Hamilton–Jacobi equations and two-person zero-sum differential games with unbounded controls

Hamilton-Jacobi Equations and Two-Person Zero-Sum Differential Games with Unbounded Controls

A two-person zero-sum differential game with unbounded controls is considered. Under proper coer-civity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower Hamilton–Jacobi–Isaacs equations, respectively. Consequently, when the Isaacs' condition is satisfied, the upper and lower value functions coincide, leading...

A TRANSITION FROM TWO-PERSON ZERO-SUM GAMES TO COOPERATIVE GAMES WITH FUZZY PAYOFFS

In this paper, we deal with games with fuzzy payoffs. We proved that players who are playing a zero-sum game with fuzzy payoffs against Nature are able to increase their joint payoff, and hence their individual payoffs by cooperating. It is shown that, a cooperative game with the fuzzy characteristic function can be constructed via the optimal game values of the zero-sum games with fuzzy payoff...

Zero-Sum Two Person Games

Linear Quadratic Zero-Sum Two-Person Differential Games

As in optimal control theory, linear quadratic (LQ) differential games (DG) can be solved, even in high dimension, via a Riccati equation. However, contrary to the control case, existence of the solution of the Riccati equation is not necessary for the existence of a closed-loop saddle point. One may “survive” a particular, non generic, type of conjugate point. An important application of LQDG’...

Part II . Two - Person Zero - Sum Games