Dynamic sequential decision problems with asymmetric information: Some existence results

The first part of the thesis studies three problems pertinent to games with asymmetric information. In the first problem, a refinement concept for Nash equilibrium is presented, called common information based Markov perfect equilibrium (CIMPE), for a class of two-player dynamic linear-Gaussian (LG) games of asymmetric information satisfying two general conditions. A two-step solution approach is adopted to prove the results and devise the algorithm. In the first step, a two-player virtual game of symmetric and perfect information is constructed. It is shown that every Nash equilibrium of the original LQG game can be mapped to a Nash equilibrium of the virtual game and vice-versa. Thereafter, in the second step, a Markov perfect equilibrium of the virtual game is used to construct a Nash equilibrium of the original LQG game. The algorithm to compute a Markov perfect equilibrium of the virtual game is used to devise an algorithm to compute a CIMPE for the original game.;The second problem pertains to a finite-horizon dynamic incentive design problem, in which the decision makers have asymmetric information at every stage of the game. A central agency designs incentives dynamically, so that decision makers behave in a desired manner at every stage of the game. The goal of the central agency is to optimize its own utility function, which may depend on the utility functions of all the decision makers. We introduce a new equilibrium concept for dynamic incentive design games, which we call common information based incentive scheme. We show that under certain assumptions, the central agency is able to design a common information based incentive scheme which forces decision makers to behave according to the desired strategies at all time steps.;In the third problem, the refinement concept (CIMPE) is extended to a multi-player dynamic game in which decision makers have resource constraints across time. A similar two-step approach is used as in the first problem to show the existence of a Nash equilibrium under certain assumptions on the game. A key step in the proof is to show that the amount of resource used by decision makers up to a time step into the game forms a set of states of the game, which is then augmented with other states of the game to compute a Nash equilibrium.;The second part of the thesis resolves three issues pertaining to teams with asymmetric information. The first problem of this second part, and also the fourth problem of the thesis, considers a static team of asymmetric information, in which the decision makers do not share their observations with each other. Such an information pattern is referred to as the no-observation sharing information structure. Under certain assumptions on the observation channels of the decision makers, existence of a team-optimal solution is established.;In the fifth problem of the thesis, dynamic teams with no-observation sharing information structures are considered. The proof techniques developed for static teams are used sequentially in a specific manner to prove the existence of optimal solutions in a large class of dynamic teams with no-observation sharing information structures. Consequently, a large class of dynamic linear-quadratic-Gaussian (LQG) teams with no-observation sharing information structures and cost functions with a specific structure is proven to admit optimal solutions.;In the sixth and final problem of the thesis, the results for teams with no-observation sharing information structure are used to establish the existence of team-optimal solutions in a class of teams with observation sharing information structures. Consequently, several teams, with or without observation sharing information structures, are shown to admit optimal solutions, for which proofs of existence did not exist previously. Furthermore, optimal encoding-decoding policies are shown to exist in a large class of multivariate Gaussian channels, where existence of optimal policies were known only for a few cases and under stringent assumptions, and the proof relied on certain information-theoretic techniques. (Abstract shortened by UMI.).