Political Campaigning: Two candidates are competing in a political race. Each candidate i can spend s; ≥ 0 on ads that reach out to voters, which in turn increases the probability that candidate i wins the race. Given a pair of spending choices (S1, S2), the probability that candidate i wins is given by Si If neither spends any resources then each wins with probability 1. Each candidate values winning at a payoff of v > 0, and the cost of spending s; is just si. $1+$2 a. Given two spend levels (S1, S2), write down the expected payoff of a candidate i. b. What is the function that represents each player's best-response func- tion? C. Find the unique Nash equilibrium. d. e. υ What happens to the Nash equilibrium spending levels if v increases? What happens to the Nash equilibrium levels if player 1 still values winning at v but player 2 values winning at kv, where k > 1?
Political Campaigning: Two candidates are competing in a political race. Each candidate i can spend s; ≥ 0 on ads that reach out to voters, which in turn increases the probability that candidate i wins the race. Given a pair of spending choices (S1, S2), the probability that candidate i wins is given by Si If neither spends any resources then each wins with probability 1. Each candidate values winning at a payoff of v > 0, and the cost of spending s; is just si. $1+$2 a. Given two spend levels (S1, S2), write down the expected payoff of a candidate i. b. What is the function that represents each player's best-response func- tion? C. Find the unique Nash equilibrium. d. e. υ What happens to the Nash equilibrium spending levels if v increases? What happens to the Nash equilibrium levels if player 1 still values winning at v but player 2 values winning at kv, where k > 1?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Political Campaigning: Two candidates are competing in a political race.
Each candidate i can spend s; ≥ 0 on ads that reach out to voters, which in
turn increases the probability that candidate i wins the race. Given a pair of
spending choices (S1, S2), the probability that candidate i wins is given by
Si If neither spends any resources then each wins with probability 1. Each
candidate values winning at a payoff of v > 0, and the cost of spending s; is
just si.
$1+$2
a. Given two spend levels (S1, S2), write down the expected payoff of a
candidate i.
b. What is the function that represents each player's best-response func-
tion?
C. Find the unique Nash equilibrium.
d.
e.
υ
What happens to the Nash equilibrium spending levels if v increases?
What happens to the Nash equilibrium levels if player 1 still values
winning at v but player 2 values winning at kv, where k > 1?
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