilibrium points are designated as Stackelberg–Nash–Saddle equilibrium (SNE) points. An off-policy method is employed for the RL algorithm, addressing input constraints by using excitation input instead of real-time update polices as control inputs. Moreover, a model-free method is implemented for the off-policy RL algorithm, accounting for the challenge posed by incomplete information. The goal of this paper is to develop an off-policy model-free RL algorithm to obtain approximate SNE polices of the robust hierarchical game with incomplete information and input constraints. Furthermore, the convergence and effectiveness of the off-policy model-free RL algorithm are guaranteed by proving the equivalence of Bellman equation between nominal SNE policies and approximate SNE policies. Finally, a simulation is provided to verify the advantage of the developed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study Berge equilibria in linear-quadratic mean-field-type game problems under a jump-diffusion-regime switching state dynamics that incorporate mean-field terms in both the states and cost functional. In the cost functional, we consider conditional variance of the states and control actions, conditional mean of states and control actions, and conditional covariance terms. The underlying Berge problem is solved in a semi-explicit way by using the direct method and an illustrative numerical example is presented. [ABSTRACT FROM AUTHOR]

This paper addresses a pursuit-evasion problem between two identical Differential Drive Robots (DDRs). The pursuer wants to capture the evader in minimal time, while the evader wants to delay capture as much as possible. The game takes place in a Euclidean plane without obstacles. In this work, the motion primitives and time-optimal motion strategies for both players are presented. Based on the initial positions of the players, it is possible to solve the decision problem of determining the winner of the game. Simulations of the pursuit-evasion game showing the time-optimal motion primitives of the players are provided for both cases, when the pursuer wins and when the evader escapes. [ABSTRACT FROM AUTHOR]