Question: Consider the following private value auction with two bidders: A bidder can either be the high-type with probability 0.75, having a valuation of 100 for

Consider the following private value auction with two bidders: A bidder can either be the high-type with probability 0.75, having a valuation of 100 for the item being auctioned, or the low-type with probability 0.25, having a valuation of 70. Assume that bids can only be in increments of 10. While the payoff to a bidder from winning the auction is his valuation minus the price he pays, the payoff to a losing bidder is zero. If both players bid the same amount, then the tie is broken randomly (i.e. there's a 50 percent chance that either player wins). Is the symmetric strategy profile in which a bidder bids 90 if he is the high-type A and 50 if he is the low-type A Bayesian Nash equilibrium?

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