Dynamic Decision Problems with Cooperative and Strategic Agents and Asymmetric Information.

There exist many real world situations involving multiple decision makers with asymmetric information, such as communication systems, social networks, economic markets and many others. Through this dissertation, we attempt to enhance the conceptual understanding of such systems and provide analytical tools to characterize the optimum or equilibrium behavior. Specifically, we study four discrete time, decentralized decision problems in stochastic dynamical systems with cooperative and strategic agents. The first problem we consider is a relay channel where nodes' queue lengths, modeled as conditionally independent Markov chains, are nodes' private information, whereas nodes' actions are publicly observed. This results in non-classical information pattern. Energy-delay tradeoff is studied for this channel through stochastic control techniques for cooperative agents. Extending this model for strategic users, in the second problem we study a general model with $N$ strategic players having conditionally independent, Markovian types and publicly observed actions. This results in a dynamic game with asymmetric information. We present a forward/backward sequential decomposition algorithm to find a class of perfect Bayesian equilibria of the game. Using this methodology, in the third problem, we study a general two player dynamic LQG game with asymmetric information, where players' types evolve as independent, controlled linear Gaussian processes and players incur quadratic instantaneous costs. 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. Finally, we consider two sub problems in decentralized Bayesian learning in dynamic games. In the first part, we consider an ergodic version of a sequential buyers game where strategic users sequentially make a decision to buy or not buy a product. In this problem, we design incentives to align players' individual objectives with the team objective. In the second part, we present a framework to study learning dynamics and especially informational cascades for decentralized dynamic games. We first generalize our methodology to find PBE to the case when players do not perfectly observe their types; rather they make independent, noisy observations. Based on this, we characterize informational cascades for a specific learning model.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133294/1/dvasal_1.pd

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

Differential games with asymmetric information and without Isaacs condition

We investigate a two-player zero-sum differential game with asymmetric information on the payoff and without Isaacs condition. The dynamics is an ordinary differential equation parametrised by two controls chosen by the players. Each player has a private information on the payoff of the game, while his opponent knows only the probability distribution on the information of the other player. We show that a suitable definition of random strategies allows to prove the existence of a value in mixed strategies. Moreover, the value function can be characterised in term of the unique viscosity solution in some dual sense of a Hamilton-Jacobi-Isaacs equation. Here we do not suppose the Isaacs condition which is usually assumed in differential games