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Game Theory

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Module 1 — strategic form games

1.1 players strategies payoffs 1.2 pure vs mixed strategies 1.3 dominance and iterated elimination 1.4 best response correspondences 1.5 zero sum games and minimax 1.6 normal form as universal representation

Module 2 — nash equilibrium

2.1 nash equilibrium definition 2.2 pure strategy nash equilibrium 2.3 mixed strategy nash equilibrium 2.4 nash existence theorem 2.5 rationalizability 2.6 correlated equilibrium

Module 3 — extensive form games

3.1 game trees and sequential moves 3.2 information sets and imperfect information 3.3 strategies in extensive form 3.4 backward induction 3.5 subgame perfect equilibrium 3.6 centipede game and common knowledge

Module 4 — information and beliefs

4.1 bayesian games 4.2 types and type spaces 4.3 bayesian nash equilibrium 4.4 perfect bayesian equilibrium 4.5 signaling games 4.6 sequential equilibrium

Module 5 — repeated games

5.1 finitely repeated games 5.2 infinitely repeated games and discounting 5.3 trigger strategies and punishment 5.4 folk theorem 5.5 reputation and chain store paradox 5.6 cooperation in repeated prisoners dilemma

Module 6 — mechanism design

6.1 social choice and incentive compatibility 6.2 revelation principle 6.3 auction theory foundations 6.4 optimal auction design 6.5 implementation theory 6.6 matching and stable allocations

Module 7 — evolutionary game theory

7.1 replicator dynamics 7.2 evolutionarily stable strategies 7.3 hawk dove and asymmetric contests 7.4 population games 7.5 stochastic evolution and mutation 7.6 adaptive dynamics

Module 8 — network games

8.1 graph games and strategic topology 8.2 coordination on networks 8.3 diffusion and cascades 8.4 public goods on graphs 8.5 network formation games 8.6 strategic complementarities

Module 9 — learning in games

9.1 fictitious play 9.2 no regret learning 9.3 counterfactual regret minimization 9.4 multiplicative weights and hedge 9.5 convergence to equilibrium 9.6 reinforcement learning in games

Module 10 — strategic systems integration

10.1 games embedded in institutions 10.2 layered mechanisms 10.3 contracts and principal agent 10.4 commitment and credibility 10.5 political economy and collective choice 10.6 strategic ecosystems and meta games