Consider two agents simultaneously deciding whether to contribute to a public good - the good is said to be public because,if it is made available,an agent who free-rides by paying nothing gets just as much pleasure from its enjoyment as an agent who paid for it.If at least one agent contributes to the construction of the public good,both agents will enjoy a payoff of four from the public good.To ensure the public good is constructed,player one must pay c₁ or player two must pay c₂.Assume that c₁

Question

Consider two agents simultaneously deciding whether to contribute to a public good - the good is said to be public because,if it is made available,an agent who free-rides by paying nothing gets just as much pleasure from its enjoyment as an agent who paid for it.If at least one agent contributes to the construction of the public good,both agents will enjoy a payoff of four from the public good.To ensure the public good is constructed,player one must pay c₁ or player two must pay c₂.Assume that c₁ < 4 and c₂ < 4.If neither contributes,the good is not constructed and neither player gets enjoyment from the project.If one or both players contribute,then the good is constructed and each player enjoys a payoff of four minus the contribution cost if that player has contributed.The grid below shows this:
  
Assume that the costs are common knowledge to both players.
a.Find any pure-strategy Nash Equilibrium(s)to the game.
b.Find the Mixed Strategy Nash Equilibrium - the probabilities you find will be functions of the cost parameters.
c.If c₁ = c₂ = 1,write out the mixed strategy NE and find the probability that the public good is provided?
d.If c₁ = c₂ = 3,write out the mixed strategy NE and find the probability that the public good is provided?

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The Answer of Consider two agents simultaneously deciding whether to contribute to a public good - the good is said to be public because,if it is made available,an agent who free-rides by paying nothing gets just as much pleasure from its enjoyment as an agent who paid for it.If at least one agent contributes to the construction of the public good,both agents will enjoy a payoff of four from the public good.To ensure the public good is constructed,player one must pay c₁ or player two must pay c₂.Assume that c₁ < 4 and c₂ < 4.If neither contributes,the good is not constructed and neither player gets enjoyment from the project.If one or both players contribute,then the good is constructed and each player enjoys a payoff of four minus the contribution cost if that player has contributed.The grid below shows this:
  
Assume that the costs are common knowledge to both players.
a.Find any pure-strategy Nash Equilibrium(s)to the game.
b.Find the Mixed Strategy Nash Equilibrium - the probabilities you find will be functions of the cost parameters.
c.If c₁ = c₂ = 1,write out the mixed strategy NE and find the probability that the public good is provided?
d.If c₁ = c₂ = 3,write out the mixed strategy NE and find the probability that the public good is provided?

Consider Two Agents Simultaneously Deciding Whether to Contribute to a Public