From the following pay-off matrix, determine:
(i) The optimal strategy for each individual.
(ii) Value of the game.
| Player 1 | Player 2 | |||||
| Strategies | I | II | III | IV | V | |
| I | 9 | 3 | 1 | 8 | 0 | |
| II | 6 | 5 | 4 | 6 | 7 | |
| III | 2 | 4 | 3 | 3 | 8 | |
| IV | 5 | 6 | 2 | 2 | 1 | |
The given pay-off matrix represents a simplified version of a two-player game, with Player 1 on the rows and Player 2 on the columns. The numbers in the cells represent the payoffs to Player 1 (the row player) and Player 2 (the column player) for each combination of strategies. The goal is to determine the optimal strategy for each player and the value of the game.
(i) Optimal Strategy for Each Individual:
Player 1: Player 1's optimal strategy, in this case, is to choose the strategy that maximizes their payoff for each column (Player 2's strategy). Let's analyze the maximum payoffs for each column:
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