EC930 Theory of Industrial Organisation Auctions/Bargaining/Pricing (week 5)

1. EC930 Theory ofIndustrial OrganisationAuctions/Bargaining/Pricing(week 5) 2013-14, spring term

2. Outline: Price Discrimination – charging different prices to different consumers Bargaining – pricing to split the surplus and implications for merger analysis (I) Case: Wembley-O2 merger Auctions – pricing when we don’t know demand General informational assumptions English Auctions (ascending bids) – bid valuation Dutch Auctions (descending bids) – bids shade down valuation Sealed Bid Auctions (in brief) Choice of auction design – revenue equivalence (in brief) The “Winner’s Curse” – systematic overbidding Readings: Lecture notes 4 Problem Set 5 Game Theory Appendix Cabral – ch 10; Tirolech 3

3. So Far… Instruments for Capturing Surplus: Market structure (eg entry, differentiation) Market Conduct (eg dominance, strategic variable) Contract Structure/Conditions of Sale (eg switching costs) We have not looked at pricing. We will do this today. Three passes – price discrimination very briefly: capturing surplus when you know a lot about demand and can prevent arbitrage bargaining: capturing surplus when buyer has power auctions – capturing surplus when you know little about demand

4. Price Discrimination A firm that sells all units at the same price will not capture some consumer surplus, in general. This is even true for a monopolist. This suggests a price discrimination strategy, where each consumer is charged a different price, reflecting his/her willingness to pay. For a monopolist, for example, this results in a larger area of profit and no deadweight loss, so it is good for social surplus as well: P CS for monopolist who prices uniformly PM Profit for monopolist who prices uniformly Profit for monopolist who perfectly price discriminates MC MR Demand Q

5. Other types of price discrimination are possible as well: Second Degree Price Discrimination: different units of the good priced differently, but all consumers face the same pricing schedule. They “self select” into different end prices. Third Degree Price Discrimination: different groups of consumers face different price schedules. But all these types of price discrimination face several barriers in real markets: Avoiding arbitrage. Learning the willingness to pay of buyers. Avoiding competition. If arbitrage is a problem that cannot be controlled, then uniform pricing may be the right strategy, regardless of competition, where little buyer power. If arbitrage is not a problem and consumer valuations are known, then price discrimination is probably a good strategy as long as competition not too fierce…

6. In some common markets, competition is not a problem: Technology markets (if sellers have some monopoly power via a patent over the item for sale) Regulated markets where monopoly sanctioned (such as some energy markets) Markets with significant differentiation and limited entry (airline landing slots) But what if few buyers and each sale unique? Technology markets, eg. We have implicitly assumed that buyers have no power… What if valuations are not known? We have assumed that demand is known so far… but this is not always a good assumption. How do we price in such cases? Will do *brief* survey… and will not deal with strategies of “pricing to learn demand”.

7. Bargaining All bargaining situations have in common: the total payoff to the parties should be greater than the sum of the individual payoffs to the parties so that “surplus” exists to be split. These gains may not materialise, but they need to be anticipated. eg, may hope for ticket sales at a venue but fans may not purchase Bargaining is not zero-sum in the sense that if surplus exists, the parties wish to divide it… but if no agreement reached, then the parties for sure get zero. Implicit threat is this zero alternative vs. positive gains for one/both parties. The final agreement in reality depends on many complexities that we will not investigate. Consider the Nash cooperative solution:

8. A and B split a total value v that they can only achieve if reach an agreement. If no agreement, A gets a and B gets b. (“backstop payoffs” or “reservation payoffs”) a+b < v so that there is a positive surplus from bargaining. Consider the following rule: Each player gets reservation payoff plus share of surplus Such that A gets a + h(v-a-b) and B gets b + k(v-a-b). x = a + h(v-a-b)  x-a = h(v-a-b) and y = b+k(v-a-b)  y – b = k(v-a-b) In other words, surplus is divided in ration k:h or (y-b)/(x-a) OR y = b+(k/h)(x-a) Further, if all the surplus is divided we have x+y = v OR y = v-x These are equations of two lines in x,y space:

9. y P is the backstop or reservation payoff for the two players. Q is the payoff after agreement. y = b+(k/h)(x-a) Q ● b ● P V=x+y a x

10. We can interpret h and k as bargaining power (often they are set to ½) If we specify more generally that y = f(x) for all gains to be exhausted (here, v = x+y) so that we bargain along the efficient frontier, then the Nash cooperative solution such as point Q solves: Max (x-a)h(y-b)ks.t. y = f(x) Where x and y are outcomes a and b are backstops h + k = 1 Often, we assume h = k = ½ so that we maximise surplus by splitting the gains relative to backstops. y (x-a)h(y-b)k = constant y = f(x) x

11. Wembley-O2 merger Wembley capacity 12,500; O2 capacity 20,000 (owned by AEG) Industry: Act and its Manager expresses interest to Promoter who engages venue and sets ticket prices for final customer. Venue price fixed based on projected ticket sales. Most of Wembley revenue comes from venue hire; Most of O2 from aftermarket sales (food, parking, etc) Three segments: < 5000; 5000-12,500; >12,500 Only Wembley and O2 in 5000-12,500 segment. (Despite Earls Court, Alexandra Palace and Excel – all differ on other grounds) By any HHI/CR measure, this was a merger to monopoly, then. “Normally”, then, would not be approved.

12. Is the standard Posted Price model the correct one? Bertrand with capacity constraints? Venues do have standard prices for hire but discounts also standard based on these Hence, each customer effectively gets a different price based on discount. Is Price Discrimination the correct one? First degree or maybe Third Degree Price Discrimination? Both these models assume all bargaining power with the purchaser and no arbitrage possibility. Three problems here: First, in <12,500 segments competition exists. Second, share of profits going to promoter is large and highest for >12,500 segment where only one supplier Third, average discount same across capacity segements

13. Natural Experiment: Can AEG extract more profit if fewer competitors? <5000 lots of competition; 5000-12,500 two competitors >12,500 monopoly

14. Why no evidence of market power as market concentrates?

15.  Maybe there is buyer power Evidence: interviews of how purchase occurs in this industry. few promoters O2 loses a lot if dark night O2 owner, AEG, has many venues throughout world that same promoters feed so multi-market effects to raising price at O2. Also, evidence from discounting behaviour: Non-peak discounts about the same as peak discounts: no market power exercised when “demand high” Small promoter discounts about the same as large promoter discounts: no market power exercised against promoters for whom don’t interact in other markets. No greater discounts in segments where O2 and Wembley compete than in monopoly segment.  Bargaining model appropriate?

17. If one accepts a bargaining framework, a shift in bargaining power may shift rents but does not affect sales volume or overall welfare if bargaining efficient. No reason to expect merger will change efficiency of bargaining. Further, change in business model at Wembley to include greater revenues from footfall at ancillary services mean that ticket prices may actually fall due to merger from current level upon modifications to venue.

18. Other issues here: not clear venues are substitutes – some acts play at both differentiate on more than just capacity – also look and feel and image of artist Evidence? Where Wembley booking team expected 6000-12,500 attendance (possible to book O2), O2 generally not viewed as major competitor and where O2 booking team viewed event as <12,500, Wembley generally not considered as main competitor differentiation on more than capacity. No smaller margins for arenas where booking team had identified competition between Wembley and O2. For events booked at one venue and playing at other, switch not due to price considerations but rather other elements (such as ability/time to build sets). We will do further analysis later in term.

19. Auctions Auctions are a way to elicit buyer valuations and also extract a high amount of surplus. Auctions get around arbitrage to some degree by ensuring that the item is sold to higher valuation customers (so resale not profitable). They get around unknown valuations by ensuring that bids reveal these. We’ll study some auction mechanisms today for the special case where there is only a single item to sell… and where the mechanisms are about as simple as possible …in particular, we won’t look at auctions where it costs to enter in the first place or where the seller sets a reserve price – as is common on eBay. For those interested in more complex versions, see Klemperer readings in references.

20. Auction Markets Posted price: a fixed “reservation price” is set by seller and all buyers take this price as given. Non-posted price: the buyers offer prices, and the seller selects among these offers in some way eg, in a second price auction, the highest bidder wins but pays the second highest price

21. Examples: Internet/eBay sites Broadcast rights to Premiership games Art sales House sales some industrial markets (basic chemicals, energy markets) limited resources (gas/oil, radiotransmission spectrum, timber) privatisation sales Treasury Bills Historical example: Praetorian Guard auction off the entire Roman empire in 193 AD after killing previous emperor. DidiusJulianus outbids competitors and becomes emperor, but is beheaded by Septimus Severus shortly after… We’ll look at Winner’s Curse, but not such an extreme version.

22. 4G auction (results announced last February) At auction: airwaves to transmit mobile internet signals. Devices to pick up such signals owned currently by about half of UK population. New spectrum of radio frequencies – amounting to ~70% of the current spectrum used – to be added for new transmission capacity. (freed up when TV switched from analog to digital recently). Main benefit to end customers is speed of transmission and coverage, but this will require additional infrastructure (such as transmission masts) not currently in place. To be added by mobile companies. Auction Design: 7 companies participated, but some of spectrum reserved for a certain number of firms, including some reserved for possibly a new entrant. Some obligations for winners (such as coverage). Initial round with reserve prices (minimum prices). Later rounds of 15 minutes or more duration, with bids published at the discretion of seller. Earnings: £2.34Bbn, less than then £3.5Bbn forecast by Chancellor or £4BBn by analysts (about £40 pp earned).

23. 3G auction (2000): Per person revenues varied greatly by country: 600 euros per person (Germany, UK) 100 Austria 170 Netherlands 240 Italy (predicted: 400 euros pp) Switzerland (predicted: 400 euros pp) Value of spectrum unknown at the time. Possibly more uncertainty on value now. Designs differed greatly among these auctions, and so did revenues compared to predictions. Today we’ll just go through some basics of auctions. We’ll come back to some of the pitfalls of auctions informally today and then again later in the term.

24. Informational Assumptions: Possibilities we’ll consider: (Certain) Independent Private Values: Individual knows his/her own worth for item, vi, which may differ. All individual know that others’ valuations drawn from distribution F over [0, V] (Uncertain) Independent Private Values: Individuals get a signal of own valuation, si = vi+i, where E(i) = 0, cov(i,j) = 0 for example, beliefs – based on own studies of geology – about value of gas tract may differ substantially.

25. Informational Assumptions: Possibilities we’ll consider: Common Values: Individuals get a signal of own valuation, si = v+i, where E(i) = 0, cov(i,j) = 0 …so that all individuals have same true valuation of item. …This means that others’ bids are informative about v.

26. Canonical Auction Mechanisms – (Certain) independent private values • Open Ascending Price/English Auction • Eg, consider all bidders in a room with hand raised. As auctioneer calls out higher • prices, hands go down. Last hand up wins at bid at which second last hand dropped. • For bidder with value vi, at what level should hand fall? • Hand should not fall above vi since would obtain lower net surplus, vi – p, at price • above vi than if simply left auction. • Hand should not fall below vi since, if others still in auction, would obtain positive • surplus by staying in and zero from dropping out. If others have dropped out of • auction, then no cost to keeping hand up (since price rises no further than bid at • which second last hand dropped). • Hence, dominant strategy is to keep hand up until vi and then drop hand. • Equilibrium is that highest valuation customer wins at second highest valuation. • Efficient since highest valuation customer wins. • For uniform distribution on [0, vmax], expected highest bid = (n-1)/(n+1)vmax.

27. Think Question: Why did Kiyoshi Kimura bid so much for bluefin tuna in first fish sale of year in Tokyo in 2013? Probably expected to lose money on it ($1.76 million  10,000 pieces of sushi)? Why was price less than 5% of 2013 price this year, even though Kimura says quality the same? Answer 1(?): The bid reflected the true value. There were non-monetary considerations in the bidding…including personal prestige for owner of restaurant chain or “good luck”. There may have been some indirect reputational issues for the restaurants resulting in higher prices …Probably not large enough to justify bidding price per se. Answer 2 (?): “Overheated bidding last year” – the bids reflected auction design. …we have no “overheating” in our equilibrium. Where might this come from?

28. Descending/Dutch Auction Examples: Tulips Fish (sometimes) TV Channel Sales Eg. As auctioneer calls out lower and lower price, the first hand to be raised wins the item at the announced price. For bidder with valuation vi , when should hand be raised? If raise at value vi, then obtain zero surplus, so this is never best…but waiting longer means that trade–off is the probability of losing (payoff zero) versus the probability of winning at a price less than valuation and obtaining some surplus. Indeed, the optimal strategy will depend on what others do, since if they raise hands at their true valuation, waiting is less attractive to me. If they wait more, I want to wait more as well…but I don’t necessarily know what others’ valuations are so I don’t know what they’ll do for sure. To solve formally, need concept of Bayesian Nash Equilibrium…Won’t do this today.

29. We can solve these for the optimal bidding strategy, b, as a function of the number • of bidders, n, and the valuation of the individual, v: • = optimal bid, b, for uniform distribution. • Hence, we see that as the number of bidders or the valuation rises, the bid rises since • the value is “shaded” less . • This means that the “profit margin” for each bidder decreases as the number of • bidders rises so that “competitive bidding” does, indeed, reduce “profits”. • The equilibrium price in the Dutch auction is equal to the highest bid, b*(vmax). • Will this generate the same revenue as the ascending auction? • The highest bidder’s expected bid is [(n-1)/n]E(vmax). • Uniform distribution on [vmin, vmax] : E(vmax) = n/(n+1)vmax • winning bid = [(n-1)/n][n/(n+1)]vmax= (n-1)/(n+1)vmax

30. We can assert, then, that Seller benefits from more buyers since the price increases with n (in fact, as n approaches infinity, the price approaches the maximum valuation). The buyer does not benefit from more buyers, since the price rises with n. As the number of bidders rise, the Dutch auction equilibrium bidding strategy approaches then English auction bidding strategy of bidding the true valuation; although the price is the same for both (ie, the winning bid) since the English auction only yields the second highest expected bid (=v-v/n). In other words, the shading of the top bid in the Dutch auction reduces the top bid to the expected level of the second bid…So purchasers are able to “figure out” where the second bid would fall and adjust their bid accordingly. Similarly, the payoffs for the two types of auction are the same. This is a “revenue equivalence” result, which is relatively general, under certain assumptions that we have satisfied here in this simple example, but which may not hold more generally (such as independent valuations and risk neutrality).

31. Sealed Bid First Price Auction Sealed Bid Second Price/Vickrey Auction Eg. All bidders submit bids in a sealed envelope (or electronic message). Winning bid is the highest bid in a first price auction; it is the second highest bid in a second price auction. First Price: As in the Dutch auction, submitting true valuation in the envelope only yields zero surplus at best, so it is always better to “shade” the bid. How much depends on the same trade-off as in the Dutch auction. The two types are equivalent, in fact, and are efficient. Second Price: As in the English auction, the winning price depends on another bidder’s valuation, so the dominant strategy is to bid the true valuation (to increase the chance of winning). This auction is equivalent to the English auction and is efficient.

32. Winner’s Curse: Canonical Auctions with Common Values Now, bidders only receive a signal of their true valuation… Suppose they bid as they did before. This would mean that an individual with a higher signal would tend to win in our canonical auctions. But this means that one is more likely to win if one has overvalued the item. This is the essence of the “winner’s curse”: if one wins, one is likely to have paid too much (more than v)!

33. Example: Suppose v = 500 A and B are in a Vickrey (second price, sealed bid) auction. ε distributed uniformly on [-400, 400] – so that the chance of receiving a signal anywhere between 100 and 900 is equal. si = v+εi What if both bidders submit their signals (ie the best information they independently have about their true valuation)?

34. Example: We know that B’s signal is less than A’s if A wins. How much less? Since the signals are distributed uniformly, we expect that B’s signal is the average signal over the range that it must occur (between the minimum of 100 and a maximum of A’s signal). Expected Bid (B) = Hence, A receives her true value, 500 – expected price = , decreasing in sA In fact, if A receives the most optimistic signal possible, she receives no surplus at all in expectation. She does not receive negative surplus, though, in expectation even at this very optimistic signal.

35. Example: What if we had three bidders, A, B and C? (And A wins, as before). We know that B’s and C’s signals are less than A’s if A wins. Say SC <SB <SA Since the signals are distributed uniformly, we expect that the two smaller signals are the average signal over the range that they must occur (between the minimum of 100 and a maximum of A’s signal). Expected bid (C) = Expected Bid (B) =  A obtains: 500 – = 475 – (1/2)sA – (1/4)sB decreasing in sA and sB Now, A can easily receive negative surplus in expectation. While participation probably paid with this bidding strategy and only two bidders, it is not clear that it still pays…

36. Indeed, the winner’s curse is more general in common value auctions since it is generally the case that if bidders only receive signals of their true value, those who are more optimistic also tend to be winners…which opens the door for overoptimistic bidders to win. Rational bidders should bid less aggressively in the presence of the winner’s curse. Note, too, that bidders may decide not to participate in auctions where the winner’s curse may be present. Implication: Recall that an auction that attracts few bidders is less profitable (in expectation) for the seller…This is likely to be the case here.

37. Are all auctions revenue equivalent? In a broader setting than our initial examples (independent value, constant numbers of bidders for each auction, risk neutrality), they may not be. Dynamic (esp ascending) auctions may generate low outcomes if weaker bidders view themselves as unlikely to win since they tend to bid unaggressively even if they enter. (Empirical evidence that takeover battles, which are ascending auctions, tend to generate few bidders if one firm already has a “toehold” shareholding position). Winners curse may generate low outcomes as participants shade their bids and some decline to participate. Since shading varies depending on the type of auction, revenue equivalence may no longer hold. (Second price auctions tend to do better) As we see in the problem set, risk aversion can make the first price auction generate higher bids than the second price auction. So the exact auction design does matter more generally. We will add to this by considering collusion in next lecture.

38. Think question 2: So…why did Kiyomura bid so much for that tuna? Answer (2): Maybe winner’s curse elements – first tuna of the season may have more uncertain characteristics than later tunas of the season…and certainly there is some element of correlation in the bidding since bluefin tuna’s main use is sushi. Other issues in this bid: Reputational issues for future bidding season. This may be like “burning money”. This can signal that likely to win certain bidding contests (so don’t bother/don’t enter bidding against this restaurant – which decreases the number of bidders, lowering the expected price paid by Kiyomura)…maybe “luck for year” operates through this mechanism? It can also signal to investors and others that the chain is very successful and so an investment possibility with little risk (lowering price of money for Kiyomura). May have reputational benefits that are more direct for business – eat at the restaurants also for prestige reasons.

39. Auctions also used for buyers purchasing a service (bidding for lowest price) Eg. Procurement of defence equipment Procurement of externally sourced services in general (security contracts, eg) Procurement of work on a house extension Any other purchase where sellers in competition for a single, differentiated, buyer (desirable students sought by universities, desirable employees…) Here, instead of valuations, the sellers have costs that determine profitability. Bids reflect these in the same way as valuations of buyers in the previous examples, so all former results go through by analogy. Hence, larger number of sellers tends to depress price; however, there is a counter-acting effect when the winner’s curse is present: Since winner’s curse gets worse as n increases, the procurement price tends to rise as number of bidders increases, since bidders attempt to avoid winner’s curse.

40. Summary If we know a lot about demand and can isolate groups well, price discrimination probably best pricing policy…if little buyer power. Otherwise, we may bargain. If we know a lot about demand but can’t isolate groups well, we can use uniform pricing…again, if little buyer power. If we know little about demand, we can use auctions to elicit demand information. While all auction formats yield revenue equivalence in some circumstances, in more generally auction design matters. In particular, dynamic auctions susceptible to collusion (more next lecture) Ascending auctions susceptible to low participation with even moderate asymmetries Winner’s curse affects bid levels and can make second price auctions generate more revenue; on the other hand, risk aversion tends to favour first price auctions. If buyers have power, then different prices may be negotiated for different buyers, but a bargaining framework is the more appropriate model.

41. References Klemperer, Paul (1999) “Auction Theory: A Guide to the Literature”, CEPR Discussion Paper 2163. ______________(2000) “Why Every Economist Should Learn Some Auction Theory”, CEPR Discussion Paper 2572. ______________(2004) Auctions: Theory and Practice. Princeton University Press. (HF 5476 in library. Also 7 day loan in student collection) Dixit, A. and S. Skeath (2009) Games of Strategy, 3rd Edition. (QA 269.D5 in library) Muthoo, Abhinay (1999) Bargaining Theory with Applications. Cambridge University Press. (HB 199.M8 in library. Also 7 day loan in student coll’n)