Consider Google and Safari in a simultaneous-move game. Google can choose to play T or B. Safari can opt for an action of either L or R. The payoffs are as follows. If Google opts for T and Safari L, the payoffs are (4, 5) to Google and Safari, respectively. If the actions are B and L the payoffs are (2, 9). If the actions are (T, R) the payoffs are (8, 4). Finally, if Google opts for B and Safari R the payoffs are 7 to Google and 6 to Safari respectively. Which of the following statements are trueGroup of answer choicesThis is not a prisoners' dilemmaGoogle has a dominant strategySafari has a dominant strategyThere is no dominant strategy equilibriumThe dominant strategy equilibrium is (T, L).The dominant strategy equilibrium is (T, R)
Question
Consider Google and Safari in a simultaneous-move game. Google can choose to play T or B. Safari can opt for an action of either L or R. The payoffs are as follows. If Google opts for T and Safari L, the payoffs are (4, 5) to Google and Safari, respectively. If the actions are B and L the payoffs are (2, 9). If the actions are (T, R) the payoffs are (8, 4). Finally, if Google opts for B and Safari R the payoffs are 7 to Google and 6 to Safari respectively. Which of the following statements are trueGroup of answer choicesThis is not a prisoners' dilemmaGoogle has a dominant strategySafari has a dominant strategyThere is no dominant strategy equilibriumThe dominant strategy equilibrium is (T, L).The dominant strategy equilibrium is (T, R)
Solution
To answer this question, we first need to understand what a dominant strategy is. A dominant strategy is a strategy that results in the highest payoff for a player no matter what the other player does.
Let's look at Google's options first. If Safari chooses L, Google gets a higher payoff by choosing T (4 > 2). If Safari chooses R, Google also gets a higher payoff by choosing T (8 > 7). So, Google has a dominant strategy, which is T.
Now, let's look at Safari's options. If Google chooses T, Safari gets a higher payoff by choosing L (5 > 4). However, if Google chooses B, Safari gets a higher payoff by choosing R (6 > 9). Therefore, Safari does not have a dominant strategy.
The dominant strategy equilibrium is when both players play their dominant strategies. Since Safari does not have a dominant strategy, there is no dominant strategy equilibrium.
So, the statements "Google has a dominant strategy" and "This is not a prisoners' dilemma" are true. The statements "Safari has a dominant strategy", "There is no dominant strategy equilibrium", "The dominant strategy equilibrium is (T, L)", and "The dominant strategy equilibrium is (T, R)" are false.
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