Mr. T. is the front-runner in a political race. Mr. R and Mr. C are two other rival candidates, and will simultaneously decide on their strategies for the upcoming debate. In this question, consider this interaction as a one-shot (ie., not repeated), and completely ignore the third player, Mr. T.
Mr. R is more popularly known than Mr. C, so every time he insults Mr. T, he receives a large bump in polls if Mr. C chooses not to insult. However, if Mr. C insults Mr. T while Mr. R does not, Mr. C sees a bump in the polls but not as large as Mr. R does. If they both insult, they receive the same benefit.
During the upcoming debate, each player can either insult the front-runner, or engage in a personal attack to the rival (Mr. R for Mr. C, Mr. C for Mr. R), or focus on policy. Like in all cases with strategic interactions, a player's payoff depends not only on his own strategy but also on the other player's strategies.
The payoff matrix below describes the payoff structure in this game. This is a complete information game, and both players are risk-neutral.
Mr. C |
||||
Insult Mr. T |
Attack the Rival |
Focus on Policy |
||
Mr. R |
Insult Mr. T |
3 , 3 |
9 , 6 |
10 , 2 |
Attack the Rival |
6 , 7 |
4 , 4 |
1 , 2 |
|
Focus on Policy |
2 , 6 |
2 , 1 |
7 , 7 |
There are two pure strategy Nash equilibria. They are:
Mr. R insults Mr T and Mr. C attack the rival. And, Mr R
attack the rival while Mr. C insult Mr. T.
(Given that Mr R choose Insult Mr T, MR C's best response is
Attack the rival(6).
Given that Mr R choose Attack the rival, MR C's best response is
Insult Mr T(7).
Given that Mr R choose Focus on policy, MR C's best response is
Focus on policy(7).
Given that Mr C choose Insult Mr T, MR C's best response is Attack
the rival(6).
Given that Mr C choose Attack the rival, MR C's best response
Insult Mr T(9).
Given that Mr C choose Focus on policy, MR C's best response is
Insult Mr T(10).
There are 2 NE as best response occurs simultaneously at two sets.
They are one will attack the rivala and other will insult Mr. T =
(9, 6), and (6, 7).)
False
(Focus on policy is a dominant strategy for neither of the
players.)
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