Games of production development in manufacturing

We consider a class of games which is suggested from production development in manufacturing, where two players, Player I and II, compete to obtain the market of a new product. The market has a value V(t) which is non-increasing with respect to the elapsed time t. The competition begins at their announcements, and then each of the players continues the research to develop a new product according to his schedule. The winner is the one who can keep the research going longer than his opponent. In such a situation, it is natural to assume that each player spends the costs depend on how long he keeps researching. Each has to select a time to give up the competition. This model yields us a certain class of non-zero sum infinite games on some square. There are two patterns of information available to the players. We deal with three cases, that is, the noisy version, the silent version and the silent-noisy version.