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Two Level Recursive Reasoning by Humans Playing Sequential Fixed-Sum Games

MSDM Workshop @ AAMAS-09. Two Level Recursive Reasoning by Humans Playing Sequential Fixed-Sum Games. Authors: Adam Goodie, Prashant Doshi , Diana Young Depts. of Psychology and Computer Science University of Georgia. Outline. Introduction Recursive reasoning Related work

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Two Level Recursive Reasoning by Humans Playing Sequential Fixed-Sum Games

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  1. MSDM Workshop @ AAMAS-09 Two Level Recursive Reasoning by Humans Playing Sequential Fixed-Sum Games Authors: Adam Goodie, Prashant Doshi, Diana Young Depts. of Psychology and Computer Science University of Georgia

  2. Outline • Introduction • Recursive reasoning • Related work • Experimental study • Problem setting • Participants • Methodology • Results • Discussion

  3. Recursive reasoning • Strategic recursive reasoning in multi-agent settings (what do I think that you think that I think...) • Multi-agent decision making frameworks • RMM • I-POMDP • Theory-of-Mind • Real-world application settings • UAV

  4. Related work (I) • Harsanyi (1967) • agent types • common knowledge • Mertens and Zamir (1985) • hierarchical belief system • Aumann (1999) • recursive beliefs

  5. Related work (II) TOM and Behavioral game theory • Stahl and Wilson (1995) • a symmetric 3×3 matrix game • 4% of subjects attributed recursive reasoning to their opponents • Hedden and Zhang (2002) • a sequential, two player, general-sum game(Centipede game) • subjects predominantly began with first-level reasoning • low percentage of subjects use second-level reasoning, when pitted against first-level co-players • Ficici and Pfeffer (2008) • a 3-player, oneshot negotiation game • subjects reasoned about others while negotiating • insufficient evidence to distinguish whether level two models better fit the observed data than level one models

  6. Experimental study • Problem setting • Participants • Methodology • Opponent models • Payoff structures • Design of task

  7. Problem Setting • Two-player alternating-move • Fixed-sum • Complete and perfect information

  8. UAV cover story scenario

  9. Probabilities for players I and II in the cover story scenario

  10. Participants • 162 subjects • Undergraduate students enrolled in lower-level Psychology courses at the University of Georgia • Incentives • performance-contingent monetary rewards • partial course credit

  11. Methodology • Opponent models • myopic • predictive • Payoff structure • Design of task • training phase • test phase

  12. Opponent models • Myopic (First-level reasoning) • Player II chooses its action based on the outcomes at states B and C

  13. 2. predictive (Second-level reasoning) Player II chooses its action by reasoning what player I will do rationally.

  14. Payoff Structure • trivial games • D < C < B < A • A < B < C < D • diagnostic game • C < B < A < D • Different action choices for different opponent models

  15. Design of Task • Training phase • trivial games • criterion • no rationality errors in the 5 most recent games • initial phase • 15 games • kickoff • failed to meet the criterion after 40 total training games

  16. Test phase • 40 diagnostic games • intersperse with 40 C < A < B < D and D < B < A < C • groups based on opponents • half against myopic ones • half against predictive ones • In each opponent model group • half played with abstract version • half played with the UAV cover story and the abstract version

  17. Results • Time period • three months(September-November 2008) • Monetary incentives • 50 cents/correct action, average $30/participant • Training Phase • 162 subjects ( 26 kicked off) • Test Phase • 136 participants (70 female)

  18. More accurate choices when opponent is predictive model • No significant difference for two versions of games mean proportion of accurate choices across all participants in each of the 4 groups

  19. mean proportions marginalized over the abstract and realistic versions

  20. mean proportions marginalized over myopic and predictive opponents

  21. Count of participants grouped according to different proportions of accurate choice

  22. Discussion • UAV cover story neither improved nor reduced the performance • This particular cover story had no effect • Did the subjects employ Minimax or Backward Induction? • Exit questionnaire revealed most subjects did not use these • Independent evaluators concurred that most subjects thought recursively • In some settings humans tend to reason at higher levels of recursion

  23. Thank you Questions?

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