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In an auction setting, two individuals are bidding on an item and clearly the bidder with the highest bid receives the item. However, these individuals

In an auction setting, two individuals are bidding on an item and clearly the bidder with the highest bid receives the item. However, these individuals have to pay the amount they bid even though they do not receive the item at the end. The utility of receiving the item for the bidders is calculated as the value of the item ($10) minus their bids. If they do not receive the item the utility is the negative value of what they bid. For example, if the first player bids ($3) and the second player bids ($8), the second player will get the item and the utilities (payoffs) will be -3 and 2 (10-8) respectively. Find the set of all Nash Equilibria.

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