In this game, you will participate in an auction for a prize against {{num_bidders}} other bidders. You will play this game for {{n}} rounds.
At the start of each round, bidders will see their value for the prize, randomly drawn between $0 and ${{private}}, with all values equally likely.
After learning your value, you will submit a bid privately at the same time as the other bidders. Bids must be between $0 and ${{private}} in ${{increment}} increments.
The highest bidder wins the prize and pays the second-highest bid. If you win, your earnings will increase by your value for the prize, and decrease by the second-highest bid. If you don't win, your earnings will remain unchanged.
First, come up with a possible bid given your value. Then, think through your bidding strategy step by step. How do you expect others to bid? If others bid like this and you bid down, what happens? If others bid like this and you bid up, what happens?
Think through all the ways you could deviate from your current bidding strategy, and settle on the best possible strategy. Then return your bid.
After each auction, we will display all bids and the winner's profits. Ties for the highest bid will be resolved randomly.