Randomization can be defensive and allows to avoid

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-randomization can be defensive and allows to avoid behavioral patterns that can be exploited - Harsanyi: mixed equilibrium can describe an outcome when There are many agents in the population They are matched randomly History (reputation) is not observed Each agent plays just one strategy Harsanyi’s theory has some empirical validity Randomization in experiments: even when they know they need to randomize, they do not do it well Lecture 18/19 Behavioral models of randomization: Feature matching heuristic: subjects have memory of length m and they are more likely to pick a strategy at step (m+1) that balances the previous sequence of length m. Example: poker game: current pot $10, possible bet is $20 Step 1: identify pure strategies; note that strong hands should be bet NE(nash equilibria) in mixed strategies have qualitative predictions -frequency of bluffs need to be randomized well (do not alternate too often) -they do not exploit people’s patterns either Fictitious play (learning) people keep track of relative frequencies of strategies and play best response to the observed frequencies. In the long run, this learning converges to some NE -pattern ABBAAABB ABBAAABB is exploitable, but subjects usually fail to see it Bayesian learning: people start with prior beliefs about structure of game and adjust their beliefs by the Bayes rule Example: basketball game, players observe frequencies of various moves for other players (fictitious play learning) -When a new player arrives, players rely on prior beliefs and prejudgments -Bayesian learning is more sophisticated and harder to model bc it can depend on many parameters
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Lecture 20 Rules of open bid auctions: open bid means people can observe price action English -price goes up in small increments from a very low level until there is 1 bidder left. Private utility model; equivalent to the one where agents make open themselves Dutch - price goes down in small increments from high level until there is 1 bidder who is willing to pay this price(called “decreasing price auctions”) Rules of closed bid auctions: all bidders submit their bids discreetly and cannot observe others’ actions First price: highest bid wins and becomes price Second price (vickrey auction): highest bid wins and second highest bid is price All-pay: highest bid wins, but all bids must be paid Example: sports contest, lobbying Reservation value : limit on the price of a good/service(private if it does not depend on values of other bidders) -reservation values can be interdependent if the value of agent i can be affected by the value of agent j -this is plausible if bidders plan to resell the good later, or if the bidders are better informed about the quality of the good Standard model: auctions are games Bidders observe their types (private values and other signals) Bidders choose bidding strategies Bidding strategies determine the outcome: The winner The price=seller’s revenue Average revenue across many observations
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