Homework 5 Solution

# Homework 5 Solution - Spring 2008 UGBA 143 Homework 5...

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Spring 2008, UGBA 143 Homework 5 Solution Problem 1 a) The strategies below are truly final offers from labor union (L) and management (M), and the outcomes  represent their losses (in cents, compared with their initial offers), based on the final wage.  M(6.00) M(6.10) M(6.20) M(6.30) M(6.40) M(6.50) L(6.00) (-50,0) (-50,0) (-50,0) (-50,0) (-50,0) (-25,-25) L(6.10) (-40,-10) (-40,-10) (-40,-10) (-40,-10) (-25,-25) (0,-50) L(6.20) (-30,-20) (-30,-20) (-30,-20) (-25,-25) (-10,-40) (0,-50) L(6.30) (-20,-30) (-20,-30) (-25,-25) (-20,-30) (-10,-40) (0,-50) L(6.40) (-10,-40) (-25,-25) (-30,-20) (-20,-30) (-10,-40) (0,-50) L(6.50) (-25,-25) (-40,-10) (-30,-20) (-20,-30) (-10,-40) (0,-50) b) Note that: M(6.20) dominates M(6.30), M(6.40) and M(6.50) M(6.10) dominates M(6.00) L(6.30) dominates L(6.20), L(6.10) and L(6.00) L(6.40) dominates L(6.50) Therefore, the set of dominated strategies includes L(6.20), L(6.10), L(6.00),  L(6.50), M(6.00),  M(6.30), M(6.40) and M(6.50). There are no dominant strategies. c) After eliminating dominated strategies, we can write the reduced game: M(6.10) M(6.20) L(6.30) (-20, -30) (-25, -25) L(6.40) (-25, -25) (-30, -20) Here, dominant strategies are L(6.30) and M(6.20). Hence, truly final offers would be \$6.30 from labor

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• Spring '08
• XuanmingSu
• Game Theory, Necessary and sufficient condition, Domination, dominant strategies, truly final offers

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