Stackelberg strategies in linear-quadratic stochastic differential games

This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution

Difference games and policy evaluation: A conceptual framework

Economics

On Concurrent Solutions in Differential Games

We examine solutions in which neither player is worse off from the leadership of one in a policy maker-public game. The loop model of dynamic games is used. Outcome space is dotted with equivalence classes of solutions. The Dynamic Stochastic General Equilibrium (DSGE) results and their New Keynesian variants might represent one category. The economy is the neighborhood of a market-clearing equilibrium with Pareto-optimal properties modulo frictions. Our interest lies in the ‘old’ Keynesian genus where the representative state is one of involuntary unemployment. Two information sets are relevant. In the first case, agents look to the past and the present. In the second, they are bound by the information provided in the present. The standard analysis pertains to DSGE models under full information. We show, in contrast, that in a situation of structural disequilibrium and feedback information, all parties are better off reneging on the social compact to achieve a superior class of solutions.information structures, time consistency, credibility and reputation

On expectations, information and dynamic game equilibria

Economics