Optimization & Numerical Methods

Convex optimization, LP, dynamic programming, gradient methods, fixed-point theorems.
TUTORIALS

Optimization & Numerical Methods

Convex optimization, LP, dynamic programming, gradient methods, fixed-point theorems.

Gradient Descent Methods for Finding Nash Equilibria

optimization-numerical-methods
gradient-descent
nash-equilibrium

Implement gradient-based optimisation algorithms for finding Nash equilibria in continuous games, including best-response dynamics, the Nikaido-Isoda function approach, and simultaneous gradient descent with convergence analysis in R.

May 8, 2026

Interior Point Methods for Solving Game-Theoretic Optimization Problems

optimization-numerical-methods
interior-point-methods
zero-sum-games
linear-programming

Implement barrier methods for the linear programming formulation of zero-sum games, visualise the central path and barrier parameter convergence, and apply log-barrier techniques to compute correlated equilibria.

May 8, 2026

The Lemke-Howson algorithm for computing Nash equilibria

optimization-numerical-methods
lemke-howson
equilibrium-computation

Implement the Lemke-Howson pivoting algorithm for bimatrix games in R, trace the complementary path from an artificial equilibrium to a Nash equilibrium, and visualise the pivot steps on the best-response polytope.

May 8, 2026

Simulated annealing for equilibrium computation

optimization-numerical-methods
simulated-annealing
nash-equilibrium
metaheuristic

Apply simulated annealing to find Nash equilibria in complex games, comparing temperature schedules and neighborhood structures with gradient-based methods.

May 8, 2026

Support enumeration algorithm for Nash equilibria

optimization-numerical-methods
nash-equilibrium
support-enumeration
bimatrix-games

Implement the support enumeration method to find all Nash equilibria of bimatrix games by solving indifference conditions for each support pair, with applications to games with multiple equilibria.

May 8, 2026
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