Foundations

Equilibrium concepts, information, repeated games, computational complexity — the formal core of game theory.
TUTORIALS

Foundations

Equilibrium concepts, information, repeated games, computational complexity — the formal core of game theory.

Backward induction and the centipede game paradox

foundations
backward-induction
centipede-game
paradox

Implement backward induction for the centipede game in R, demonstrate the dramatic gap between theory and observed play, and analyse how finite vs infinite horizons shape rational behaviour.

May 8, 2026

Common knowledge and its paradoxes

foundations
common-knowledge
epistemic-game-theory
paradoxes

Formalise common knowledge using Aumann’s partition model in R, implement the muddy children puzzle to show how public announcements create common knowledge, and analyse how failures of common knowledge lead to coordination failures, speculative trade, and the electronic mail game paradox.

May 8, 2026

Correlated equilibrium — coordination through shared signals

foundations
correlated-equilibrium
equilibrium-concepts
coordination

Implement Aumann’s correlated equilibrium in R via linear programming, compare it with Nash equilibrium, and visualize how a public correlating device expands the set of achievable payoffs.

May 8, 2026

Dominant strategies and iterated elimination of dominated strategies

foundations
dominance
rationality
normal-form

Define strict and weak dominance in normal-form games, implement iterated elimination of dominated strategies (IEDS) in R, and show how rationality assumptions progressively simplify strategic analysis.

May 8, 2026

Epsilon-equilibrium and approximate Nash equilibria

foundations
epsilon-equilibrium
approximate-equilibrium
computational-complexity

Implement epsilon-Nash equilibrium in R, analyse when approximate solutions suffice for practical predictions, compute the epsilon required for various games, and connect to computational complexity of exact Nash equilibrium finding.

May 8, 2026

Extensive-form games and subgame-perfect equilibrium

foundations
extensive-form
subgame-perfection
backward-induction

Formalize sequential games as extensive-form game trees in R, implement backward induction to find subgame-perfect equilibria, and visualize the difference between Nash equilibria and credible equilibria.

May 8, 2026

Folk theorem with perfect monitoring

foundations
repeated-games
folk-theorem
subgame-perfection

Prove and visualize the folk theorem for infinitely repeated games: any individually rational, feasible payoff can be sustained as a subgame-perfect equilibrium when players are sufficiently patient.

May 8, 2026

The Nash bargaining solution

foundations
bargaining
nash-bargaining
cooperative-gt

Derive and implement Nash’s axiomatic bargaining solution in R, compute the Nash product for two-player bargaining problems, and visualize the Pareto frontier with the bargaining outcome.

May 8, 2026

Mixed-strategy Nash equilibrium in 2×2 games

foundations
nash-equilibrium
mixed-strategies
2x2-games

How to compute a mixed-strategy Nash equilibrium for a 2×2 normal-form game, with R and Python implementations and interactive visualizations.

May 8, 2026

Rationalizability and iterated dominance — the epistemic foundation of game theory

foundations
rationalizability
dominance
epistemic-game-theory

Define rationalizable strategies as those surviving iterated deletion of never-best-responses, implement the algorithm in R for arbitrary games, and show the relationship to IESDS and common knowledge of rationality.

May 8, 2026

The revelation principle — why truth-telling mechanisms suffice

foundations
revelation-principle
mechanism-design
incentive-compatibility

Prove and implement the revelation principle in R, showing that any outcome achievable by any mechanism can be replicated by a direct mechanism where truthful reporting is optimal, with applications to auctions and public goods provision.

May 8, 2026

Signaling games and perfect Bayesian equilibrium

foundations
signaling-games
perfect-bayesian-equilibrium
incomplete-information

Model strategic communication under asymmetric information in R, compute perfect Bayesian equilibria with separating and pooling strategies, and visualize how informed players signal their types.

May 8, 2026

Trembling Hand Perfect Equilibrium

foundations
equilibrium-refinement
trembling-hand-perfection
nash-equilibrium

Implement Selten’s trembling hand perfection refinement to eliminate unreasonable Nash equilibria by requiring robustness to small probability mistakes, with applications to coordination games and weakly dominated strategies.

May 8, 2026

Zero-sum games and the minimax theorem

foundations
zero-sum
minimax
linear-programming

Prove and implement von Neumann’s minimax theorem for two-player zero-sum games in R, compute minimax strategies via linear programming, and visualize the security level geometry.

May 8, 2026
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