$A$ and $B$ have each $\$100000$ in cash and they are equal partners in business worth $\$60000$. They wish to dissolve partnership and they agree that each of them will make a sealed bid between $\$0$ and $\$100000$ for the business. The higher bidder $X$ gets the business and pays the other partner $Y$ what $X$ bid. If there is a tie in the bidding, the business will be sold for $\$60000$, which will be divided evenly. What bid should $A$ and $B$ make?
They should both bid $\$30000$. If their partner bids less, they get the second half of the business for the $\$30000$ it's worth. If their partner bids the same, they get the $\$30000$ that their half of the business is worth. If their partner bids more, they get more than it's worth. Thus at least a zero outcome is guaranteed, and this is the best that can be achieved in a symmetric zero-sum game.