Kari’s company is currently involved in negotiation with its union on the upcoming wages contract.

Positive sign wages increase while negative sign represent wages reduction. What are the optimal strategies with the company as well as the union? What is the game value?

union
U1 u2 u3 u4
C1 +0.25 +0.28 +0.14 -0.16
company C2 +0.20 +0.20 -0.20 +0.16
C3 +0.14 +0.22 +0.18 +0.15
C4 +0.25 +0.13 +0.10 -0.9

To determine the optimal strategies for both the company and the union, as well as the game value, we can use the concept of the Nash equilibrium.

Nash equilibrium is a solution concept in game theory where each player picks their best response to the strategies chosen by the other players, leading to a stable outcome. In this case, the company and the union are the players.

To find the Nash equilibrium, we need to examine each row and column in the table and identify the highest value for each player.

For the company, the strategy with the highest value in each row is as follows:
- C1: The highest value for the company is +0.28 when the union chooses U2.
- C2: The highest value for the company is +0.20 when the union chooses U1.
- C3: The highest value for the company is +0.22 when the union chooses U2.
- C4: The highest value for the company is +0.25 when the union chooses U1.

For the union, the strategy with the highest value in each column is as follows:
- U1: The highest value for the union is +0.25 when the company chooses C4.
- U2: The highest value for the union is +0.28 when the company chooses C1.
- U3: The highest value for the union is +0.18 when the company chooses C3.
- U4: The highest value for the union is +0.16 when the company chooses C1.

Based on these calculations, the optimal strategies for the company and the union are as follows:
- Company: Choose C1 when the union chooses U2, C2 when the union chooses U1, C3 when the union chooses U2, and C4 when the union chooses U1.
- Union: Choose U2 when the company chooses C1, U1 when the company chooses C2 or C4, and U3 when the company chooses C3.

The game value represents the outcome of the game (wages contract negotiation) achieved when both players play their optimal strategies. In this case, the game value would be +0.28, which occurs when the company chooses C1 and the union chooses U2.

Note: The values provided in the question ("+0.25", "+0.28", etc.) are representative of the wage increases or reductions.