The labor union and management of a particular company have been negotiating a new labor contract. However, negotiations have now come to an impasse, with management making a "final" offer of a wage increase of $1.10 per hour and the union making a "final" demand of $1.60 per hour increase. Therefore, both sides have agreed to have an impartial arbitrator set the wage increase somewhere between $1.10 per hour and $1.60 per hour (inclusively). The arbitrator has asked each side to submit to her a confidential proposal for a fair and economically reasonable wage increase (rounded to the nearest dime). From past experience, both sides know that this arbitrator normally accepts the proposal of the side that moves the most from its "final" figure. If neither side changes its final figure, or if they both give in the same amount, then the arbitrator normally compromises halfway between ($1.35 in this case). Each side now needs to determine what wage increase to propose for its own maximum advantage.
(a) Formulate this problem as a two-person, zero-sum game.
(b) Use the concept of dominated strategies to determine the best strategy for each side.
(c) Without eliminating dominated strategies, determine the best strategy for each side.