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 (8, 7) to Google and Safari, respectively. If the actions are B and L the payoffs are (3, 5). If the actions are (T, R) the payoffs are (3, 4). Finally, if Google opts for B and Safari R the payoffs are 2 to Google and 3 to Safari respectively. Which of the following statements are true?Group of answer choicesThe dominant strategy equilibrium is (T, L)Safari does not have a dominant strategyNone of the other answers are correct.The dominant strategy equilibrium is (B, R)The game is a prisoners's dilemmaGoogle has a dominant strategy
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 (8, 7) to Google and Safari, respectively. If the actions are B and L the payoffs are (3, 5). If the actions are (T, R) the payoffs are (3, 4). Finally, if Google opts for B and Safari R the payoffs are 2 to Google and 3 to Safari respectively. Which of the following statements are true?Group of answer choicesThe dominant strategy equilibrium is (T, L)Safari does not have a dominant strategyNone of the other answers are correct.The dominant strategy equilibrium is (B, R)The game is a prisoners's dilemmaGoogle has a dominant strategy
Solution
Step 1: Read the question carefully and understand what is being asked.
Step 2: Identify the key terms in the question, such as "Google," "Safari," "actions," "payoffs," and "dominant strategy equilibrium."
Step 3: Determine the dominant strategy equilibrium by finding the best response for each firm given the other's choice.
- If Safari chooses L, Google's best response is to choose T, since 8 > 3. If Google chooses T, Safari's best response is to choose L, since 7 > 4. Therefore, (T, L) is a dominant strategy equilibrium.
- Safari does not have a dominant strategy, since its best response depends on Google's choice.
- (B, R) is not a dominant strategy equilibrium, since Google's best response to Safari choosing R is to choose T, since 8 > 2.
- The game is not a prisoner's dilemma, since the payoffs do not satisfy the condition that the dominant strategy equilibrium leads to a suboptimal outcome for both players.
- Google does not have a dominant strategy, since its best response depends on Safari's choice.
Step 4: Based on the above analysis, the correct answer is:
- The dominant strategy equilibrium is (T, L).
- Safari does not have a dominant strategy.
- None of the other statements are correct.
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