Fast Second and Speedo are trying to decide what to bid for a license in a cellular phone auction where the possible values of the new license are $10 million, $20 million, $30 million, $40 million, $50 million, and $60 million, each equally likely.
The auction is single-round sequential, both parties have exactly the same value for the asset but neither knows its true value from the possible distribution (i.e., a so-called common-value auction), and Fast Second gets to bid after Speedo. Each company has invested in marketing research about the value of the license, which can come out one of two ways: possible values of $20, $30, or $50 million, or possible values of $20, $40, or $60 million. Whichever result arises is known to be 100 percent accurate (i.e., the license is worth one of the three identified amounts with certainty). Speedo proceeds with a bid of $33 million. Fast Second has marketing research saying that the value of the license is $20, $40, or $60. How much should Fast Second bid?
Set up the Bayesian probability rule for Fast Second of BAYES PROB ($40 million value/Forecast of $33 million bid by Speedo).