Limitations of Classical Game Theory

1. 1 Limitations of Classical Game Theory A Presentation by Moritz Niehaus in the Seminar �Research on Games in Social Psychology�

2. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 2 Structure Introduction Expected Utility Theory Game Theory and its Limitations Assumptions of Game Theory Indeterminacy Nash equilibrium Social Dilemmas Psychological Game Theory Team Reasoning Stackelberg Reasoning Summary and Conclusion Discussion

3. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 3 Introducing Example You are going to have a blind date in Jena� � but you don�t know where you will meet the other person Only if you two choose the same location as a meeting point the date will actually take place To make it a little easier�assume there are only two places to go: �Bier-Eck� in Lobeda and �Caf� Stilbruch� in the Wagnergasse Where would YOU go?

4. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 4 Expected Utility Theory Developed by von Neumann & Morgenstern (1947) In short: The option with the greatest utility is chosen Based on the three assumptions (axioms): Completeness: If there are 2 alternatives, an agent will prefer A or B or is indifferent between A and B Transitivity: If an agent prefers A over B and B over C, he will also prefer A over C Context-free ordering: If an agent prefers A over B, he will still do this when additional alternatives (C, D, �) are available

5. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 5 Expected Utility Theory Allows to create utility functions A choice is rational if it yields the maximum utility Expected Utility Theory is concerned with individual games against nature For interactive games we need to look at�

6. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 6 Structure

7. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 7 Game Theory � is an idealized abstraction of reality � is a normative, not a descriptive theory It states only how people should behave if they wish to maximize their utility It does not describe how people actually behave � can be tested empirically Experimental gaming experiments

8. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 8 Game Theory: Assumptions There are two assumptions of Common Knowledge and Rationality (CKR) CKR 1: The specification of the game (e.g. number of players, payoff functions) are known to all players CKR 2: All players are rational in the sense of Expected Utility Theory ? All players will choose strategies that will maximize their individual expected utilities

9. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 9 Structure

10. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 10 Game Theory: Indeterminacy A simple game: Heads or Tails? Two combinations (H,H and T,T) yield the maximum utility Game theory does not predict which strategy is chosen The theory is indetermined

11. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 11 . In real life there are focal points: a strategy that is more salient than other ones Example: 86% of players choose heads, only 14% tails Example: Meet at �Bier-Eck� (B) �Caf� Stilbruch� (S) Game Theory fails to predict this coordination without rationality Game Theory: Indeterminacy

12. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 12 Structure

13. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 13 Game Theory: Nash Equilibrium A Nash equilibrium can be seen as a cell in a payoff matrix and thus a certain combination of players� actions Definition: no player has anything to gain by unilaterally changing his or her strategy A game can have more than one Nash equilibrium Note: equilibria are highlighted by red boxes

14. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 14 Example: Your task: Find the Nash equilibrium / equilibria Game Theory: Nash Equilibrium

15. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 15 Structure

16. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 16 Prisoner�s Dilemma Game (PDG) Where is the Nash equilibrium? What is the motive structure? Defection (D) is� Dominant and rational because C is not the best strategy to reply to C self-defeatingbecause both players will receive less (2, 2) than they would, if they cooperated (3, 3) Game Theory: Social Dilemmas PDG is a mixed motive structure, heads/tails is not PDG is a mixed motive structure, heads/tails is not

17. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 17 Game Theory: Social Dilemmas Experimental evidence shows that about 50% of strategy choices in PDGs are cooperative (Rapoport & Chammah, 1965) This is not due to heuristics or other biases ? �Hard-nosed game thoery cannot explain the data. [�] that theory has failed.� (Ledyard, 1995)

18. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 18 Structure

19. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 19 Psychological Game Theory Based on Behavioral Game Theory (Camerer, 1997) Replaces descriptively inaccurate aspects with plausible explanations Better match between theory and empirical findings Psychological Game Theory (PGT) Is a descriptive theory Modifies classical game theory by introducing nonstandard reasoning processes Explains intuitions and empirical observations Is a collection of suggestions to solve the problems of classical game theory

20. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 20 PGT: Team Reasoning Explanation for cooperative behavior in social dilemmas A team reasoning player� maximizes the collective payoff chooses not by individual but by collective preference violates the second assumption of Common Knowledge and Rationality on which game theory is based upon CKR 2: �All players will choose strategies that will maximize their individual expected utilities�

21. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 21 PGT: Stackelberg Reasoning Proposed by Colman & Bacharach (1997) Assumes that players share a common sense of reason and can anticipate each other�s choices Example: Hi-Lo Matching Game Player 1 knows that maximum payoff is possible by choosing H Player 2 knows that Player 1 knows this Player 2 chooses H because he expects Player 1 to choose H as well

22. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 22 Structure

23. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 23 Summary and Conclusion Classical Game Theory� is a normative theory based on Expected Utility Theory is not able to predict decisions in all interactive situations but sometimes remains indetermined and� predicts self-defeating behavior in social dilemmas Psychological Game Theory� Suggests elements to explain empirical data which is contrary to the Classical Game Theory Conclusion: Classical Game Theory is useful to understand social interactions but needs to be modified

24. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 24 Thank you for your attention! That was the end of my part� Now it�s your turn!

25. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 25 Structure

26. May 8, 2007 Seminar: �Research on Games in Social Psychology� �Limitations of Classical Game Theory� a presentation by Moritz Niehaus 26 Discussion Some topics to talk about: What argues for the mathematical-economical approach to explain behavior and what for the psychological approach? Is the Expected Utility Theory an adequate basis to describe human behavior? Is it problematic or even a failure that Classical Game Theory does not explain all kinds of human behavior? Should Classical Game Theory be abandoned? What are the positive aspects of Classical Game Theory? What are the negative aspects of Classical Game Theory? What are your suggestions for a modification of Classical Game Theory?