5. Two players simultaneously decide whether to contribute (C) or not (N) towards producing a public good. The good is produced if at least one of them contributes. The benefits derived from the public good is 1 and the cost to player i of contributing is c₁. The payoffs are depicted in the following table. C C1-C₁, 1-C₂ N 1,1-₂ N 1-C₁, 1 0,0 The benefits are common knowledge, but each player's cost is private information. Player i j believes that cj is drawn from a uniform distribution on [0, 2], indepen- dent of c. All of this is common knowledge. Formulate this situation as a Bayesian game and find its set of Bayes-Nash equilibria (hint: consider a cutoff strategy such that C if c k).
5. Two players simultaneously decide whether to contribute (C) or not (N) towards producing a public good. The good is produced if at least one of them contributes. The benefits derived from the public good is 1 and the cost to player i of contributing is c₁. The payoffs are depicted in the following table. C C1-C₁, 1-C₂ N 1,1-₂ N 1-C₁, 1 0,0 The benefits are common knowledge, but each player's cost is private information. Player i j believes that cj is drawn from a uniform distribution on [0, 2], indepen- dent of c. All of this is common knowledge. Formulate this situation as a Bayesian game and find its set of Bayes-Nash equilibria (hint: consider a cutoff strategy such that C if c k).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![5. Two players simultaneously decide whether to contribute (C) or not (N)
towards producing a public good. The good is produced if at least one of them
contributes. The benefits derived from the public good is 1 and the cost to player i
of contributing is c₁. The payoffs are depicted in the following table.
с
C1-C₁, 1-C₂
N 1,1-₂
N
1-C₁, 1
0,0
The benefits are common knowledge, but each player's cost is private information.
Player i j believes that cj is drawn from a uniform distribution on [0, 2], indepen-
dent of c₁. All of this is common knowledge. Formulate this situation as a Bayesian
game and find its set of Bayes-Nash equilibria (hint: consider a cutoff strategy such
that C if c; <k and N if c; > k).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F094417f3-df05-4742-9cce-815e609c7f38%2F18e2b955-7cbf-4288-93d2-afdee90d1cc9%2Fwdyx2z8_processed.png&w=3840&q=75)
Transcribed Image Text:5. Two players simultaneously decide whether to contribute (C) or not (N)
towards producing a public good. The good is produced if at least one of them
contributes. The benefits derived from the public good is 1 and the cost to player i
of contributing is c₁. The payoffs are depicted in the following table.
с
C1-C₁, 1-C₂
N 1,1-₂
N
1-C₁, 1
0,0
The benefits are common knowledge, but each player's cost is private information.
Player i j believes that cj is drawn from a uniform distribution on [0, 2], indepen-
dent of c₁. All of this is common knowledge. Formulate this situation as a Bayesian
game and find its set of Bayes-Nash equilibria (hint: consider a cutoff strategy such
that C if c; <k and N if c; > k).
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