In this paper, we investigate a two-person zero-sum game with fractional loss function, which we call the two-person zero-sum fractional game. We are interested in a game value and a saddle point of the two-person zero-sum game and observe that they exist under various conditions. But, in many cases, it seems to be difficult to search directly for a game value and a saddle point of the fraction...

Gameplay in real-time strategy games seems somehow to be confined to a de facto standard where economical micromanagement is equally important as combat strategy, if not more important. To enable stronger combat-oriented gameplay without sacrificing other key aspects of the genre, we propose an automated system for scheduling unit training, which we believe may allow the exploration of new para...

This short note demonstrates how one can define a transformation of a non-zero sum game into a zero sum, so that the optimal mixed strategy achieving equilibrium always exists. The transformation is equivalent to introduction of a passive player into a game (a player with a singleton set of pure strategies), whose payoff depends on the actions of the active players, and it is justified by the l...