Week 6 Game Theory

# Week 6 Game Theory - Topic (6) : Asymmetric Information and...

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Topic (6) : Asymmetric Information and Auctions Week 6 Lecture Notes: Game Theory Pricing decisions are interdependent, and a firm needs to take into account the decisions of rivals when making their own decisions. Nash Equilibrium At the Nash Equilibrium, each player in a game chooses the strategy that yields the highest payoff, given the strategy chosen by the other players Eg. In above example the Nash Equilibrium is for both Ford and Holden to build. Given the other’s behaviour, the best response is always to build. Therefore, the Nash equilibrium = (16,16) Note that the Nash equilibrium does not maximise profit. If both cooperated and neither built, total profits are greater. The Nash equilibrium can be played with: (1) One Shot Game (where there is only one round), (2) Repeated Games (Continued Rounds – Need to consider punishments below), or a (3) Sequential Game (One player mover before another – The one who moves first has a strategic first mover advantage) Nash Equilibrium Punishments for breach of collusion agreement It is better off if two firms collude (In the above example, eg. When payoffs = 18,18). However, if the firms do collude, but one firm cheats, there will be punishments. 1. ‘Tit for Tat’ : if the other firm cheats this period, you punish next period and then start cooperating again. 2. ‘Grim Trigger’ : if the other firm cheats this period, you cheat for the rest of the game (i.e. forever). Whether it is worth it to cheat or collude depends on;

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1. The type of punishment 2. The market discount factor. 3. Whether the threat is credible Chapter 12 McAfee – Auctions (pg 303) Bidding There are two types of bidding (1) Bidding to buy, and (2) Bidding to Sell Auction Types Private Value Environment Assumption: Bidders two know their value for the good of sale (rare). Happens when you do not learn anything about your own value of the good for sale from the bidding or from other’s willingness to pay. 1. The English Auction In an English Auction (Eg. Antiques Roadshow), the price starts low and is increased successively. At each increment of the price, some bidder holds the item unless the price is challenged. That bidder wins the item at that price if no other bidder will pay more. For a private value bidder, the strategy does not depend on the behaviour of bother bidders. The effect of this optimal bidding is that bidders with the second-highest value will drop out when the price reaches their value. Therefore, the English auction captures the second-highest valuation for the seller. 2. The Sealed-Bid Auction In a sealed-bid auction, each bidder submits a bid, typically in a sealed envelope. These bids are opened at the same time, and the higher bidder wins the item. The expected profits of the bid is =(Value – Bid) x Probability that the bid is this highest. Therefore, as Bid goes up, value goes down, probably of bid winning increases. Due to the high amount of uncertainty, the bid is often
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## This note was uploaded on 08/11/2009 for the course ECOF 3001 taught by Professor - during the Three '09 term at University of Sydney.

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Week 6 Game Theory - Topic (6) : Asymmetric Information and...

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