Two paintings, whose worth is known in advance, are auctioned, and there are only two bidders, Ann and Beth. The paintings are auctioned in a known order. Starting bid is always $1000, and it is increased by $1000 in each round. The two bidders alternate bidding.
After one passes, the other one gets the painting, but then the one passed has the first offer for $1000 for the new painting. There is one exception, however: If Ann passes in the first round for $1000, then Beth can also bid for $1000. If she passes too, then nobody gets the first painting, and Ann gets the first offer for $1000 for the second painting.
Note that players can bid more than they have. As long as they don't have to pay it in the end, it doesn't matter. But if they have to pay more than they have at the end (when both paintings have been auctioned), then the player is bancrupt and gets a payoff of -100000. Note also that each player knows how much cash each player has.
Ann's and Beth's goal is to maximize the sum of cash money plus the value in paintings. The bidders goal is not to be better than the other bidder---they don't care about each other.
(Click the "New Game" button if you want to play once more)