We study incentive designs for a class of stochastic Stackelberg games with one leader and a large number of (finite as well as infinite population of) followers. We investigate whether the leader can craft a strategy under a dynamic information structure that induces a desired behavior among the followers. For the finite population setting, under convexity of the leader's cost and other sufficient conditions, we show that there exist symmetric \emph{incentive} strategies for the leader that attain approximately optimal performance from the leader's viewpoint and lead to an approximate symmetric (pure) Nash best response among the followers. Leveraging functional analytic tools, we further show that there exists a symmetric incentive strategy, which is affine in the dynamic part of the leader's information, comprising partial information on the actions taken by the followers. Driving the follower population to infinity, we arrive at the interesting result that in this infinite-population regime the leader cannot design a smooth ``finite-energy'' incentive strategy, namely, a mean-field limit for such games is not well-defined. As a way around this, we introduce a class of stochastic Stackelberg games with a leader, a major follower, and a finite or infinite population of minor followers. For this class of problems, we establish the existence of an incentive strategy and the corresponding mean-field Stackelberg game. Examples of quadratic Gaussian games are provided to illustrate both positive and negative results. In addition, as a byproduct of our analysis, we establish the existence of a randomized incentive strategy for the class mean-field Stackelberg games, which in turn provides an approximation for an incentive strategy of the corresponding finite population Stackelberg game.
Performance of a delay-tolerant network has strong dependence on the nodes participating in data transportation. Such networks often face several resource constraints especially related to energy. Energy is consumed not only in data transmission, but also in listening and in several signaling activities. On one hand these activities enhance the system's performance while on the other hand, they consume a significant amount of energy even when they do not involve actual node transmission. Accordingly, in order to use energy efficiently, one may have to limit not only the amount of transmissions, but also the amount of nodes that are active at each time. Therefore, we study two coupled problems: 1) the activation problem that determines when a mobile will turn on in order to receive packets; and 2) the problem of regulating the beaconing. We derive optimal energy management strategies by formulating the problem as an optimal control one, which we then explicitly solve. We also validate our findings through extensive simulations that are based on contact traces.
We develop the first model-free policy gradient (PG) algorithm for the minimax state estimation of discrete-time linear dynamical systems, where adversarial disturbances could corrupt both dynamics and measurements. Specifically, the proposed algorithm learns a minimax-optimal solution for three fundamental tasks in robust (minimax) estimation, namely terminal state filtering, terminal state prediction, and smoothing, in a unified fashion. We further establish convergence and finite sample complexity guarantees for the proposed PG algorithm. Additionally, we propose a model-free algorithm to evaluate the attenuation (robustness) level of any estimator or smoother, which serves as a model-free solution to identify the maximum size of the disturbance under which the estimator will still be robust. We demonstrate the effectiveness of the proposed algorithms through extensive numerical experiments.
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We study control of congestion in general topology communication networks within a fairly general mathematical framework that utilizes noncooperative game theory. We consider a broad class of cost functions, composed of pricing and utility functions, which capture various pricing schemes along with varying behavior and preferences for individual users. We prove the existence and uniqueness of a Nash equilibrium under mild convexity assumptions on the cost function, and show that the Nash equilibrium is the optimal solution of a particular "system problem". Furthermore, we prove the global stability of a simple gradient algorithm and its convergence to the equilibrium point. Thus, we obtain a distributed, market-based, end-to-end framework that addresses congestion control, pricing and resource allocation problems for a large class of of communication networks. As a byproduct, we obtain a congestion control scheme for combinatorially stable ad hoc networks by specializing the cost function to a specific form. Finally, we present simulation studies that explore the effect of the cost function parameters on the equilibrium point and the robustness of the gradient algorithm to variations in time delay and to link failures.
In this paper, we address the issue of malicious intrusion in the communication network present in a team of autonomous vehicles. In our current scenario, we consider the special case of two teams with each team consisting of two mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they try to split their available power between the tasks of communication and jamming the nodes of the other team. Contrary to our earlier work, this paper addresses the scenario in which each player has an omni-directional antenna for jamming the communication between the members of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team. We model the problem as a zero-sum differential game between the two teams and use Isaacs' approach to obtain the necessary conditions for the optimal trajectories. We model the adaptive modulation problem as a zero-sum matrix game which in turn gives rise to a continuous kernel game to handle power control. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy saddle-point equilibrium (PSSPE). This leads to a switching behavior in the optimal communication strategy within a team, over the time horizon of the entire game. This behavior is illustrated in our simulations for the case when the agents are holonomic.
We study in this paper fluid approximations for a class of monotone relay policies in delay tolerant ad-hoc networks. This class includes the epidemic routing and the two-hops routing protocols. We enhance the relay policies with a probabilistic forwarding feature where a message is forwarded to a r
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