# Two person zero-sum game question

$A$ 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? • what do you think? – Marc Apr 2 '16 at 14:57 • Firstly, this is not zero sum. If they bid the same, then they both win 30000.... – Jimmy R. Apr 3 '16 at 19:38 • @JimmyR.: No, they both had half a business worth$\$30000$ to begin with. Taking that into account, it's zero-sum. – joriki Apr 3 '16 at 20:04
• @Joriki. Yes, as you think it, it is ok. – Jimmy R. Apr 3 '16 at 20:17

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.