We present comparison and global existence results for solutions of coupled matrix Riccati differential equations appearing in closed loop Nash games and in mixed H2/H∞-type problems. Convergence of solutions is established for the diagonal case. Solutions of the corresponding algebraic equations are discussed using numerical examples.

This paper considers equilibrium directed search with a finite number of heterogeneous workers and firms, where firms compete in direct mechanisms. Unlike previous findings, Nash equilibrium here does solve the problem of coordination failure. Restricting the match value function to be supermodular, and that firms use truthful strategies also imply positive assortative matching and decentralize...

We study a common-pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource. To capture decision making under such uncertainty, we model each player’s risk preference according to the value function from prospect theory. We show the existence and uniqueness of a pure strategy Nash equilibrium when the players have arbit...

By using the KAM theory we investigate the stability of equilibrium solutions of the Gumowski-Mira equation: xn+1=(2ax n)/(1+x n2)-xn-1, n=0,1,…, where x-1, x0∈(-∞,∞), and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.

Kawamoto had reported that eel hemoglobin has a hyperbolic oxygen equilibrium function, with n in the Hill equation equal to 1. On the basis of Kawamoto's data and with new measurements, it is shown that the equilibrium function is in fact S-shaped, as in most other vertebrates, and n in Hill's equation equals 1.8.

A mechanical equilibrium equation of a vesicle membrane under a generalized elastic bending energy is obtained in this paper. Moreover, the derivation of this equilibrium equation bases on some shape optimization tools. This approach is new and more concise than the tensorial tools previously used for this problem.

We discuss the approach to equilibrium of systems governed by the Fokker-Planck equation. In particular, we focus on problems involving barrier penetration and the associated Kramers’ time. We also describe the connection between stochastic processes and quantum mechanics. Keywards: Fokker-Planck equation; Approach to equilibrium; Barrier penetration

A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum which includes zero. An elementary construction shows that the equilibrium is not stable.

A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum which includes zero. An elementary construction shows that the equilibrium is not stable.

We study the boundary exact controllability for the quasilinear wave equation in the higher-dimensional case. Our main tool is the geometric analysis. We derive the existence of long time solutions near an equilibrium, prove the locally exact controllability around the equilibrium under some checkable geometrical conditions. We then establish the globally exact controllability in such a way tha...