9. A partnership firm with two partners has a net worth of W. Each of the partners owns half of the business and, in addition, has a personal bank account of amount K. Of late, the partners are not on talking terms. Finally, they have agreed through a mediator that one of them would buy other's share of business according to the following plan. Each partner submits a sealed bid B (0 ~ B ~ K). The partner making the higher bid would pay the amount bid to his associate in return of full ownership of the business. In case the bids are equal, the mediator would assign business to any one of them through a flip of a coin and without any payment. Taking K = 4, W = 4 and B = 0, 1, 2, 3, 4, draft the above as a two-person, zero-sum game. Find the optimal strategY(ies) of the partners and the value of the game.

Is the game a fair one?