We consider a class of games which is suggested from a timing problem for putting some kind of farm products on the market. Two players, Player I and II, take possession of the right to put some kind of farm products on the market with even ratio. Each of the players can put the farm products at any time in (0, 1). The price of them increases over (0,m) ⊂ (0, 1) and decreases over (m, 1) with pass time t so long as both of the players do not sell them, however if one of the two players puts his farm products on the market, the price falls discontinuously and then fluctuates analogously as before. Both players have to put their farm products on the market within the unit interval (0, 1). In such a situation, each player wishes to put at the optimal time which gives him the highest price, considering opponents action time with each other. This model yields us a certain class of two person non-zero sum infinite games on the unit square. 1 Introduction We consider a class of games which is suggested from the correlative phenomena between the price fluctuations and supply in a market on farm products. Two players, Player I and II, take possession of the right to put some kind of farm products on the market with even ratio. We call such kind of products product A in this paper. We can harvest product A at a specific season every year periodically. Each of the two players wants to decide the optimal time to put his product A on the market until the next harvest season. We consider one time period where the harvest time in each year is the beginning and the next harvest time is the end. The price of product A increases smoothly until some point and then decreases with time as long as the both players don't put on the market and keep their own products. But, when one of the players puts his product A on the market, the price of product A possessed by his opponent falls discontinuously and then fluctuates with time analogously as before until his opponent puts the rest on the market. In such a situation, each player has to decide the optimal action time considering the current price and his opponent's action time, with each other. This problem is applicable to the correlation phenomena between the price and supply on land, not only to the problem of farm products. As well as the usual games of timing (1,2), we have to introduce two patterns of information available to the players. If a player is informed of his opponent's action time as soon as his opponent put product A on the market, we say they are in a noisy version. If neither player learns when nor whether his opponent has put product A on the market, we say both players are in a silent version. We shall discuss three cases according to the information patterns mentioned above, as follows: 1. Both players are in a noisy version. We call this case noisy game. 2. Both players are in a silent version. We call this case silent game.