Non-additive two-option ski rental

We consider the following generalization of the classical problem of ski rental. There is a game that ends at an unknown time, and the algorithm needs to decide how to pay for the time until the game ends. In our generalization, there are two “payment plans” called “options,” such that each option i   (for i=1,2i=1,2) consists of two kinds of costs: bibi is the (one time) cost to start using Option i  , and aiai is the (ongoing) usage cost per unit of time for Option i  . We assume w.l.o.g. that a1>a2a1>a2 and b1