a
To find:Each player’s dominant strategy.
a
Explanation of Solution
Tabular presentation of player 1 and 2 game.
Player 2 | ||||
Player 1 | D | E | F | |
A | -200,150 | 350,100 | -50,600 | |
B | 200,-300 | 400,400 | 300,100 | |
C | -150,200 | -250,550 | 750,-350 |
Dominant strategy is the selection of move in the game which pays the maximum payoff given other player strategy.
According to the table,
Selection by Player 2 | Reaction of player 1 |
D | B |
E | B |
F | C |
It is noted that, when player 2 selects D, for getting the maximum payoff, player 1 selects B. Similarly, If E is selected by 2nd player, 1 will choose B and so on. Thus, no dominant strategy exists for player 2 as player 2 choices rely on player 1 moves.
Thus, dominant strategy does not occur as players do not have independent moves.
Introduction:
Dominant strategy is the selection of move in the game which pays the maximum payoff given other player strategy.
b)
To ascertain: Each player secure strategy.
b)
Explanation of Solution
According to the game, there are various moves available for player second.
When player 2 choses strategy D, Player 1 has two options, that is, strategy A and C. With selection of A strategy, worst outcome is $-200 and at strategy C, worst outcome is -150.
When player 2 choses strategy E, player 1 has a worst outcome of -50 when strategy E is selected.
When player 2 choses strategy F, Player 1 has two options, that is, strategy A and C. With selection of A strategy, worst outcome is -50 and at strategy C, worst outcome is -350.
To get the secure strategy, maximum payoff available which is $200, $400 or $300 when strategy B is selected. Hence, strategy B is considered as secure strategy for player 1.
Introduction:
A strategy is secure when any deviation from player 2 does not affect the payoff of player 1 having no dominant strategy.
c)
To ascertain: The Nash equilibrium.
c)
Explanation of Solution
Nash equilibrium occurs when both players are maximizing their payoffs given other player’s move.
Therefore, Nash equilibrium occurs when player A choses B strategy while player B choses strategy E which gives payoff equal to each player.
Therefore, the Nash equilibrium in the game is (B,E).
Introduction:
Nash equilibrium is a stable state in which different participants interact each other, in which no participant gain unilaterally, if strategy of other remains unchanged.
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Chapter 10 Solutions
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