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.
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