Consider Two Agents Simultaneously Deciding Whether to Contribute to a Public

question 10

Essay

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?

---

Definitions:

Average Revenue

The amount of income generated per unit of sale or services rendered, calculated by dividing the total revenue by the number of units sold.

Total Revenue

The overall amount of money generated by a firm from selling its products or services, calculated as the quantity of goods sold multiplied by the price of the goods.

Perfectly Elastic

A situation where a small change in price leads to an infinite change in quantity demanded or supplied, depicted as a horizontal line on a graph.

Perfectly Inelastic

A situation in which the quantity demanded or supplied does not change regardless of changes in price.