Difference between revisions of "Curl Summer 2019"

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Problems in economics are often modeled as multiplayer games. In a model where each player chooses between multiple strategies according to a probability distribution, of interest are the so called Mixed Nash Equilibria: situations where no player can benefit by changing their probability of using a particular strategy. In this project we will cover background material on solving polynomial systems, and then study the polynomial formulation of various Mixed Nash Equilibria problems. We will focus on using software to compute many examples, and forming observations and conjectures about the real solutions. With remaining time we aim to prove theoretical results or develop implementations.
 
Problems in economics are often modeled as multiplayer games. In a model where each player chooses between multiple strategies according to a probability distribution, of interest are the so called Mixed Nash Equilibria: situations where no player can benefit by changing their probability of using a particular strategy. In this project we will cover background material on solving polynomial systems, and then study the polynomial formulation of various Mixed Nash Equilibria problems. We will focus on using software to compute many examples, and forming observations and conjectures about the real solutions. With remaining time we aim to prove theoretical results or develop implementations.
  
===Finding Exceptional Mechanisms in Kinematics===
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===Computational algebraic geometry for Algebraic Kinematics ===
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'''Student:''' Jacob Zoromski '''Mentors:''' [https://www.math.wisc.edu/~jose/ Jose Israel Rodriguez], Colin Crowley

Revision as of 09:35, 16 May 2019

This summer there are two students participating in CURL, each doing a project in applied algebraic geometry.

Computing Mixed Nash Equilibria

Student: Jacob Weiker Mentors: Jose Israel Rodriguez, Colin Crowley

Problems in economics are often modeled as multiplayer games. In a model where each player chooses between multiple strategies according to a probability distribution, of interest are the so called Mixed Nash Equilibria: situations where no player can benefit by changing their probability of using a particular strategy. In this project we will cover background material on solving polynomial systems, and then study the polynomial formulation of various Mixed Nash Equilibria problems. We will focus on using software to compute many examples, and forming observations and conjectures about the real solutions. With remaining time we aim to prove theoretical results or develop implementations.

Computational algebraic geometry for Algebraic Kinematics

Student: Jacob Zoromski Mentors: Jose Israel Rodriguez, Colin Crowley