This brief designs a distributed stochastic annealing algorithm for nonconvex cooperative aggregative games, whose players’ cost functions not only depend on players’ own decision variables but also rely on the sum of players’ decision variables. To seek the social optimum of cooperative aggregative games, a distributed stochastic annealing algorithm is proposed, where the local cost functions are nonconvex and the communication topology between players is time-varying. The weak convergence to the social optimum of the algorithm is further analyzed. A numerical example is finally given to illustrate the effectiveness of the proposed algorithm.

The moving target defense (MTD) is a defense paradigm in repeated security games within the realm of cybersecurity. The defender's strong Stackelberg equilibrium (SSE) strategy is optimal for deployment as an MTD strategy, assuming that the attacker adopts a best-response strategy after observing the defender's actions. However, computing SSE strategies in repeated games is complex due to the non-convexity of players' expected utilities, especially when dealing with multiple targets in large-scale problems. Thus, we propose to use the zero-determinant (ZD) strategy as an MTD strategy to reduce computational complexity. To this end, we identify the conditions for the existence of the ZD strategy. Also, we provide a novel approach to construct the required ZD strategy.

Sensor network localization (SNL) is a challenging problem due to its inherent non-convexity and the effects of noise in inter-node ranging measurements and anchor node position. We formulate a non-convex SNL problem as a multiplayer non-convex potential game and investigate the existence and uniqueness of a Nash equilibrium (NE) in both the ideal setting without measurement noise and the practical setting with measurement noise. We first show that the NE exists and is unique in the noiseless case, and corresponds to the precise network localization. Then, we study the SNL for the case with errors affecting the anchor node position and the inter-node distance measurements. Specifically, we establish that in case these errors are sufficiently small, the NE exists and is unique. It is shown that the NE is an approximate solution to the SNL problem, and that the position errors can be quantified accordingly. Based on these findings, we apply the results to case studies involving only inter-node distance measurement errors and only anchor position information inaccuracies.

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 equation to 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/root k) to yield the convergence rates of O(1/k) and O(1/root 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.

We investigate the equilibrium stability and robustness in a class of moving target defense problems, in which players have both incomplete information and asymmetric cognition. We first establish a Bayesian Stackelberg game model for incomplete information and then employ a hypergame reformulation to address asymmetric cognition. With the core concept of the hyper Bayesian Nash equilibrium (HBNE), a condition for achieving both the strategic and cognitive stability in equilibria can be realized by solving linear equations. Moreover, to deal with players' underlying perturbed knowledge, we study the equilibrium robustness by presenting a condition of robust HBNE under the given configuration. Experiments evaluate our theoretical results.

There has been significant recent interest in a class of three-player leader-follower game models in many important cybersecurity scenarios. In such a tri-level hierarchical structure, a defender usually serves as a leader, dominating the decision process by the Stackelberg equilibrium (SE) strategy. However, such a leader-follower scheme may not always work, and the Nash equilibrium (NE) strategy may provide an alternative choice. Thus, we need to reveal the consistency between SE and NE in the three-player model to help the leader evaluate its strategy impact and avoid a choice dilemma. To this end, we first provide a necessary and sufficient condition such that each SE is an NE, which not only provides access to seek a satisfactory SE but also makes a criterion for an obtained SE. Then, we apply the results for case studies with a unique SE or with at least one SE being an NE. Moreover, when the consistency condition falls short, we give an upper bound of the deviation between SE and NE to help the leader tolerably adopt an SE strategy. Finally, we apply our consistency analysis to practical scenarios, including secure wireless transmission and advanced persistent threat defense.

We study the computation of the global generalized Nash equilibrium (GNE) for a class of non-convex multi-player games, where players' actions are subject to both local and coupling constraints. Due to the non-convex payoff functions, we employ canonical duality to reformulate the setting as a complementary problem. Under given conditions, we reveal the relation between the stationary point and the global GNE. According to the convex-concave properties within the complementary function, we propose a continuous-time mirror descent to compute GNE by generating functions in the Bregman divergence and the damping-based design. Then, we devise several Lyapunov functions to prove that the trajectory along the dynamics is bounded and convergent.

In this paper, we propose a game theory framework to solve advanced persistent threat problems, especially considering two types of insider threats: malicious and inadvertent. Within this framework, we establish a unified three-player game model and derive Nash equilibria in response to different types of insider threats. By analyzing these Nash equilibria, we provide quantitative solutions to advanced persistent threat problems pertaining to insider threats. Furthermore, we have conducted a comparative assessment of the optimal defense strategy and corresponding defender’s costs between two types of insider threats. Interestingly, our findings advocate a more proactive defense strategy against inadvertent insider threats in contrast to malicious ones, despite the latter imposing a higher burden on the defender. Our theoretical results are substantiated by numerical results, which additionally include a detailed exploration of the conditions under which different insiders adopt risky strategies. These conditions can serve as guiding indicators for the defender when calibrating their monitoring intensities and devising defensive strategies.

In this article, we consider a continuous-type Bayesian Nash equilibrium (BNE) seeking problem in subnetwork zero-sum games, which is a generalization of either deterministic subnetwork zero-sum games or discrete-type Bayesian zero-sum games. In this model, because the feasible strategy set is composed of infinite-dimensional functions and is not compact, it is hard to seek a BNE in a noncompact set and convey such complex strategies in network communication. To this end, we give a two-step design. One is a discretization step, where we discretize continuous types and prove that the BNE of the discretized model is an approximate BNE of the continuous model with an explicit error bound. The other is a communication step, where we adopt a novel compression scheme with a designed sparsification rule and prove that agents can obtain unbiased estimations through the compressed communication. Based on the two steps, we propose a distributed communication-efficient algorithm to practically seek an approximate BNE, and further provide the convergence analysis and explicit error bounds.

We consider solving distributed constrained optimization in this article. To avoid projection operations due to constraints in the scenario with large-scale variable dimensions, we propose distributed projection-free dynamics by employing the Frank-Wolfe method, also known as the conditional gradient. Technically, we find a feasible descent direction by solving an alternative linear suboptimization. To make the approach available over multiagent networks with weight-balanced digraphs, we design dynamics to simultaneously achieve both the consensus of local decision variables and the global gradient tracking of auxiliary variables. Then, we present the rigorous convergence analysis of the continuous-time dynamical systems. Also, we derive its discrete-time scheme with an accordingly proved convergence rate of O(1/k). Furthermore, to clarify the advantage of our proposed distributed projection-free dynamics, we make detailed discussions and comparisons with both existing distributed projection-based dynamics and other distributed Frank-Wolfe algorithms.