Models of population growth. Malthus - geometric progression / exponential function. Malthusian catastrophe - arithmetic progression versus geometric progression. Growth by Fibonacci numbers. Regression - linear and exponential (optimization as a black box). Calibration of the exponential model with real data (IBGE census, for example). Logistic model of population growth - differences equation. Calibration of the logistic model with real data. Oscillatory behavior; chaos. Schelling's segregation model in Social Sciences. Computational experiments. Principles of micro-economy: Consumer choice. Firm theory. Balance. Elements of game theory: Duopolies and the models of Cournot and Bertrand. Player with complete information: rational; best-reply. Player with incomplete information: Reinforcement Learning / Relative Payoff Sum.
Basic Information
Mandatory:
- Moacyr Alvim Silva. Modelos Matemáticos em Ciências Sociais, notas de aula. 2014;
- John Maynard Smith. Mathematical Ideas in Biology – Cambridge University Press, 1968;
- Howard Weiss. A Mathematical Introduction to Population Dynamics. IMPA. 2009.
Complementary:
- Fragelli Cardoso, R. Introdução à Teoria Econômica. Mimeo, 2008;
- Dixit, Avinash K. Thinking strategically : the competitive edge in business, politics, and everyday life. W.W. Norton & Company- 1991;
- Noam Nisan. Algorithmic game theory.Cambridge University Press. 2007;
- Ralph Teixeira, Augusto Morgado. Teoria da Probabilidade. FGV/EPGE, 2009;
- Mark Newman. Networks : an introduction. Oxford University Press, 2010.