This course aims to provide students with the basic methods relative to logic of propositions and logic of reasoning and to present the main elements of the theory of rational decisions which, lies at the root of many of today’s most important theories and applications in both an economic environment and in a more general sense within social science.
Logic of prepositions
Introduction to logic. Propositions and operations between prepositions.
Equivalence of prepositions. Inference rules. Truth tables.
Sets. Operations between sets. Relations between sets: relation of order and equivalence. Correspendence, applications, functions. Outline of numerical sets.
Introduction. Random experiments, sampling. Probability, axiomatic definition and different interpretations of probability. Properties of measuring probability.
Calculating probability. Casual uni-dimensional discrete variables. Average and variance.
Introduction. Rationality. Intelligence. Rational choice: certainty, uncertainty, strategic interaction. Choosing under conditions of certainty. Relations of preference. Utility functions. Indifference curves. Indifference maps. Marginal utility. Choosing under conditions of uncertainty. Lottery. Theory of expected utility.
Elements of the theory of games
Games in strategic form: introduction, definition and general principles. Various examples. Dominant strategies. The Nash equilibrium in pure strategies. Mixed strategies. Belief. The Nash equilibrium in mixed strategies. The Nash theorem.
Reading list will be indicated during the course.
Lectures and exercises, course material available online.
Written examination followed by an oral examination.
Further information can be found on the lecturer's webpage at http://docenti.unicatt.it/web/searchByName.do?language=ENG or on the Faculty notice board.