In this article we address the problem of finding feedback Nash equilibria for linear quadratic differential games defined on descriptor systems. First, we decouple the dynamic and algebraic parts of a descriptor system using canonical projectors. We discuss the effects of feedback on the...

Nash (1951) claimed that every game must have a solution, even if it means a mixed strategy. His method is to find a probability that equalizes the two expected payoffs. Though simple, the calculation can be tedious. To avoid unnecessary mistake, this paper works out an algorithm to do the...

We analyze the problem of time-dependent channel coordination in the face of uncertain demand. The channel, composed of a manufacturer and a retailer, is to address a time-varying and uncertain price-dependent demand. The decision variables of the manufacturer are wholesale and (possibly zero)...

Almost every vendor faces uncertain and time-varying demand. Inventory level and price optimization while catering to stochastic demand are conventionally formulated as variants of newsvendor problem. Despite its ubiquity in potential applications, the time-dependent (multi-period) newsvendor...

We develop and implement methods for determining whether introducing new securities or relaxing investment constraints improves the investment opportunity set for prospect investors. We formulate a new testing procedure for prospect spanning for two nested portfolio sets based on subsampling and...

Unique-lowest sealed-bid auctions are auctions in which participation is endogenous and the winning bid is the lowest bid among all unique bids. Such auctions admit very many Nash equilibria (NEs) in pure and mixed strategies. The two-bidders' auction is similar to the Hawk-Dove game, which...

In this note we reconsider Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption that every player can stabilize the system on his own. In...