4-26-2012Lecture 4:2I. Ex post regretsII. Asymmetrical InformationA. Placement of Nature NodesB. Ex post regretsIII. Uncertainty about PreferencesA. Nature chooses "Type"B. Solving Games with TyplesI. Ex post regrets = part of interpretation of games with uncertaintyDecisions are less systematic and less algorithmic; has more to do with interpreting than solving.Allow Not 0p 1-p Crash Not-10 5EUM(Allow) = p(-10) + (1-p)(5) = 5 - 15pThe expected value allows us to compare to other uncertainty or certainty.Case 1: p < 1/3 Allowoptimal decision: allow when 5-15p > 0p < 1/3crashes happen with probability p sometimes it is easier to assign a number. p = 1/10Case 2: p > 1/3 Not Allowoptimal decision: not allow when p > 1/3We are not going to see if the crash happens but we are still going to have ex post regrets.The mom's son could have been okay; could have not crashed but we would never know. With probability 1-p the other decision would have worked out better.Biking situation: to wear a helmet or notMomNatureIf you wear the helmet and not crash, then when you get back home, your ex post regret would be "Oh, I could have not worn my helmet", but that does not necessarily mean the nexttime you will not wear a helmet because the costs of a crash are too high.Ex post regrets = interpretation. LOOK AT THE STORY.Cases are defined by inequalities.Particular situations defined by equations.Game:Aid No(0, 0) Edu Limos(2, 2) p 1-pRiot Not (-2, -2) (-2, 5)Case 1: p > 3/7RE: Rich: Aid Poor: Edu if AidRiots are relatively likelyRiots are more likely because it is greater than the threshold 3/7. (tip: includes 1)ex post regret: Poor government because with probability 1-p, they could have had Limos & No Riots . The poor government is taking it safe.ex post regret probability ≠ 4/7ex. p = 1/4 → p = 3/4Case 2: p < 3/7RE: Rich: No Aid Poor: Limos if AidRiots are less likely (tip: includes 0)no ex post regrets in equilibrium: There is no way Rich government decision is going to be wrong.RichPoorNatureII. Asymmetrical Informationplayers are different; there is still uncertainty but only Rich gov has uncertaintyDifferent Story:Aid Not(0, 0)p 1-p Riot conditions No Riot conditions(2, 2) (-2, 5) Edu Limos Edu Limos (2, 2) (-2, -2) (2, 2) (-2, 5)Player who knows the outcome 's decision below uncertain player's uncertainty.Don't need the EU for the Poor player because there are no Poor nodes above this.EUR(Aid) = p(2) + (1-p)(-2) = 4p - 2Rich chooses Aid if 4p - 2 > 0 p > 1/2Riot conditions = If Poor chooses Limos there will be a Riot.Poor knows if Riot conditions are present.Rich only know Riot conditions are present with probability p.Case 1: p > 1/2RE: Rich: Aid Poor: Edu if Aid & Riot Conditions, Limos if Aid & No Riot ConditionsRiot conditions are likelyRich will have ex post regret when poor chooses Limos.(like Crash)ex. p = 2/3 → mistake = 1/3Even though the Rich thought 2/3 was high Case 2: p < 1/2RE: Rich: No AidRichNaturePoorPoorPoor: Edu if Aid & Riot Conditions, Limos if Aid & No Riot ConditionsRich will have ex post regret: ex. p = 1/4 ex ante decision will be not to send aidThere are not always decisions with ex post regrets, and there is no rule whether to use p or 1-p.It is hard to step out of a systematic game to interpret. SLOW DOWN! it's