Chapter 17 Auctions and Bargaining. Outline. Auctions

Transcription

1 Part IV: Extending the Microeconomic Toolbox 15. Trade-offs Involving Time and Risk 16. The Economics of Information Social Economics 1 / 39

2 Chapter / 39

3 1 2 3 / 39

4 Q: How should you bid in an ebay auction? 4 / 39

5 are increasingly used to sell goods and services. There are four major types of auctions: English, Dutch, sealed bid first price and sealed bid second price auctions. Economic theory predicts that under certain assumptions they yield identical revenues for the seller. 5 / 39

6 is another frequent way that goods and services are exchanged. power importantly determines the terms of exchange. 6 / 39

7 17.1 An auction is a market process in which potential buyers bid on a good and the highest bidder receives the good. Some goods, such as painting, don t have well-established prices, making auctions a particularly useful method of selling that encourages price discovery. 7 / 39

8 Exhibit 17.1 Percent of U.S. Adults Participating in Online by Month Just over the last decade, the percent of U.S. adults who participating in online auction have roughly doubled, increasing from 10% to more than 20%. Today more than $300 billion is sold annually in auctions. 8 / 39

9 Exhibit 17.2 Bidder Valuations for Raiders Tickets Auction item: Two Oakland Raiders NFL football tickets being bid upon by five bidders. Assume that bidders have private value that is unknown to other bidders and seller. 9 / 39

10 Type of can be split along two features: 1. How people place their bids: open outcry: bids are public and bidders compete actively against one another. sealed bid: bidders place their bids privately. 2. How price is determined: People pay what they actually bid. People pay another bidder s bid, usually the next highest bid. These two distinctions lead to four major auction types: Open outcry English auctions Open outcry Dutch auctions Sealed bid first-price auctions Sealed bid second-price auctions. 10 / 39

11 1. Open-Outcry English An English auction is an open-outcry auction in which the price increases until there is only one standing bid. The last bidder wins the item and pays the bid. English auctions are commonly used to sell real estate, foreclosed homes, cars, and antiques and are popular to raise money for charity. 11 / 39

12 Optimizing in an English Auction Exhibit 17.2 Bidder Valuations for Raiders Tickets Say that the auctioneer begins at a price of $25, all five bidders would bid. When bidding reaches $50, Eli will no longer bid. This process continues until price reaches $200. Only Ashley will bid. Ashley wins the Raiders tickets and pay $200, with $50 of consumer surplus. 12 / 39

13 It is a dominant strategy to bid until the price is above your value for the item. The Nash equilibrium is for everyone to bid in this manner. In equilibrium, the winner will be the highest-value bidder, and she will pay a price equal to the second-highest value, the seller should expect to receive approximately $200 in revenues. 13 / 39

14 2. Open-Outcry Dutch The Dutch auction is an open-outcry auction in which the price decreases until a bidder stops the auction. The bidder who stops the auction wins the item and pays that bid. The Dutch auction is an open-outcry descending price auction, whereas the English auction is an open-outcry ascending price auction. Dutch auctions are used by the Department of the Treasury in the U.S. to sell securities. 14 / 39

15 Optimizing in a Dutch Auction Bidding starts at $500. No one bids since this is above everyone s limit. Auction price then is lowered down to $250. If you are Ashley, what do you do? Bid at $250 with zero surplus or let it ride? How about $240? The higher she bid, the lower her surplus, but also the higher the likelihood that she ll be the first bidder and win the tickets. 15 / 39

16 Let s assume Ashley is risk neutral. Ashley knows how many bidders there are, but doesn t know their highest values. She has 4 competitors. There are totally 5 bidder in the auction. Her optimal bid = 4 5 $250 = $200. (Why?) It turns out that this type of strategy is a Nash equilibrium for all bidders. In general, as the number of bidders gets really low say, just two bidders you bid much less aggressively. Ashley should bid $250 1/2=$125 with two bidders. Bid at $200, Ashley will receive $50 in consumer surplus, and the sellers receives $200 in revenues. The expected revenues are the same under English and Dutch auctions. 16 / 39

17 3. Sealed Bid: First-Price Auction Unlike open outcry auctions, sealed bid auctions are private and submitted simultaneously. The winner is the person who has submitted the highest bid and pays a price equal to her bid. If you are Ashley, what do you bid? Ashley s dilemma here is exactly the same as it was in the Dutch auction bidding enough to win the tickets, but not so much that she doesn t get any surplus. So she should bid $200, and everyone else should bid 4/5 of their maximum value. Ashley wins the tickets and gets $50 of surplus. 17 / 39

18 4. Sealed Bid: Second-Price Auction In sealed bid second-price auctions, the highest bidder pay a price equal to the second-highest bid. What should Ashley bid? Three choices: Bid more than $250 Bid less than $250 Bid exactly $250 It is a dominant strategy to bid exactly your willingness to pay for the item. Bidding $250 is a dominant strategy for Ashley in this case. Why? 18 / 39

19 A. Why shouldn t Ashley bid more than $250?) e.g. $ 350 i. If the second-highest bid is less than $250, e.g. $200. She would have done just as well by bidding her value $250 she gains nothing by bidding more than her value. ii. If the second-highest bid is higher than $250, e.g. $300. If Ashley wins, she has to pay an amount that is greater than her value, leading to negative surplus. Anytime you bid above your value in a sealed bid second-price auction, you expose yourself to losses at no gain. 19 / 39

20 B. Why shouldn t Ashley bid less than $250? e.g. $150 If other bids are close to her value, e.g., highest bid is $200. If Ashley bids less than $200, she loses the tickets, even though she values them the highest. If other bids are very low, so that the highest bid is, e.g. $100. Ashley could win the auction by bidding her value $250 and still pay $100. There is no advantage to bidding below $250. Anytime you bid below your value in a sealed bid second-price auction, you gain nothing and you risk not getting the good even though it is selling below your valuation. 20 / 39

21 Therefore, in a sealed bid second-price auction, it is a dominant strategy to bid one s value. Bidding their values is a Nash Equilibrium. In all four auctions the winnder is the bidder with the highest valuation. All four auctions have the same expected revenue. 21 / 39

22 The Revenue Equivalence Theorem Exhibit 17.3 Summary of Revenue Determination in the Four Auction Types In all four cases, the bidder with the highest value (Ashley) wins. It is not necessarily the case the each auction format will generate the same revenue, the result is that they will generate the same expected revenue. This is known as the revenue equivalence theorem: the four major auction types will, in expectation, raise the same amount of money for the auctioneer. 22 / 39

23 William Viekrey, a Nobel Prize-winning economist, was the first to point out the revenue equivalence theorem. He went even further to develop the following insights. Bidder should view Dutch auctions and sealed bid first-price auctions in the same way. A bidder in the Dutch auction should wait until the price falls to the exact amount she would have bid if she had been participated in a sealed bid first-price auction. In both the English auction and the sealed bid second-price auction, dominant strategy are at work. 23 / 39

24 Q: How should you bid in an ebay auction? 24 / 39

25 Chapter 17 Economist David Reiley ran auctions on the Internet to test whether real-world bidding behavior follows the predictions of auction theory. He purchased over $2,000 of Magic cards a collectible card game and resold them via the four auction formats. 25 / 39

26 His basic procedure was to auction two copies of the same card in two different auction formats to make direct comparisons of the revenue earned in each one. Reiley found that he could expect to earn $0.32 more selling the card through a Dutch auction than through a sealed-bid first-price auction. (the cards sold for $4.50 on average). He found that there were not significant differences between bidding in an English auction and a sealed bid second-price auction, consistent with the revenue equivalence theorem. 26 / 39

27 17.2 What Determined Outcomes? A different form of exchange is bilateral bargaining that has one seller actively negotiating with one buyer over the terms of trade. The most important element that determines final outcomes is called bargaining power, which has two components: the cost of not coming to an agreement the influence of one participant over the other 27 / 39

28 power relates to who holds the chips or who have the power in the negotiations. The person who has (1) a lower cost of not coming to an agreement (has other options) (2) a greater influence over the other person, has the bargaining power and holds the chips. 28 / 39

29 in Action: The Ultimatum Game Exhibit 17.4 The Ultimatum Game The person with no bargaining power (Responder) get nothing? If you were a Proposer, how much would you choose to offer? The lowest possible amount say, one penny? If you were the Responder, would you accept one penny? 29 / 39

30 Proposers usually end up with more than half of the $10 when Responders accept their offer. When Responder does not know how much money there is to split, the Proposer s gains are much closer to the entire $10. Agents with a reputation for being a tough bargainer have more bargaining power. 30 / 39

31 and the Coase Theorem This is Adam and Barb. Adam wants a divorce; Barb does not. 31 / 39

32 Suppose Adam is willing to sacrifice $5,000 to obtain a divorce and Barb is willing to sacrifice $10,000 to avoid a divorce. If they live in a state that requires two people to seek a divorce, ( need two to divorce ) who has the bargaining power? Can Barb be persuaded to divorce? If they live in a state that requires only one person to seek a divorce, ( need only one to divorce ) who has the bargaining power? Can Adam be persuaded to stay married? 32 / 39

33 Exhibit 17.5 The Coase Theorem in Action No matter whose side the law falls on, the decision to (not) get a divorce does not change. Because divorce laws determine the distribution of bargaining power, they have an impact on how the gains from the efficient outcome is divided. 33 / 39

34 Q: Who determines how the household spends its money? 34 / 39

35 Regarding a dollar in the pocket of one spouse the same as a dollar in the pocket of the other is called a unitary model. If we instead think of the household decisions as determined by a bargaining game, how will things change? In the late 1970s, the UK changed the receipt of child benefit income from fathers to mothers in two-parent families. There was a dramatic shift toward increased expenditures on women s and children s clothing relative to men s clothing. 35 / 39

36 Economist Nancy Qian found that an increase in the value of tea, which is generally produced by women in China, improved female survival rates. Price increases in tea influenced educational attainment of both boys and girls by about 0.2 years. Increasing male income (through increases in the value of orchard products) by the same amount actually decreased educational attainment of girls and had no effect on the educational attainment of boys. The likely explanation is that women care much more about the health and education of their children than their husbands do, and when they earn more, they spend more more to improve these outcomes. 36 / 39

37 Sex Ratios Change Power Too Another channel for increasing female bargaining power is the sex ratio the ratio of men to women. As sex ratio rises, women become relatively more scarce and therefore will have greater bargaining power. Because one-child policy did not apply as strictly to China s ethnic minorities, and because one-child policy creates a more distorted sex ratio, the sex ratio in areas with lower share of minorities is higher than areas with high shares of minorities. 37 / 39

38 John List and colleagues found that in areas where sex ratios are higher, female bargaining power is stronger in that women report more decision-making power, are more likely to handle household finances, and are more likely to have the collective allocation choice match their private choice. 38 / 39

39 勞工是否有 bargaining power ( 議價能力 )? 議價能力大小如何決定? 39 / 39