in this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation xa=b to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. as applications, we derive sufficient and necess...

We examine robustness of stability under learning to observability of exogenous shocks. Regardless of observability assumptions, the minimal state variable solution is robustly stable under learning provided the expectational feedback is not both positive and large, while the nonfundamental solution is never robustly stable. Overlapping generations and New Keynesian models are considered and co...

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually ratio...

We examine local strong rationality (LSR) in multivariate models with both forward-looking expectations and predetermined variables. Given hypothetical common knowledge restrictions that the dynamics will be close to those of a specified minimal state variable solution, we obtain eductive stability conditions for the solution to be LSR. In the saddlepoint stable case the saddle-path solution is...

It is proven that an autonomous system verifying some conditions has exactly one stable stationary trajectory. The proof of the result is based upon continuation methods. 2002 Elsevier Science Inc. All rights reserved.