Assume that two collectors, X and Y are in a first prize sealed bid auction for a batch of vintage comic books.

X and Y have different valuations (V) for this batch of comic books e.g. V_X And V_B are between $2000 and $4000.

Both collectors know their own V but does not know the V of the other collector. All they know is that the other collector’s V is a uniformly distributed number between $2000 and $4000.

Assume risk neutrality for X and Y e.g. expected payoff for X is: (V_X – b_X)Pr(b_X) and expected payoff for Y is (V_Y – b_Y)Pr(b_Y). These collectors will make their bids strategically.

Show how X’s bidding strategy is b_X = ½ V_x + 1 and Y’s is b_Y = ½ V_y +1 in a Nash equilibrium.