Question

In: Economics

1. (Public Goods Game) Suppose that there are two people, Agent 1 and Agent 2 in...

1. (Public Goods Game) Suppose that there are two people, Agent 1 and Agent 2 in a town.
Assume that there is no street light in the town. To build a street light, someone should pay
costs and once it is built, everyone can enjoy the benefit of street light as there is no way to
force not to use it. Once the street light is build, while Agent 1 has 10 payoff, Agent 2 has 5
payoff. If only one person paid for it, the cost of building a street light is 6. If both agents
paid, each person needs to pay only half of it, thus the cost in this case is 3. As a result, the
payoff matrix of this public goods game is as follows.

pay not pay
pay 7,2 4,5
not pay 10,1 0,0

(a) What are BR1(Pay) and BR1(Not Pay)? And what are BR2(Pay) and BR2(Not Pay)?
(b) What is the Nash Equilibrium (NE)?
(c) Suppose that there are many agents who have the same preference of Agent 2. In that
case, what would be the NE? Please explain this with Free Rider problem.

Solutions

Expert Solution

a) BR1(Pay) ie the best response function of agent 1 when agent 2 is paying

BR1(Pay)= not pay

BR1(not pay ) best response function of agent 1 when agent 2 is not paying

BR1(not pay )= pay

Br2(pay ) = not pay

BR2( not pay) = pay

b) Agent 1 would prefer to pay when agent 2 is not paying because in that case his utility is more. Then agent 1 prefers to not pay when agent 2 is paying because his payoff would be more in that case.

Similarly for agent 2

Agent 2 would prefer to pay when agent 1 is not paying because in that case his utility is more. Then agent 2 prefers to not pay when agent 1 is paying because his payoff would be more in that case.

So the nash equilibrium in this case is (pay, not pay ) and (not pay , pay )

c) If many agents have a preference similar to agent 2, then it implies that they have lesser payoff than agent 1. Also it implies that there would be a free rider problem in this case. Since street light is a public good , it would be provided when even 1 of the residents pay for it . So there is an incentive for the other agents to hide their true value and free ride when the good is provided.

This free rider problem sometines leads to market failure when all of the agents try to free ride and at the end no one ends up paying for the provision of public good which would make the payoffs (0,0) if no one pays which would be the nash equilibrium.

(you can comment for doubts )


Related Solutions

There are two agents in an exchange economy with two goods. Agent 1 has an initial...
There are two agents in an exchange economy with two goods. Agent 1 has an initial endowment vector ω1 = (2, 0) and a utility function u1 = x1 + x21/2. Agent 2 has an initial endowment vector ω2 = (0, 2) and a utility function u2 = x1 + x21/3. If we change the initial endowments for the two agents so that both have the same initial endowment, ω1 = (1, 1) = ω2, what would happen to the...
Two streptococcus pneumonia strains, agent 1 and agent 2, are administered to groups of animals at...
Two streptococcus pneumonia strains, agent 1 and agent 2, are administered to groups of animals at different doses. Mortality rates are then measured for the animals that received each dose level of each agent. Agent 1 found to have an LD50 of 400. Agent 2 was found to have an LD50 of 600. a) Which one is producing a capsule and which one is not? Why? b) Briefly explain 2 ways in which bacterial capsules facilitate host colonization and pathogenesis.
Consider an economy with three people and two goods, one public (g) and one private (x)....
Consider an economy with three people and two goods, one public (g) and one private (x). The utility functions for the three people are UA = xA +20lng, UB = xB +30lng, and UC = xC +10lng. The marginal cost of g is constant at 10. According to the Samuelson condition, what is the socially efficient amount of the public good in this economy? Explain why the Samuelson condition picks out the efficient amount of a public good.
Public Goods Two people living in the same small neighborhood make up the total demand for...
Public Goods Two people living in the same small neighborhood make up the total demand for streetlights: P1= 200-2Q P2= 100-Q assume streetlights in the area a pure public good. A. Define Pure Public good. Briefly explain why the private sector might fail to produce enough pure public goods. B. Assume the streetlights can be provided at $240 per unit. Why would it be inefficient to just charge each person $120 per lighthouse (split the cost between them)? C. What...
Using game theory, illustrate why it is difficult to finance public goods. Discuss the players, the...
Using game theory, illustrate why it is difficult to finance public goods. Discuss the players, the strategies, and the payoff matrix. How might one solve the problem of financing public goods? Provide examples.
Using game theory, illustrate why it is difficult to finance public goods. Discuss the players, the...
Using game theory, illustrate why it is difficult to finance public goods. Discuss the players, the strategies, and the payoff matrix. How might one solve the problem of financing public goods? Provide examples.
2.) Pure public goods are those supplied by the public sector and private goods are those supplied by the private sector.
  2.) Pure public goods are those supplied by the public sector and private goods are those supplied by the private sector. 3.) Nonrival goods may be provided by the private sector, but only if they are excludable.
Suppose that people consume only three goods. Also assume that quantities of the goods are fixed...
Suppose that people consume only three goods. Also assume that quantities of the goods are fixed during this period of time, as follows: 100 tennis balls, 10 tennis racquets, and 200 Gatorade bottles. The prices of the goods for the years 2011 and 2012 are shown in the table below Year Balls Racquets Gatorade 2011 $2 $40 $1 2012 $2 $60 $2 What is the percentage change in the price of each of the three goods? What is the percentage...
Referring to game theory, why is it difficult to finance public goods? can you also mention...
Referring to game theory, why is it difficult to finance public goods? can you also mention the players, playoff matrix and strategies used? thanks
1.   Both public goods and common property resources involve externalities. a)   Are the externalities associated with public goods...
1.   Both public goods and common property resources involve externalities. a)   Are the externalities associated with public goods generally positive or negative? Use examples in your answer. Is the free-market quantity of public goods generally greater or less than the efficient quantity? b)  Are the externalities associated with common resources generally positive or negative? Use examples in your answer. Is the free-market use of common resources generally greater or less than the efficient use?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT