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Matthias Blonski, Peter Ockenfels, Giancarlo Spagnolo

Co-operation in Infinitely Repeated Games Extending Theory and Experimental Evidence ESA Conference, Rome, June 2007. Matthias Blonski, Peter Ockenfels, Giancarlo Spagnolo. consider PD-specifications. in which game is co-operation easier if played repeatedly ?. (repeated) game theory.

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Matthias Blonski, Peter Ockenfels, Giancarlo Spagnolo

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  1. Co-operation in Infinitely Repeated GamesExtending Theory and Experimental EvidenceESA Conference, Rome, June 2007 Matthias Blonski, Peter Ockenfels, Giancarlo Spagnolo

  2. consider PD-specifications in which game is co-operation easier if played repeatedly?

  3. (repeated) game theory

  4. (repeated) game theory for δ≥ ½ co-operate! (Pareto-dominant equilibrium) for δ < ⅔do not co-operate!

  5. intuition “sucker’s payoff” should matter

  6. idea imagine my discount rate is δ=.9 my long run incentive to co-operate in both games is

  7. idea short-run incentive to defect „what do I lose if I co-operate and my partner does not?“ equilibrium selection concern: strategic risk “sucker’s payoff”

  8. idea adding up all incentives for δ=.9 co-operate! don’t co-operate!!!

  9. “old” co-operation criterion

  10. “old” co-operation criterion

  11. co-operation criterion δ* “strategic risk disincentive” to co-operate

  12. co-operation criterion δ*

  13. further theoretical support for δ* • Blonski & Spagnolo 2004 formulate a theory of strategic risk for the repeated PD. • this latter theory is related – but not identical – to Harsanyi and Selten’s (1978) risk dominance based on the bicentric prior and the tracing procedure. • Blonski & Spagnolo’s theory compares co-operation supported by grim punishment with always-defect. Risk dominance in the corresponding 2x2-game also yields δ*.

  14. our main hypothesis

  15. experimental design 6 sessions: in each 20 students seated randomly in the computer lab, 10 pairs, absolute stranger design → every player experiences up to 19 matches all had to answer questions correctly after being instructed and before start, then first 3 matches for training (with payoffs…) no communication among players discount factor → continuation probability

  16. our specifications

  17. experimental results

  18. experimental results

  19. co-operation rates in δ - δ*

  20. co-operation rates in δ -

  21. experimental results

  22. experimental results

  23. experimental results

  24. experimental results

  25. experimental results

  26. Table 5: Rate of co-operation in some experiments reported in the literature DF = Dal Bó and Frèchette (2006) DO14 = Duffy and Ochs (2006), 14 subjects; DO6 = Duffy and Ochs (2006), 6 subjects D = Dal Bó (2005), game 1 FH = Feinberg and Husted (1993) MR = Murnighan and Roth (1982) RM = Roth and Murnighan (1978)

  27. conclusions • theories ignoring the role of the “sucker’s payoff” yield wrong or at least misleading predictions • institutions designed to foster co-operation or prevent it (collusion, corruption) should take into account the “sucker’s payoff”. • accumulated experimental evidence supports δ - δ* as qualitative predictor better than any other theory so far.

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