Linear Algebra & Matrices

Eigenvalues, SVD, positive definite matrices, Perron-Frobenius, graph Laplacians.
TUTORIALS

Linear Algebra & Matrices

Eigenvalues, SVD, positive definite matrices, Perron-Frobenius, graph Laplacians.

Eigenvalue methods for repeated game analysis

linear-algebra-matrix
repeated-games
markov-chains
eigenvalue-decomposition

Use eigenvalue decomposition to compute stationary distributions, convergence rates, and long-run cooperation levels for Markov strategies in the repeated Prisoner’s Dilemma, including Tit-for-Tat, Grim Trigger, and stochastic strategies.

May 8, 2026

LP duality and zero-sum game solutions

linear-algebra-matrix
linear-programming
zero-sum-games
minimax

Explore the formal connection between linear programming duality and the minimax theorem for zero-sum games, implementing both primal and dual formulations to solve a 3x3 game.

May 8, 2026

Markov Chains for Strategy Dynamics in Game Theory

linear-algebra-matrix
markov-chains
evolutionary-dynamics

Model strategy updating as a Markov chain in populations playing 2x2 games, computing transition matrices, stationary distributions, and mixing times for imitation dynamics and mutation-selection processes.

May 8, 2026

Matrix games — linear algebra foundations for game theory

linear-algebra-matrix
matrix-games
numerical-methods

Express strategic games as matrices, compute mixed-strategy Nash equilibria using linear algebra operations including eigenvalues, null spaces, and linear programming, and build a foundation for numerical game theory in R.

May 8, 2026

Singular value decomposition for game analysis

linear-algebra-matrix
svd
payoff-matrices
dimensionality-reduction

Apply SVD to analyze payoff matrices, identify dominant strategic dimensions, construct low-rank game approximations, and connect matrix rank to mixed strategy structure.

May 8, 2026
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