# Carefully describe, also through a numerical example, how cooperation can be achieved as an equilibrium outcome for an infinitely repeated prisoners dilemma game.

by zaza14 (student)

Name: Zarfishan Malik        Course: BSc Economics and Statistics                     Lecturer: Dr Emanuela Sciubba

Assignment

Q2: Carefully describe, also through a numerical example, how cooperation can be achieved as an equilibrium outcome for an infinitely repeated prisoners’ dilemma game.

Cooperation can arise in the case of infinitely repeated prisoner’s dilemma as is implied by the Folk theorem which says that “virtually any pattern of action can be generated by the equilibrium of infinitely repeated games, if the discount rate is sufficiently low.”[1] If ostracism is possible and its penalty is large enough relative to the low discount factor, cooperation can be achieved.

Example-

Initially the Nash equilibrium will be attained at (confess, confess) strategy and both will get imprisonment for 5 years. However, if the game is repeated infinite number of times, ultimately cooperation can be achieved and both will be imprisoned for 2 years each.

Q3: "Education can serve as a signal of high ability even when it does not increase knowledge and productivity." Explain why and under which conditions this statement holds true.

‘Education can serve as a signal of high ability even when it does not increase knowledge and productivity.’ This holds true in case of asymmetric information, which occurs in the market situation when the buyers and sellers have different information while making the transaction.

Education undoubtedly can raise one’s productivity. But, as has been stressed by Spence,[2] in his model of signalling, even if education does not improve one’s productivity, it will still be a useful signal of productivity because it is easier and less costly for more productive persons to obtain a higher level of education as compared to low productivity persons. More productive persons are more intelligent, highly motivated, more hard working and are therefore likely to obtain a higher level of education which can be used as signal of their higher productivity to enable them highly lucrative jobs. For all these reasons firms are right in thinking that education is a signal of productivity.

The hiring firms do not know about the worker’s productivity but education serves as a signal and a person’s education level can be easily measured by the number of years of schooling, the degrees obtained, the college or university where s/he studied, the grade obtained etc.

Q5: What is a public good and how can one determine the optimal level of provision of a public good?