set of actions of each player: set of possible bids (nonnegative numbers)
preferences of player i: represented by a payoff function that gives player i vi − p if she wins (where vi is her valuation and p is the second-highest bid) and 0 otherwise.
This is a sealed-bid second-price auction. How to break ties in bids?
Simple (but arbitrary) rule: number players 1, . . . , n and make the winner the player with the lowest number among those that submit the highest bid.
Assume that v1 > v2 > · · · > vn.