Signaling equilibria for dynamic LQG games with asymmetric information

We consider a finite horizon dynamic game with two players who observe their types privately and take actions, which are publicly observed. Players' types evolve as independent, controlled linear Gaussian processes and players incur quadratic instantaneous costs. This forms a dynamic linear quadratic Gaussian (LQG) game with asymmetric information. We show that under certain conditions, players' strategies that are linear in their private types, together with Gaussian beliefs form a perfect Bayesian equilibrium (PBE) of the game. Furthermore, it is shown that this is a signaling equilibrium due to the fact that future beliefs on players' types are affected by the equilibrium strategies. We provide a backward-forward algorithm to find the PBE. Each step of the backward algorithm reduces to solving an algebraic matrix equation for every possible realization of the state estimate covariance matrix. The forward algorithm consists of Kalman filter recursions, where state estimate covariance matrices depend on equilibrium strategies

Partially Observed Discrete-Time Risk-Sensitive Mean Field Games

In this paper, we consider discrete-time partially observed mean-field games with the risk-sensitive optimality criterion. We introduce risk-sensitivity behaviour for each agent via an exponential utility function. In the game model, each agent is weakly coupled with the rest of the population through its individual cost and state dynamics via the empirical distribution of states. We establish the mean-field equilibrium in the infinite-population limit using the technique of converting the underlying original partially observed stochastic control problem to a fully observed one on the belief space and the dynamic programming principle. Then, we show that the mean-field equilibrium policy, when adopted by each agent, forms an approximate Nash equilibrium for games with sufficiently many agents. We first consider finite-horizon cost function, and then, discuss extension of the result to infinite-horizon cost in the next-to-last section of the paper.Comment: 29 pages. arXiv admin note: substantial text overlap with arXiv:1705.02036, arXiv:1808.0392

On Design and Analysis of Cyber-Physical Systems with Strategic Agents

In contrast to traditional CPS where a designer can specify an action plan for each agent, in CPS with strategic agents, every agent acts selfishly and chooses his strategy privately so as to maximize his own objective. In this dissertation, we study problems arising in the design and analysis of CPSs with strategic agents. We consider two classes of design problems. In the first class, the designer utilizes her control over decisions and resources in the system to incentivize the agents via monetary incentive mechanisms to reveal their private information that is crucial for the efficient operation of the system. In particular, we consider market mechanism design for the integration of renewable energy and flexible loads into power grids. We consider a model that captures the dynamic and intermittent nature of these resources, and demonstrate the advantage of dynamic market mechanism over static market mechanisms that underly the existing architecture of the electricity markets. In the second class of design problems, the designer utilizes her informational advantage over the agents and employ informational incentive mechanisms to disclose information selectively to the agents so as to influence the agents' decisions. Specifically, we consider the design of public and private information disclosure mechanisms in a transportation system so as to improve the overall congestion. We also study the analysis of CPS with strategic agents as a stochastic dynamic game of asymmetric information. We present a set of conditions sufficient to characterize an information state for each agent that effectively compresses his private and common information over time. This information state provides a sufficient statistic for decision-making purposes in strategic and non-strategic settings. Accordingly, we provide a sequential decomposition of the dynamic game over time, and formulate a dynamic program that enables us to determine a set of equilibria of the game. The proposed approach generalizes and unifies the existing results for dynamic teams with non-classical information structure and dynamic games with asymmetric information.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/140850/1/tavaf_1.pd