This course provides an introduction to game-theoretic models, with a focus on the theory and algorithms for the solution of equilibrium problems over continuous strategy sets. Specifically, we will develop convergence theory for centralized and distributed approaches for the solution of a variety of game-theoretic problems. Course topics will include fixed-point theorems, Nash equilibrium problems, generalized Nash equilibrium problems and Stackelberg equilibrium problems. We will draw on applications from communication networks, electricity markets, supply-chain networks and traffic equilibrium problems. Students will be expected to implement some of the algorithms on Matlab. Apart from students in IESE, this course would be of interest to students from math, ECE, civil engineering, chemical engineering, computer science, general engineering, economics and the operations management program in the business school. No prior background in optimization or game-theory is necessary. However, students would be required to have some background in multivariate calculus and linear algebra. The following books will be adhered to with volume 1 of the first set of references serving as the class text.
[1]
F. Facchinei,et al.
Finite-Dimensional Variational Inequalities and Complementarity Problems
,
2003
.
[2]
Dimitri P. Bertsekas,et al.
Nonlinear Programming
,
1997
.
[3]
Etienne Loute,et al.
Convex optimization and limit analysis: Application to Gurson and porous Drucker-Prager materials
,
2008
.
[4]
Richard W. Cottle,et al.
Linear Complementarity Problem.
,
1992
.
[5]
Bethany L. Nicholson,et al.
Mathematical Programs with Equilibrium Constraints
,
2021,
Pyomo — Optimization Modeling in Python.
[6]
I. Konnov.
Equilibrium Models and Variational Inequalities
,
2013
.