Property of all equilibria
In all equilibria the object is obtained by the player who values it most highly (player 1)
If player i = 1 obtains the object then we must have bi > b1.
But there is no equilibrium in which bi > b1:
if bi > v2 then i’s payoff is negative, so she can do better by reducing her bid to 0
if bi ≤ v2 then player 1 can increase her payoff from 0 to v1 − bi by bidding bi.
(v1, v1, v3, . . . , vn) Outcome: player 1 obtains the object at the price v1.
As before, player 2’s action may seem “risky”: if there is any chance that player 1 submits a bid less than v1 then there is a chance that player 2’s payoff is negative.