Discrete control and algorithms for solving antagonistic dynamic games on networks

Abstract

The concept of antagonistic games for classical discrete control problems is applied and new classes of zero-sum dynamic games on networks are formulated and studied. Polynomial-time algorithms for solving max–min paths problem on networks are proposed and their applications (which might occur within certain financial applications) for solving max–min control problems and determining optimal strategies in zero-sum cyclic games are described. In addition max–min control problems with infinite time horizons which lead to cyclic games are studied and polynomial-time algorithm for solving zero value cyclic games is proposed.

Keywords:

• max–min control problem
• antagonistic dynamic game
• max–min path
• positional games
• c-game on financial networks

AMS Subject Classifications::

• PACS 90B10
• 90C35
• 90C27