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Gametheory Mathematical theory of games

Gametheory Mathematical theory of games. (A) Introduction: General ideas (B) non-cooperative theory 1 Verbal description of strategic games 2 Extensive n-persons games and games in tree form 3 n-person games in normal form 4 Matrix games (C) Experimental and behavioural Economics.

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Gametheory Mathematical theory of games

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  1. GametheoryMathematical theory of games • (A) Introduction: General ideas • (B) non-cooperative theory • 1 Verbal description of strategic games • 2 Extensive n-persons games and games in tree form • 3 n-person games in normal form • 4 Matrix games • (C) Experimental and behavioural Economics

  2. Gametheory Johann von Neumann 28.12.1903 in Budapest Oskar Morgenstern 24.01.1902 in Görlitz Spieltheorie und wirtschaftliches Verhalten, 1944

  3. Material: Chess and cart games Players are conflict partners Goal: maximal payoff Stefan Zweig : Schachnovelle (1938-41) Rational decisions/ optimal behaviour!!!

  4. Examples for games: • All sorts of competiotion, e.g. beween states • Competition on markets, • Bargaining on fees, salaries and so on, • Elections • Coalitions for governments

  5. Strategic Interaction Payoff maximization does NOT only dependon the OWN behaviour, but also on others (partners, contras) Open question: How to reach this goal in a rational way?

  6. Cooperative gametheory Cooperative Theory: Assumption: binding contracts Coalition bargaining e.g. after votings Problem: Large number of possibilities for cooperations 3 participants: A,B,C, AB, AC, BC, ABC, { } 5 participants: 32 possibilities

  7. Cooperative Theory 2 Problems: • Many different solution concepts e.g.: Shapley-value = power index bargaining set by Aumann/Maschler • Individualbehaviour can not be characterised Personality items are missing.

  8. Non cooperative game theory ONE solution concept: NASH Equilibrium point John Nash

  9. John Nash 1950: Dissertation in Princeton Nobelprice for economics 1994 withJohn Harsanyi and Reinhard Selten John Harsanyi Reinhard Selten

  10. Theory : Empiricism Diskrepance

  11. Human behaviour in conflict situations • Not always: fully rational – • Not always: maximal profit Experimental Economics: Starting point: limited rationality

  12. Empirical research: • watching • description • quantification • questionnaire • simulation • experimentation

  13. Laboratory Experiments Situations of the real world are brought into the laboratory – there the decisions have to be done! Obviously some disadvantages. Advantages: No disturbance or interference, easy to be replicated !!! Financial rewards depending on the behaviour/performance!

  14. Nobelprice laureats in economics: 1994 John C. Harsanyi, John F. Nash, Reinhard Selten: Analysis of equilibrium point in non-cooperative games. 2002Daniel Kahneman& Vernon L. Smith: Research of human behaviour in economic situations. • 2005 Thomas Schelling & Robert Aumann: General ideas in game theory. • 2007 Leonid Hurwicz, Eric S. Maskin, Roger B. Myerson: Development of "Mechanism Design"-Theory. • 2012 Lloyd Shapley & Al Roth: Market Design &Exp Ecs • 2014 Jean Tirole • Industrieökonomie & Oligopoltheorie

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