Microeconomic Theory

Course Outline

Lectures

1. General Equilibrium: economy with production; feasible allocation; Edgeworth box; Pareto efficiency; competitive equilibrium; local non-satiation; first welfare theorem; competitive equilibrium with transfers; convex preferences and production sets; quasi-equilibrium with transfers; second welfare theorem; separating hyperplane theorem; differentiable economies; marginal conditions for Pareto optimality; equilibrium existence; excess demand correspondence; Walras' law; Brouwer's fixed point theorem; existence proof; Nash existence theorem; uniqueness and stability; Mantel-Sonnenschein-Debreu theorem; Brown-Matzkin theorem; gross substitutes: uniqueness; stability and comparative statics.

   • Recommended Readings:

     • Jehle, G., Reny, P. Advanced Microeconomic Theory. Pearson 3rd ed. (2011), Ch. 5.

     • Kreps, D. Microeconomic Foundations I. Princeton Univ. Press (2012), Chs. 14 & 15.

     • Mas-Collel, A., Whinston, M., Green, J. Microeconomic Theory. Oxford Univ. Press (1995), Chs. 16 & 17.

2. Social Choice & Mechanism Design: majority rule; Condorcet’s paradox; social welfare function; Arrow’s conditions (unrestricted domain, transitivity, IIA, weakly Paretian, no dictatorship); Arrow’s impossibility theorem; single-peakedness; Black’s theorem; median voter theorem; Pareto indifference principle; strict welfarism; anonymity; Hammond equity; Ralws’ maxmin principle; utilitarian principle; social choice function; dictatorship; strategy-proofness; Gibbard-Satterthwaite theorem; direct mechanism; partial implementation; truthful implementation; dominant strategy & Bayesian implementation; revelation principle; quasi-linear environments; Vickrey-Clarke-Groves mechanism; pivotal mechanisms; Green-Laffont theorem; budget balance; AGV (expected externality) mechanism.

   • Recommended Readings:

     • Jehle, G., Reny, P. Advanced Microeconomic Theory. Pearson 3rd ed. (2011), Ch. 6.

     • Kreps, D. Microeconomic Foundations I. Princeton Univ. Press (2012), Ch. 8.

     • Mas-Collel, A., Whinston, M., Green, J. Microeconomic Theory. Oxford Univ. Press (1995), Chs. 21 & 23.

3. Nash Equilibrium: strategic form; mixed strategy; Nash equilibrium, Nash’s existence theorem (finite games); reaction correspondence; Kakutani’s fixed point theorem; infinite (continuous) games; Debreu-Glicksberg-Fan’s theorem (pure strategies); equilibrium correspondence; Glicksberg’s theorem (mixed strategies); weak convergence; alpha-approximation; epsilon-equilibrium; essentially finite approximation; discontinuous games; upper semi-continuity; continuous maximum; Dasgupta-Maskin theorem (pure strategies); weakly lower semi-continuity; better reply security; reciprocally upper semi-continuity; payoff security; Reny’s theorems (pure and mixed strategies); supermodularity; ordered set; lattice; Tarsky’s fixed point theorem; supermodular function; monotone optima; increasing differences; Topkis’ theorem; supermodular games; endogenous sharing rules.

   • Recommended Readings:

     • Dasgupta, P., Maskin, E. The existence of equilibrium in discontinuous economic games, Review of Economic Studies 53, pp. 1-26 (1986).

     • Fudenberg, D., Tirole, J.: Game Theory. MIT Press (1991), Chs. 1 & 12.

     • Reny, P.: On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica 67 (5), pp. 1029-1056 (1999).

     • Vives, X. Oligopoly Pricing, MIT Press (1999), Ch. 2.

Problem Sets and Solutions: available at the module's website in Blackboard.