Why does the probability in this maximization problem become theta hat? Suppose we try to implement this

Why does the probability in this maximization problem become theta hat?

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Suppose we try to implement this social choice function. Assume that the buyers are expected utility maximizers. We now ask: If buyer 2 always announces his true value, will buyer 1 find it optimal to do the same? For each value of 0, buyer I's problem is to choose the valuation to announce, say , so as to solve or Max (0 0,) Prob (0, < ,) Max (0 )n, _ 81 Suppose we try to implement this social choice function. Assume that the buyers are expected utility maximizers. We now ask: If buyer 2 always announces his true value, will buyer 1 find it optimal to do the same? For each value of 0, buyer I's problem is to choose the valuation to announce, say , so as to solve or Max (0 0,) Prob (0, < ,) Max (0 )n, _ 81

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The problem can be formulated as follows For each v... View the full answer