Question

Mr. T. is the front-runner in a political race. Mr. R and Mr. C are two...

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

  1. What is the pure-strategy Nash Equilibrium/Equilibria of the Game?
  2. True or False? Explain: “Focus on Policy is the dominant strategy for both players”?

Homework Answers

Answer #1

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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