How game theory can be used to model oligopolistic markets.
Suppose that graduating from a university only serves as a signal of high ability (and
is not useful in any other way) and that only high-ability individuals can graduate from
university. The costs of a university education are denoted by c. Furthermore, the
productivity of low-ability workers is £20,000 while the productivity of high-ability
workers is £80,000. Firms pay wages according to the (expected) productivity of their
workers. The share of high-ability individuals among the population is θ, the share of
low ability individuals is 1 − θ.
a) What is the difference between a pooling equilibrium and a separating equilibrium?
b) Under which conditions does
(i) a separating equilibrium exist, and
(ii) a pooling equilibrium exist?
Explain the conditions carefully. What are the wages in these equilibria? (60 marks)
c) Specify the parameters c and θ such that (i) a separating equilibrium exists and (ii)
high-ability individuals are better-off in this separating equilibrium than in a
hypothetical situation in which there is no university. (30 marks)
Explain how game theory can be used to model oligopolistic markets, illustrating your
argument with a game that takes the form of a prisoner’s dilemma. (100 marks)
Word limit: 3000 words in total. Please provide a word count at the end of each
question as well as an overall word count at the end of your essay.
Word limit includes any text in the essay (e.g. quotations, in-text references, and
footnotes). Word limit excludes title of the question/ essay, equations, tables and their
headings, diagrams and their headings, appendices, and bibliography.
Note on the use of Appendices:
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