##大致意思
I为在位者，E为新进入者。si是产品固有的属性，Ni是I公司掌握的数据，fi(Ni)  是额外的支付意愿。消费者对I产品的支付意愿为si + fi(Ni)，如果I公司在第一期获得所有消费者，那么fi(Ni) 变为fI(NI + 1)，两家公司生产成本都为c
如果消费者购买I产品获得的净效用＞消费者购买I产品获得的净效用， sI + fI (NI ) − pI ≥ sE + fE(NE) − pE，那么消费者全都从I公司购买产品。

现在作者从第二期开始博弈，假设I公司赢得第一期的所有消费者，那么第二期E公司的利润为max{sE + fE(NE) − sI − fI(NI + 1), 0}
##问题
我想知道第二期E的利润为什么不是max{sE + fE(NE) − c, 0}而是max{sE + fE(NE) − sI − fI(NI + 1), 0}或者麻烦写一下推导过程，谢谢！
##相关原文
For instance, if Ni is a measure of the data gathered from past customers – perhaps an index of the number of periods that it has attracted a large number of customers in a market – then one component of a consumer’s willingness to pay for their product is fi(Ni) which is a non-decreasing function. There is another component of a consumer’s willingness to pay for i’s product is a stand-alone value, si(≥ 0), which does not depend on data gathered and used by i but is something intrinsic to the product that i offers. Suppose there is a continuum of [0, 1] identical consumers in the market in any period. It is assumed that, in a period, the total willingness to pay for i’s product, si + fi(Ni) is the same for all consumers and consumers care about si + fi(Ni) − pi,...
The simplest setup involves i ∈ {I, E} with an incumbent (I) and an entrant (E). Each has a marginal cost of production of c and no fixed costs, meaning they will both always be active in the market even if they do not produce anything. Suppose each has data at the outset equivalent to (NI, NE) with NI > NE (as would be expected from an incumbent). They compete over an infinite number of discrete time periods with discount factor, δ ∈ (0, 1). Because consumers are symmetric in their preferences, when these firms compete on the basis of price, all consumers are choosing to buy from either I or E in a period. Specifically, they purchase from I in the first period if: sI + fI (NI ) − pI ≥ sE + fE(NE) − pE
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Given this, what is the total value to a firm i of winning the market in the current period? One way to examine this is to suppose there were just two periods. In this case, working backwards, if, say, firm I had been the market leader in the first period, then the second-period profits of each would be, for E, max{sE + fE(NE) − sI − fI(NI + 1), 0} and, for I, max{sI + fI(NI + 1) − sE − fE(NE), 0}