Degree in Mathematics – Courses in English (2015-16)

DEGREE IN MATHEMATICS – COURSES IN ENGLISH (2015-16)

FOURTH YEAR -COURSES IN ENGLISH 25073 – ECONOMICS OF INFORMATION AND UNCERTAINTY Theoretical an d practical contents (2015 -16) CONTENT. BRIEF DESCR IPTION Decision under certainty and uncertainty. Lotteries. Expected u tility. Attitudes towards risk. Introduction to moral hazard and adverse selection. Signaling. Balance with asymmetric information. THEORETICAL LESSONS : Unit 1: Reminder Unit s of microeconomics propaedeutic to the subject • Rational choice theory. • Axioms of preferences. • Utility functions and their characteristics. • Demand functions.

Unit 2: Classical theory of choice under risk • Models of choice under risk and uncertainty. • Choice under risk as a choice between lotteries. • Expected utility theory. • Von Neumann and Morgestern utility functions. • Aversion, neutrality, and love for the risk. • Main functions of utility over wealth. Functions, CRRA, HARA. • Estimation of parameters of the utility functions by maximum likelihood.

Unit 3: Choice under uncertainty and experimental economics • Introduction to the experimental methodology in economics. • Major experimental protocols to measure the risk aversion. • Experiments’ simulations.

Unit 4: Experimental evidence and "paradoxes" of the classical theory of choice under risk and uncertainty • The “St. Petersburg paradox". • The Allais paradox. • The Ellsberg Paradox.

Unit 5: Behavioral theories of choice under risk and uncertainty • Weight functions and theories of "non expected" utility. • Utility and value functions. • Loss aversion. • Ambiguity aversion. • Kanemann and Tversky Prospect theory • Unit 6. Case study. Bets on "the classic"

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Throughout the full semester, we will note down the bets quota variations for the football match Barcelona-Real Madrid in the major betting houses on the Internet. At the end of the course, we will discuss the results according to the theories studied throughout the course. 25072 - COLLECTIVE DECISION -MAKING Theoretical an d practical contents (2015 -16) CONTENT. BRIEF DESCR IPTION Individual choice versus collective choice. Voting -based methods . Aggregation of individual preferences. Rules of allocation and distribution. Applications THEORETICAL LESSONS : Unit 1: Collective Decision. Fundamentals. Preferences vs aggregation rules of collective decision.

Unit 2: Preference aggregation. Arrow theorem. Collective decision rules: Gibbard- Shatterthwaite theorem

Unit 3: Preference aggregation. Possibility results. Informational environments

Unit 4: Rules of collective Decision. Condorcet and Borda

Unit 5: Games with transferable utility. The core, the Shapley value and the Nucleolus

Unit 6: Examples of games with transferable utility

Unit 7: Bargaining games. Nash and Kalai-Smorodinsky solution

Unit 8: Arbitrage problems. Bankruptcy, pairing.

Unit 9: Social networks. Fundamentals. 25071 – GAME THEORY Theoretical an d practical contents (2015 -16) CONTENT. BRIEF DESCR IPTION Formal description of games: games in strategic form and games in extensive form. Notions of equilibrium in games. Cooperative games. Applications. THEORETICAL LESSONS : Unit 1. Introduction What is game theory? The prisoner's dilemma. The Nash equilibrium. Public goods. The war of the sexes. Cooperation. Heads or tails. Are we selfish? The ultimatum game.

Unit 2. Static games of complete information Introduction. Normal representation. Strictly dominated strategies. Best response function. Nash equilibrium. Mixed strategies. Existence of equilibrium. Applications

Unit 3. Introduction to evolutionary game theory.

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Motivation . Evolutionarily stable strat egies (EES). Biological definition. Economic definition. Polymorphic balances.

Unit 4. Dynamic games of complete information Introduction. Extensive representation. Backward induction. Strategies. Nash equilibrium. Subgame Perfect Nash equilibrium. Applications.

Unit 5. Static games of incomplete information (or Bayesian). Introduction. Normal representation of Bayesian games. Bayesian Nash equilibrium. Applications.

Unit 6. Dynamic games of incomplete information Introduction to the perfect Bayesian equilibrium. Applications

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