September 22, 2006 yang.1041@osu.edu,rrob@econ.sas.upenn.edu Eric Rasmusen, erasmuse@Indiana.edu Rafael Rob, repeated games My revised classroom powerpoints on the paper are at: http://rasmusen.org/g601/overheads/08-rob-paper.ppt My ostracism paper with David Hirshleifer actually is related as to substance, if not as to the model's driving force: ``Cooperation in a Repeated Prisoner's Dilemma with Ostracism, '' Journal of Economic Behavior and Organization (August 1989), 12: 87-106 (with David Hirshleifer). The unique Nash equilibrium of the finitely repeated n-person Prisoners' Dilemma calls for defection in all rounds. One way to enforce cooperation in groups is ostracism: players who defect are expelled. If the group's members prefer not to diminish its size, ostracism hurts the legitimate members of the group as well as the outcast, putting the credibility of the threat in doubt. Nonetheless, we show that ostracism can be effective in promoting cooperation with either finite or infinite rounds of play. The model can be applied to games other than the Prisoners' Dilemma, and ostracism can enforce inefficient as well as efficient outcomes. In tex (60K) or pdf ( http://rasmusen.org/published/Rasmusen_89JEBO.ostracism.pdf) . The last part of chapter 6 of my game theory book, 4th ed., talksa bout the Diamond model, which you should discuss. http://www.rasmusen.org/GI/chapters/chap06_pbe.pdf Aha! There MUST be some bad types, because otherwise, the cooperative eq. fails. An opportunist might as well deviate with DEFECT because he will be expelled, but his new match will eiher be an Opportunist, who chooses COOPERATE in eq., or a GOOD type. If there are no BAD types, I bet there is a mixed strategy eq. I bet it is true that there is no equilibrium IN YOUR CLASS *OR* MORE GENERALLY in which if there are no BAD players we get COOPERATE as a pure strategy equilibirum. This would make an interesting evolutionary game. In a COOPERATE eq., the GOOD and OPP types do equally well (tho it is crucial that they SWITCH AFTER DEFECT). There is no penalty to being GOOD, unlike what we normally think. But being BAD is worse. So they will diminish in number. Eventually, there will be too few, and the OPPs will start to deviate. But then being GOOD will be worse. So the GOODs will shrink, and the BADs become more numerous. I think it will settle to where everyone is BAD or OPP. You should really see if your steady state can be reached starting from an unmathced pool of alpha, beta, gamma proportions. I don't at the moment see why not. In a DEFECT equilibrium, would everybody Could you have a peculiar equilibrium like this? The OPP chooses COOP, COOP, COOP, DEFECT, COOP, and then COOP forever after, if his partner always chooses COOP. Yes, I think that can be an eq.,in the infinite period game (this would break down by the Chainstore Paradox in a finite-period model). The GOOD strategy would then be to SWITCH AFTER DEFECT, EXCEPT IF THE DEFECT IS IN ROUND 4 OF HTE RELATIONSHIP. If rho=0, there can be cooperation, even without binding contracts. Just use hte Folk Theorem type equilibrium, with the bad types going into the pool. Ah-- it owuld not be stationary, though, because the fraction of BAD in the pool would be incresaing always, and would never, however, reach 100%. For the diagram, Figure 3, label region II as II:BG, label IV as IV-G, label V as V:neither, and so forth. Also, have brackets to show the same thing, a vertical bracket labelled; GOOD EXISTS HERE nad two horizontal barckets for BAD EXISTS HERE. Harbaugh: a membership fee would be very nice. Or a big enough search cost. Both would deter BADs', or even defecting OPPs, but not the GOODs.