From the following pay-off matrix, determine: (i) The optimal strategy for each individual. (ii) Value of the game.Player 1Player 2Strategies I II III IV VI 9 3 1 8 0II 6 5 4 6 7III 2 4 3 3 8IV 5 6 2 2 1

To determine the optimal strategy for each player and the value of the game, we can use the concept of the minimax criterion.

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(i) Optimal Strategy for Each Individual (Minimax Strategy):

• For Player 1:
  Player 1 wants to maximize their minimum guaranteed payoff. Look at the minimum payoff in each row and choose the strategy corresponding to the maximum of these minimums.
• Minimum payoffs for Player 1: 1, 4, 2, 2
• Maximum of these minimums: 4 So, Player 1’s optimal strategy is II.
• For Player 2:
  Player 2 wants to minimize their maximum possible loss. Look at the maximum payoff in each column and choose the strategy corresponding to the minimum of these maximums.
• Maximum payoffs for Player 2: 9, 6, 4, 8, 8
• Minimum of these maximums: 4 So, Player 2’s optimal strategy is III.

(ii) Value of the Game:

The value of the game is the payoff associated with the cell where the optimal strategies for both players intersect. In this case, it’s the payoff in the cell where Player 1’s strategy II and Player 2’s strategy III intersect.

Value of the game = Payoff for (II, III) = 4

Therefore, the optimal strategy for Player 1 is II, the optimal strategy for Player 2 is III, and the value of the game is 4.