Necessary conditions for linear noncooperative N-player delta differential games on time scales

TL;DR

This paper establishes necessary conditions for Nash equilibria in linear noncooperative N-player delta differential games on arbitrary time scales, extending classical results to a unified time framework.

Contribution

It introduces necessary conditions for open-loop and memoryless perfect state Nash equilibria in delta differential games on general time scales, a novel extension of existing theories.

Findings

Necessary conditions for open-loop Nash equilibria.

Necessary conditions for memoryless perfect state Nash equilibria.

Extension of differential game theory to arbitrary time scales.

Abstract

We present necessary conditions for linear noncooperative N-player delta dynamic games on a generic time scale. Necessary conditions for an open-loop Nash-equilibrium and for a memoryless perfect state Nash-equilibrium are proved.