Dominant Strategies A player has a dominant strategy if there is one action that

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Dominant Strategies A player has a dominant strategy if there is one action that is the best in terms of this player's payoffs regardless of what others do. To see this, consider the babysitting game from problem 2 played by Mahala and Aruna. Aruna $15 $10 $45, $45 $80, $30 $30, $80 50, $50 Mahala $10 Suppose Aruna charges $15 per hour, so the game is restricted to the first column of the payoff matrix. If Mahala matches Aruna's price and also charges $15, she gets a payoff of $45, while her payoff is $80 if she charges $10 per hour. Because $80 is greater than $45, she prefers to charge $10 per hour If Aruna charges $10 per hour, the game is restricted to the second column of the matrix. Mahala gets a payoff of $30 a week from charging $15 per hour, as opposed to $50 if she matches Aruna's lower price. Once again she is better off charging $10 per hour. Thus, no matter what Aruna chooses to do, Mahala is better off charging $10 per hour charging $10 per hour is a dominant strategy for her The other action, charging $15 per hour, is called a dominated strategy Another way to find dominant strategies for the row player is to compare his or her row payoffs. If Mahala charges $15 per hour, she gets a payoff of either $45 or $30 while her payoff is $80 or $50 if she charges $10 per hour. The $10-per-hour row (strictly) dominates the $15-per-hour row because $80 is greater than $45 and $50 is greater than $30. Thus, charging $10 per hour is a dominant strategy for Mahala Similarly, to check whether Aruna has a dominant strategy, compare her column payoffs. If Aruna charges $15 per hour, her payoff is $45 or $30 depending on what Mahala charges; however, if Aruna charges $10 per hour, her payoff is $80 or $50. Therefore, charging $10 per hour is also a dominant strategy for the column player. (Another way to figure this out is to recall that this is a symmetric game. So if charging $10 per hour is a dominant strategy for Mahala, it must be a dominant strategy for Aruna as well)

Explanation / Answer

8.1)Dominant strategy is a strategy which a player plays irrespective of what Other player plays as it gives the maximum payoff for all rivals actions.

Mahala has dominant strategy as $10 whereas Aruna also has dominant strategy as $10. ($10,$10) is a dominant strategy nash equilibrium.Ans is A

8.2) False

Game is not a prisoner's Dilemma because both can not be made better off

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