ECB3GT Game Theory · Lecture Summaries
ECB3GT — Game Theory
Lecture Summaries, Topics 1–7
Utrecht University · 2025–2026
Coordinator: Dr. Kris De Jaegher
Textbook: Rasmusen, Games and Information (4th ed., 2006)
Final exam: Monday 22 June 2026, 13:30–16:30, Educatorium Beta (retake 6 July)
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, ECB3GT Game Theory · Lecture Summaries
Contents
Contents......................................................................................................................................................2
The big picture: four classes of games, four equilibria................................................................................4
Topic 1 — Simultaneous-move games, pure strategies...............................................................................5
Core definitions......................................................................................................................................5
Dominance.............................................................................................................................................5
Nash equilibrium and best responses.....................................................................................................5
The four benchmark 2×2 games.............................................................................................................6
Continuous games..................................................................................................................................6
Topic 2 — Simultaneous-move games, mixed strategies.............................................................................7
Mixed strategies and existence..............................................................................................................7
Solving Matching Pennies.......................................................................................................................7
Mixed equilibria in the benchmark games..............................................................................................7
Applications............................................................................................................................................7
How do players reach an equilibrium?...................................................................................................8
The “Guess 2/3 of the average” game....................................................................................................8
Topic 3 — Sequential-move games..............................................................................................................9
Extensive form........................................................................................................................................9
Why Nash is not enough: subgame-perfection.......................................................................................9
First- and second-mover advantage.......................................................................................................9
Illustrations...........................................................................................................................................10
Topic 4 — Repeated games.......................................................................................................................11
Setup....................................................................................................................................................11
Finitely repeated games — the unravelling results..............................................................................11
Infinitely repeated games.....................................................................................................................11
Reputation and applications.................................................................................................................12
Topic 5 — Bargaining and the hold-up problem........................................................................................13
Why bargaining?...................................................................................................................................13
Simultaneous bargaining: the Nash demand game..............................................................................13
Sequential bargaining...........................................................................................................................13
Rubinstein’s infinite-horizon alternating offers....................................................................................13
The hold-up problem............................................................................................................................13
Topic 6 — Simultaneous-move games, incomplete information...............................................................15
Imperfect vs. incomplete information..................................................................................................15
Bayesian games and Bayesian Nash equilibrium..................................................................................15
Worked examples.................................................................................................................................15
Bayes’ rule............................................................................................................................................15
Illustration: inferiority of unanimous jury verdicts...............................................................................16
Topic 7 — Sequential-move games, imperfect/incomplete information...................................................17
From subgame-perfect to perfect Bayesian.........................................................................................17
Two paradoxes resolved by incomplete information...........................................................................17
Signalling games...................................................................................................................................17
Illustrations...........................................................................................................................................18
One-page revision map..............................................................................................................................19
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, ECB3GT Game Theory · Lecture Summaries
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ECB3GT — Game Theory
Lecture Summaries, Topics 1–7
Utrecht University · 2025–2026
Coordinator: Dr. Kris De Jaegher
Textbook: Rasmusen, Games and Information (4th ed., 2006)
Final exam: Monday 22 June 2026, 13:30–16:30, Educatorium Beta (retake 6 July)
Page 1
, ECB3GT Game Theory · Lecture Summaries
Contents
Contents......................................................................................................................................................2
The big picture: four classes of games, four equilibria................................................................................4
Topic 1 — Simultaneous-move games, pure strategies...............................................................................5
Core definitions......................................................................................................................................5
Dominance.............................................................................................................................................5
Nash equilibrium and best responses.....................................................................................................5
The four benchmark 2×2 games.............................................................................................................6
Continuous games..................................................................................................................................6
Topic 2 — Simultaneous-move games, mixed strategies.............................................................................7
Mixed strategies and existence..............................................................................................................7
Solving Matching Pennies.......................................................................................................................7
Mixed equilibria in the benchmark games..............................................................................................7
Applications............................................................................................................................................7
How do players reach an equilibrium?...................................................................................................8
The “Guess 2/3 of the average” game....................................................................................................8
Topic 3 — Sequential-move games..............................................................................................................9
Extensive form........................................................................................................................................9
Why Nash is not enough: subgame-perfection.......................................................................................9
First- and second-mover advantage.......................................................................................................9
Illustrations...........................................................................................................................................10
Topic 4 — Repeated games.......................................................................................................................11
Setup....................................................................................................................................................11
Finitely repeated games — the unravelling results..............................................................................11
Infinitely repeated games.....................................................................................................................11
Reputation and applications.................................................................................................................12
Topic 5 — Bargaining and the hold-up problem........................................................................................13
Why bargaining?...................................................................................................................................13
Simultaneous bargaining: the Nash demand game..............................................................................13
Sequential bargaining...........................................................................................................................13
Rubinstein’s infinite-horizon alternating offers....................................................................................13
The hold-up problem............................................................................................................................13
Topic 6 — Simultaneous-move games, incomplete information...............................................................15
Imperfect vs. incomplete information..................................................................................................15
Bayesian games and Bayesian Nash equilibrium..................................................................................15
Worked examples.................................................................................................................................15
Bayes’ rule............................................................................................................................................15
Illustration: inferiority of unanimous jury verdicts...............................................................................16
Topic 7 — Sequential-move games, imperfect/incomplete information...................................................17
From subgame-perfect to perfect Bayesian.........................................................................................17
Two paradoxes resolved by incomplete information...........................................................................17
Signalling games...................................................................................................................................17
Illustrations...........................................................................................................................................18
One-page revision map..............................................................................................................................19
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, ECB3GT Game Theory · Lecture Summaries
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