A continuous-time version of the multivariate stopping problem is considered. Associated with vector valued jump stochastic processes, stopping problems with a monotone logical rule are defined under the notion of Nash equilibrium point. The existence of an equilibrium strategy and its characterization by integral equations are obtained. Illustrative examples are provided.

We address the problem of computing a Walrasian equilibrium price in an ascending auction with gross substitutes valuations. In particular, an auction market is considered where there are multiple differentiated items and each item may have multiple units. Although the ascending auction is known to find an equilibrium price vector in finite time, little is known about its time complexity. The m...

Preventive diagnostics and maintenance of complex dynamic systems such as chemical plants and aircraft engines benefit from knowledge of the system components. The conditions of the components are often represented by the parameters of the system, in which case the current conditions of the components can be deduced from the variations of the system parameters about their nominal values. This p...

We consider the design problem for a class of discrete-time and continuous-time neural networks. We obtain a characterization of all connection weights that store a given set of vectors into the network, that is, each given vector becomes an equilibrium point of the network. We also give sufficient conditions that guarantee the asymptotic stability of these equilibrium points.

In this paper we consider the classic problem of finding the market equilibrium prices under linear utility functions. A notion of approximate market equilibrium was proposed by Deng, Papadimitriou and Safra [5]. Using this notion, we present the first fully polynomial-time approximation scheme for finding a market equilibrium price vector. The main tool in our algorithm is the polynomial-time ...