Mateus Hiro Nagata
PhD in Economics and Decision Sciences - HEC Paris
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Research Projects
Axiomatic Decision Theory x Statistical Learning
How can I incorporate the ideas of VC dimension, in-sample knowledge to predict out-of-sample phenomena into preferences? Does a decision maker just use a bayesian update to formulate beliefs or does it use methods similar to machine learning to form them? How can I axiomatize this?
Currently, my work has been using Case-based decision theory and VC-dimension to voting. The idea is, is in-sample knowledge enough to determine who is the best candidate in terms of preferences for the population? Yes, it is, but functional and asymptotic conditions will be given in my (working) paper.
Epistemic Game Theory x Learning
Nash equilibrium (NE), a briliant concept for stability in strategic interaction between people, require a difficult epistemic condition: common knowledge of rationality and of payoff/utility functions. However, utility is not observable cardinally. Also, NE makes sense if there is someone making recommendations for the strategy of both players, so that no one deviates. If there is no such an entity, how can people play something stable to begin with? Even if the Nash equilibrium is unique, from the point-of-view of the player, we may never know if we are playing a Nash equilibrium, since I do not know the opponent’s payoff.
Learning in Game Theory fills the gap. This project is to see if learning when one’s game has noise in the payoffs gives the same outcomes as when there is no noise. My master’s thesis was on this topic.
Stable Distribution x Economics
Normal distributions are ubiquitous in economic modeling, empirical and theoretical alike. It does capture noise from the environment and is very tractable. One could justify its use by the Central Limit Theorem and the idea that for a given process small, independent and additive effects generate an approximately normal distribution.
However, some big economic problems do concern variables that do not fall into this frame. Especially finance. The movement of stock prices are not consistent with any distribution of finite variance, but are much more with, for instance, Lévy alpha-stable distributions. The normal distribution is the special case of this class of distributions that has finite variance and is the most tractable.
How much does the fundamental results in finance change when we consider more fat-tailed distributions? This line of inquiry is something I want to think about but never had the opportunity.
Guides
Academic
Useful links!
- Prorum A forum that has questions in numerous topics related to academia, organized by professor Cajueiro.
- Matheus Facure A website dedicated to causal relations, econometrics and machine learning in an unique way. Matheus Facure is an extremely talented guy working in Nubank.
- Tips4Economists A thread of useful links for econ students aiming to be a good grad researcher, by professor Masayuki Kudamatsu.
- How to Become a Pure Mathematician (or Statistician) For those who have an (unhealthy) deal of interest in mathematics (such as myself).
- quantecon If you believe that Python, Julia and Economics can change the world, this is how.
- https://aplicardesdemexico.github.io If tortillas are your main food source and you dream of doing a Ph.D. in Econ, this will help.
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