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 $[0, m] \subset [0, 1]$ 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.