2018년 1월 20일 토요일

[발췌] The Winner's Curse in Bilateral Negotiations


참고: Ray Fisman and Tim Sullivan, The Inner Lives of Markets, Public Affairs, 2016. pp. 55-57.

원출처: William F. Samelson and Max H. Bazerman, “The Winner's Curse in Bilateral Negotiations,” Working Paper. September 1984. Boston University & Alfred P. Sloan School of Manangement, MIT.


※ 발췌 (excerpts):

원출처를 제공하는 자료 1: https://www.researchgate.net/publication/38009562_The_winner%27s_curse_in_bilateral_negotiations


1. INTROUCTION

( ... ... ) However, Bazerman and Neale (1983; Bazerman, 1983) have provided substantial evidence that negotiators deviate from rationality in systematically predictable ways. Short of the ideal of fully rational behavior, how will negotiations proceed? How should an individual negotiate when only imperfect or limited informatin about the negotiation setting is available? When he or she has worse informatin than the other side and both know it? What negotiating procedures are successful in reaching mutually beneficial agreements?

This paper addresses these questions and presents experimental evidence on bilateral bargaiing behavior under uncertainty. A main finding is that [:]

  • under asymmetric information, negotiators systematically deviate from normative behavior and, consequently, fall prey to the "winner's curse"--that is, they consistently (and voluntarily) enter into loss-making purchases and forego profit-making opportunities. 
  • These losses results because subjects act as if the other party has the same information as themselves. For example, many uninformed buyers make expected losses on transactions because they fail to anticipate the informed opponent's profit-making bargaining behaviour. 
  • In turn, informed sellers, when given the opportunity to make price offers, fail to take full advantage of their information advantage. 
  • In short, both negotiators--informed and uninformed party alike--fail to recognize the force of information asymmetry.
The present study extends the analysis of the winner's curse to bilateral negotiations. This phenomenon has been examined for some time in the area of competitive bidding. Researchers (e.g., Carpen, Clapp, and Campbell, 1971; Bazerman and Samuelson, 1983) have asserted that it is common for "winning" bidders in competitive auctions to find that they have overpaid for the acquired commodities. The key point is that bidders tend to ignore the impact of competitor bidding behavior on their own optimal strategy.

The additional research supports the more general conclusion that competitive decision makers systematically ignore the impact that the decisions of other parties can have with respect to their optimal behavior. A good example is the dollar auction exercise (Shubik, 1971; Teger, 1980) in which the highest bidder in an oral auction pays its bid and receives the dollar, and the second highest bidder pays its bid and receives nothing in return. The common result in this auction is an escalating pattern in which individuals bid far in excess of a dollar and which produces significant profits for the auctioneer. Why do bidders get involved? One explanatin is that individuals see the potential for profit early in the auction, and fail to take the perspective of what the auction will look like to other bidders. If the bidder considers the dollar auction from the point of view of both competitors, it is easy to see the benefit of staying out of the auction. Overall, there is substantial evidence that competing decision makers fail to consider the impact of the conditional behavior of the other parties in making decision.[주]2

The analysis of the winner's curse in the negotiation setting relies on the follw[ing] example:
One firm (the acquirer) is considering making an offer to buy out another firm (the target). The complication is that the acquirer is uncertain about the ultimate value of the firm. Though it has reason to believe that the target will be worth more under its management than under present ownersip, the acquirer (even after making its best estimates) does not know the target's ultimate value. Target management, on the other hand, has an accurate estimate of the value and so shares none of the acquirer's uncertainty. In these circumstances, (1) what final price offer should the acquirer make for the target? (2) Alternatively, if the target company has the opportunity to make a take-it-or-leave-it offer, what price should it name? Should the acquirer accept it?

Two features are present in the example above. First, the aspect of the problem of greatest interest to economists is the opportunity for mutual gain. The fact that the company is more valuable in the hands of the acquirer than under present management means that ex post  there is a price at which both sides can profit from the sale. Second, the value of the transaction is uncertain, and one side has has different (better or worse) informatin about the uncertain value than the other. For example, the target firm's management ordinarily has proprietary information about its operations which is not available via published accounting reports or in other forms to the acquirer or other outsiders. (Of course, the acquirer may also have information about the firm's value under new management which the target doesn't have.)

This asymmetry of information should put the less well-informed party on guard. For instance, the management board of the acquiring firm might reason as follows:
The first fact is that we are uncertain about the ultimate value of the target. If we extend an offer to target management and it is accepted, are we going to be sold a ‘bill of goods’? After all, it is more likely that target management will unload an ailing company than a healthy one. By making a low offer, will we simply be getting what we paid for or even less than what we paid for? What constitutes a profit-making offer? Indeed, is there any offer which, if accepted, will provide a positive expected profit from the transaction?
In the reasoning above, the acquirer recognizes the presence of asymmetric information and anticipates the behavior of the better-informed target. Though this reasoning is easy to follow, the evidence suggests that the individuals consistently fail to develop this logic when faced with competitive situations. Rather, an alternative model is proposed to describe the behavior of a significant portion of competitive decision makers. In this model, negotiators behave as if the opponent possesses the same information as themselves--even when they are told that the opponent has better or worse information available. Negotiators make this "naive" assumption about the information and behavior of the opponent in order to simplify their decisions in a complex environment.

This paper presents the results of a series of bargaining experiments designed to test equilibrium and naive models of bargaining behavior under uncertainty, where, as in the example above, one party is less well-informed than the other. Our approach and conclusions are both normative and positive in nature. The normative analysis offers a prescription for a rational individual's optimal bargaining strategy and examines the welfare implications of such behavior. As will be shown, even very simple bargains under uncertainty require individuals to make subtle probabilistic inferences about the potential value of the transaction. Moreover, in contrast to agreements under certainty, bargains under uncertainty present a direct conflict between individual self-interest and group welfare. Optimal bargaining behavior may preclude the attainment of mutually beneficial agreements even when it is common knowledge that such agreement exist. In short, a normative analysis identifies imperfect information as a potential barrier to mutually beneficial transactions.

A positive analysis investigates the actual bargaining behavior of individuals under laboratory conditions. ( ... ... )  Indeed, in one bargaining experiment, the vast majority of subjects actually pursued bargaining strategies predicted to generate expected losses on average--a strategy which no rational (risk neutral or risk averse) bargainer would voluntarily pursue. Similarly, informed sellers, when given the opportunity to make price offers, failed to take full advantage of their information advantage.

A final result is that actual subject bargaining behavior, though individually suboptimal, is collectively advantageous. Because observed bargaining strategies are more "cooperative" than the normative benchmark, the frequency of agreements exceeds that which would pertain in equilibrium. ( ... ... )

Section 2: three different versions of the basic negotiation model used throughout the paper.
Section 3: normative and "naive" analysies of each version.
Section 4: an experimental test of the negotiation model.  ( ... ... )


2. THE NEGOTIATION MODEL

The basis for the experiments that were conducted consists of three versions of a short bargaining exercise entitled “Acquiring a Company”, which are reproduced in the appendix. The generic elements of the bargaining model underlying the exercise can be formally described as follows:
A target and potential acquirer are negotiating over the sale of a good of uncertain value. Denote the monetary value of the good to the target by v. This value is known by the target but not by the acquirer who regards v as a random variable with cumulative probability distribution F(v). In turn, denote the value of the good to the acquirer by w(v). This functional notation indicates that the value of the good to the target may vary with the value to the acquirer. Whatever the value of v, the good is always worth at least as much to the acquirer than to the target--that is, [w(v)- v]?? for all possible v. Both sides know the functions F(v) and w(v), but only the target knows the specific values of v and w. Concerning these last two values, the acquirer has only the probabilistic information given by F(v).

In the experiments, three different versions of the negotiation exercise were used. These were created by varying slightly the parameters of the negotiation situation. Employing the notation introduced above, the main features of each of the versions can summarized as follows:

Version 1. w(30) =  30                       0   for v < 30
                           and    F(v) =  1/2  for 30 ≤ v ≤ 60
           w(60) = 130                     1   for v ≥60

Version 2. w(v) = v + 30      and    F(v) = v/100 , for v ∈ [0, 100]

Version 3. w(v) = 1.5v        and    F(v) = v/100 , for v ∈ [0, 100]

Version 1 is the simplest of the three and employs a discret probability distribution over two values of v. Note that the acquirer's value is strictly greater than the target's value only in the case that v = 60. In turn, verions 2 and 3 shae a uniform distribution of possible values but differ in the functional form describing the acquirer's 'absolute advantage' for the good, w(v)-v. In version 2, the acquirer's advantage is constant for all v. In version 3, the advantage is proportional to v.[주]3

The bargaining procedures employed in the experiments are of a very simple kind. One party, either the acquirer or the target, makes a "fist and final" price offer which the other can accept or reject.[주]4  If the offer is accepted, a sale takes place at the offer price. If not, there is no sale, and no money changes hands. In corprate acquisitions, the most common practice is for the acquiring company to make a tender offer which the target can accept or reject. Alternatively, the target management, cognizant of the firm's true value, could name a "buy out" price. In the experiments, both procedures, acquirer and target offers, were used.


3. NORMATIVE AND NAIVE HYPOTHESIS

The analysis of the experimental results relies on two competing hypotheses about subject bargaining behavior. Under normative behavior, subjects correctly account for the presence of informatin asyemmetry and employ optimal (i.e., equilibrium) bargaining strategies. Under naive behavior, bargainers employ simpler strategies which ignore the information asymmetry. Specifically, naive model predicts that bargainers will act as if the opponent has the same information as themselves. We examine both normative and naive hypotheses under 1) acquire "bids" and 2) target offers.

Acquirer Bids (Normative Behavior).   First, consider the acquiring company's choice of bid. What price should it name for the target company's shares in each of the three versions of the bargaining model? Given the facts of Version 1, the management board of the acquiring company should reason as follows:
Any price bid between $30 and $60 will be accepted only by a low valued company worth $30. In the range, no profit is possible and the higher the price bid the larger is the possible loss. However, a price in excess of $60 per share will ^always^ be accepted by the target. Since the average acquisition value is (1/2)(30) + (1/2)(130) = $80 per share, a profit is possible at any price in the range $60 to $80 per share. Clearly, the most profitable bid is $60 per share (or if necessary, $60 + ε where ε is in the positive neighborhood of zero).

( ... ... )

Similar reasoning can be applied to determine the acquirer's optimal bid in Version 2. The management board reasons as follows:
Suppose we make a bid of (let us say) $30 per share. How often will this bid be accepted? The answer must be 30% of the time, since the target will accept if and only if the value under current management v is less than the bid. (All values between $0 and $100 per share are equally likely). What is the average value under curent management of companies thus sold? $15 per share, since all values between $0 and $30 are equally likely. The average value under our (the acquirer's) management? $45 per share, since the company is worth $30  per share more in our hands. Thus, in the event of an agreement, the average profit is $45 - $30 = $15. In turn, the acquirer's overall expected profit is (0.3)(15) or $4.5 per share.
Once again, profitable bargains are possible. The acquirer's expected profit is zero at a price of $0 per share and also at $60 per share (as is easily checked). For bids between these values, the firm earns a positive expected profit, and above a price of $60, it's expecte profit is negative. The acquirer's maximum expected profit occurs at P(A) = $30 per share (halfway between the "break-even" prices). In fact, the bid P(A) = $30 stochastically dominates any other bid -- that is, it offers strictly better odds of better profit outcomes.[주]5  Thus, any profit maximizer, regardless of his risk attitue, shoud choose P(A) = $30.

There is a subtle but significant differences between the second and third versions of the bargaining experiment. In Version 3, the company, whatever the target's value, is worth 50% per share more to the acquirer that to the target, i.e., w(v) = 1.5v for all v. With this modification and employing a line of reasoining analogous to that of Version 2, the acquiring company's management board reasons as follows:
A bid of (let's say) $60 per share will be accepted 60% of the time by targets with an average value of $30 per share. Thus, the average acquisition value of such a company is 50% more or $45 per share. If accepted, our profit from this bid is, thus $45 - $60 or -$15 per share. Consequently, a $60 per share bid is ill-consdered.
It's not hard to see that the same kind of reasoning applies to ^any^ positive price bid the acquirer might consider making. On average, the acquirer obtains a company wot 25% less than the price it pays. Thus, the acquirer's best bid is $0 per share, wiich, of course, is tantamount to making no bid.

Version 3 offers a graphic illustration of the tension between the opportunity for mutual gain and the impact of asymmetric informatin in simple bargaining situatins. Even though in all circumstances the firm is worth 50% more to the acquirer than to the target, any tender offer that the acquiring firm might make results in a loss on average. Indeed, the source of this barrier to trade stems from the presence of adverse selectin. A given bid will be accepted only by "low-value" companies with the result that the average value of acquisition falls short of the purchase price.

To sum up, the uninformed acquirer's optimal price bis are $60, $30, and $0 in the respective versions of the bargaining experiment.

( ... ... )


출처 2: Economics of Strategy (David Besank 외, John Wiley & Sons, 2009). 구글도서.

Identifying Undervalued Firms

Finally, a firm's shareholders may benefit from diversification if its managers are able to identify other firms that are undervalued by the stock market. Suppose, for ex., that firm B's stock is currently trading at $80 per share, but the manager of firm A determines that firm B is actually worth $100 per share. If firm A can purchase firm B for $80 per share, firm A will profit by $20 for each share of firm B purchased, even if no gains in efficiency are realized through the merger.

One can be somewhat skeptical of this justification for corporate diversification, esp. when the business of the acquired firm is unrelated to that of the acquiring firm. First, this argument requires that the market valuation of the target firm is incorrect ^and^ that no other investors have yet identified this fact. ( ... ... )

Second, announcement of merger proposal attract attention, frequently leading other potential acquirers to bid for the target firm. Bidding wars are not uncommon, and they serve to reduce the profit an acquiring firm can hope to earn through a merger. Consifer Verizon's February 2005 offer to purchase MCI for $6.75 billion. A rival telecom firm, Quest, quickly entered the bidding with an even higher offer. ( ... ) Verizon purchased MCI for $8.5 billion.  ( ... ... )

Third, and perhaps most troubling, is the observation that successful bidders in auctions and similar sales arrangements tend to suffer from the "winner's curse." Consider a group of acquiring firms bidding for a target. Each bidder may have an estimate of the value of the target, and each will drop out of the bidding as the price surpasses that estimate. The firm with the most optimistic assessment of the target's value will win the bidding. Has the winner paid a price low enough that it can earn a profit from the purchase? Given that all other bidders' estimates of the target's value are below the final purchase price, it is likely that the winner has overpaid. As Max Bazerman and William Samuelson point out in their article "I Won Auction but Don't Want a Prize," unless diversifying firm knows much more about the target than other bidders do, it will probably pay too much to "win" the bidding.[주]13


출처 3: Anomalies: The Winner's Curse (Richard H. Thaler, Journal of Economic Perspective, Vol.2, No. 1. Winter 1988. pp. 191-202.)

( .... ... ) Next time that you find yourself a little short of cash for lunch, try the following experiment in your class. Take a jar and fill it with coins, noting the total value of the coins. Now auction off the jar to your class (offering to pay the winning bidder in bills to control for penny aversion). Chances are very high that the following results will be obtained: (1) average bid will be significantly less than the value of the coins (bidders are risk averse); (2) the winning bid will exceed the value of the jar. Therefore, you will have money for lunch, and your stuent will have learned first-hand about the "winner's curse."

The winner's curse is a concept that was first discussed in the literature by three Atlantic Richfield engineers, Capen, Clapp, and Campbell (1971). The idea is simple. Suppose many oil companies are interested in purchasing the drilling rights to a particular parcel of land. Let's assume that the rights are worth the same amount to all bidders, that is, the auction is what is called a ^common value^ auction. Further, suppose that each bidding firm obtains an estimate of the value of the rights from its experts. Assume that the estimates are unbiased, so the mean of the estimates is equal to the common value of the tract. What is likely to happen in the auction? Given the difficulty of estimating the amount of oil in a given location, the estimates of the experts will vary substantially, some far too high and some too low.  Even if companies bid somewhat less than the estimate their expert provided, the firms whose experts provided high estimates will tend to bid more than the firms whose experts guessed lower. Indeed, it may occur that the firm that wins the auction will be the one whose experts provided the highest estimates. If this happens, the winner of the auction is likely to be a loser. The winner can be said to be "cursed" in one of two ways: (1) the winning bid exceeds the value of the tract, so the firm loses money; or (2) the value of the tract is less than the expert's estimate so the winning firm is disappointed. Call these winner's curse versions 1 and 2 respectively. Notice that the milder version 2 can apply even if the winning bidder makes profit, as long as the profit is less than expected at the time the bid was made. In either version the winner is unhappy about the outcome, so both definitions seem appropriate.

The winner's curse cannot occur if all the bidders are rational (see Cox and Isaac, 1984), so evidence of a winner's curse in marketing settings would constitute an anomaly. However, acting rationally in a common value auction can be difficult. Rational bidding requires first distinguishing between the expected value of the object for sale, conditioned only on the prior information available, and the expected value conditioned on winning the auction. Even if a bidder grasps this basic concept, version 2 of the winner's curse can occur if the bidder underestimates the magnitude of the adjustment necessary to compesate for the presence of other bidders.

In a first price auction there are two factors to consider, and they work in opposite directions. An increase in the number of other bidders implies that to win the auction you must bid more aggressively, but their presence also increases the chance that if you win, you will have overestimated the value of the object for sale--suggesting that you should bid less aggressively.[주]1  Solving for the optimal bid is not trivial. Thus, it is an empirical question whether bidders in various contexts get it right or are cursed. I will present some evidence, both from experimental and field studies, suggesting that the winner's curse may be a common phenomenom.


Experimental Evidence

The jar of coins example cited above has, in fact, been conducted under experimental conditions by Max Bazerman and William Samuelson (1983). Their subjects were MBA students taking microeconomics classes at Boston University. The objects auctioned off were jars of coins or other obects such as paper clips valued at four cents each. Unknown to the subjects, each jar had a value of $8. Subjects submitted sealed bids and were told that the highest bidder would receive the defined value of the object less his or her bid. A total of 48 auctions were conducted, 4 in each of 12 classes. No feedback was provided until the entire experiment was completed. Subjects were also asked to estimate the value of each jar (point estimates and 90% confience limits), and a $2 prize was offered for the best guess in each class.

The estimates of the actual values turned out to be biased downward. The mean estimates of the value of the jars was $5.13, well below the true value of $8.00. This bias, plus risk aversion, would tend to work against observing a winner's curse. Nevertheless, the mean winning bid was $10.01, producing an average loss to the winning bidder of $2.01. Clearly these experiments do not require large NSF granst!

Samuelson and Bazerman (1985) have run another series of experiments about the winner's curse in a different context. Try this problem yourself before continuing.
In the following exercise, you will represent Company A (the acquirer) which is currently considering acquiring Company T (the target) by means of a tender offer. You plan to tender in cash for 100% of Company T’s shares but are unsure how high a price to offer. The main complication is this: the value of the company depends directly on the outcome of a major oil exploration project it is currently undertaking.

The very viability of Company T depends on the exploration outcome. In the worst case (if the exploration fails completely), the company under current management will be worth nothing--$0 per share. In the best case (a complete success), the value under current management could be as high as $100 per share. Given the range of exploration outcomes, all share values between $0 and $100 per share are considered equally likely. By all estimates the company will be worth considerably more in the hands of Company A than under current management. In fact, whatever the value under current management, the company will be worth 50% more under management of Company A than under Company T.

The board of directors of Company A has asked you to determine the price they should offer for Company T's shares. This offer must be made now, before the outcome of the drilling project is known.
Thus, you (Company A) will not know the results of the exploration project when submitting your effort, but Company T will know the results when deciding whether or not to accept your offer. In addition, Company T is expected to accept any offer by Company A that is greater than or equal to the (per share) value of the company under its own management.
As the representative of Company A, you are deliberating over price offers in the range $0 /share to $150 / shre. What offer per share would you tender? (pp. 131-33)
※ 또 다른 원출처: William F. Samuelson and Max H. Bazerman (1985). "The Winner's Curse in Bilateral Negotiations," Research in Experimental Economics, 1985, 3, 105-137

The typical subject thinks about this problem roughly as follows: The firm has an expected value of $50 to Company T, which makes it worth $75 to Company A. Therefore if I suggest a bid somewhere between $50 and $75, Company A should make some money. This analysis fails to take into consideration the asymmetric information that is built into the problem. A correct analysis must calculate the expected value of the firm conditioned on the bid being accepted. If a bid B is accepted, the the company must be worth no more than B under current management for an average of B/2. Under new management, the average is 150% of this, or 3B/4, wihch is still less than B, so it is best not to bid at all. Thus, this problem produces an extreme form of the winner's curse in which any positive bid yields an expected loss to the bidder.

This experimentation was run in two conditins, one with monetary incentives and one without. The results, as shown in Table 1, are quite similar for the two conditions, with the bids in the condition with monetary incentives somewhat lower. In both conditions over 90% of the subects make positive bids, and a majority are in the range between $50 and $75.

Economists often respond to examples like this by hopothesizing that although people can be fooled once or twice by such a problem, they will figure out the trap with experience. Sheryl Weiner, Max Bazerman, and John Carrol (1987) have investigated this hypothesis by giving the "buy-a-firm" problem to 69 Northwestern MBA students via a microcomputer. All subjects repeated the experiment 20 times with financial incentives and feedback after each trial. The feedback included the "true" value of the company, whether their bid was accepted, and how much money they made or lost. Of the 69 subjects, 5 learned to bid one dollar or less by the end of the experiment. For these 5 subjects, the average trial in which they began to bid $1.00 or less was trial 8. There was no sign of any learning among the others; in fact the average bid drifted up over the last few trials. It may be possible to learn to avoid the winner's curse in this problem, but the learning is neither easy nor fast.

( ... ... )


출처 4: Game: The Winner's Curse

The winner's curse is a significant bidding problem that has been reported in many domains including bidding for oil leases, corporate takeovers, and baseball free agencies.[주]1  In a common value auction, the asset is worth the same amount to all the bidders. For example, when bidding on an oil lease, the value of the drilling rights are the same for all bidders. The bidders, however, might have different information on the value of the rights. Even if their estimates are, on average, unbiased, those with the highest expectatins are likely to bid the highest and, thus, are more likely to win the auction. In this situation the winner ends up a loser when the winning bid exceeds tha value of the drilling rights, leading to the bidder's profit being negative. Even in a less extreme situation in which the profit is positive, management may be disappointed if profits do not meet expectations. Note that the curse is potentially exacerbated when there are more bidders because the winning bid is likely to be even more extreme.
[주]1. For a review of the literature and in-depth discussion see Thaler, R.H., 1992, ^The Winner's Curse: Paradoxes and Anomalies of Economic Life^ (Princeton Univ. Press). 
Although researchers have shown that rational bidders will not fall prey to the winner's curse, to come up with the optimal bid is not an easy task, particularly in a new environment or as the number of bidders increases.[주]2  In addition, hubris or overconfidence may play a role in less than optimal bidding.[주]3
[주]2. On rational bidding, see Cox, J.C., and R.M. Isaac, 1984, "In search of the winner's curse," ^Economic Inquiry^ 22(4), 579-592.
[주]3. See Roll, R., 1986, "The hubris hypothesis of corporate takeovers," ^Journal of Business^ 59(2), 197-216.

A simple in-class exercise can be used to illustrate the winner's curse in a takeover game. All you need, in addtion to the one-page handout provided below, is a set of cards numbered 1-100. The exercise is from Samuelson and Bazerman who show that positive bids should not be submitted, though you will likely find that your students submit positive bids even with repetition.[주]4
[주]4. Samuelson, W. F., and M. H. Bazerman, 1985, “The winner’s curse in bilateral negotiations,” ^Research in Experimental Economics^ 3, 105-137.

In the game the student represents a firm considering a potential takeover. ( ... ) the target is worth 50% more under the new management. Still, uncertainty exists regarding the value of the target and the target's management learns its value before deciding on whether to accept an offer. The target's value falls anywhere between 0 and 100. Suppose, for example that a student bids 50. Perhaps it seems like a conservative bid to him because the expected value is 50. The target will accept the bid only if its value is less than 50. Notice that the student's expected value is incorrect because it fails to take into consideration the information the target has about firm value. If the target accepts an offer, on average the value of the target is half the bid (25 in our example). Even though the average value to the bidder is 1.5*25 = 37.5, the mean profit is negative (50 - 37.5 = -12.5). Thus, the value to the bidder is, on average, negative and the bidder can expect to lose 0.25*the bid.[주]5


STUDENT INSTRUCTIONS

You represent Company A (the acquirer) which is currently considering acquiring Company T (the target) by means of a tender offer. ( ... ... )

( ... ... ) As representative of Company A, you are deliberating over offer prices in the range of $0 to $150 per share.  Please indicate your offer for period 1 in the following table. After everyone has indicated their offers, the value of Company T will be determined by drawing a card from a set of cards numbered 0 to 100. You can then determine whether your offer is accepted and the profits for your company. We will then repeat these steps a period at a time for periods 2 through 5.

(1) Period : ...
(2) Your offer ($0 to $150) : ....
(3) Value of T under current management : ....
(4) Value of T to A [$0 if (2) < (3), otherwise (3)*1.5]  : ....
(5) Your profit [$0 if (2) < (3), otherwise (4)-(2)]  : ....

출처 5 : 생각을 경영하라(민재형 지음. 청림출판, 2014). pp. 263~269.


( ... ... ) 주의 부족이 일으키는 고질적인 판단의 덫으로 승자의 저주winner's curse 현상을 들 수 있다. 승자의 저주가 발생하는 이유는 현명한 판단을 위해 이용할 수 있는 모든 정보를 고려하지 않고 간과하는 데 있다. 다음은 세계 유수의 경영 대학원 수업에서 사용된 문제다.[주]7
회사 A(인수자)는 회사 T(목표물)를 인수하려고 한다. 당신은 A사의 인수 대리인으로 T사의 주식 전량을 현금으로 매입할 계획인데, 주당 가격을 얼마로 해야 할지 현재 확신이 서지 않는다. 주당 가격을 결정하기 어려운 주된 이유는 T사의 가치가 현재 진행 중인 대형 유전 탐사 프로젝트의 결과에 달려 있기 때문이다.

사실 T사의 생존 여부 자체가 이 프로젝트의 결과에 달려 있다고 해도 과언이 아니라. 이 프로젝트가 실패로 끝나면 현재의 경영진이 이끄는 이 회사는 아무런 가치가 없게 되고, 따라서 주가는 0달러가 된다. 그러나 이 프로젝트가 성공을 거두면, 현재의 경영진이 이 회사를 이끌더라도 이 회사의 가치는 급등해서 주가가 100달러까지도 상승할 수 있을 것으로 예측되고 있다. 이 경우 회사 T의 주가는 0달러와 100달러 사이의 어떤 값도 될 수 있으며, 각각의 확률은 동일하다.

그러나 T사는 현재의 경영진 수중에 있을 때보다 A사 경영진 수중으로 넘어가면 가치가 훨씬 높아진다. 사실 T사는 현 경영진 하에서 그 가치가 얼마든 상관없이 A사 경영진이 맡게 되면 그 가치는 50퍼센트 상승할 것으로 예측되고 있다. 물론 유전 탐사 프로젝트가 실패하면 T사의 주식은 휴지 조각이 된다. 하지만 현재 진행 중인 유전 탐사 프로젝트가 성공해 현재 경영진 수중에서 T사의 주가가 50달러가 될 경우, A사가 인수하면 그 가치는 상승해 T사의 주가는 75달러가 된다. 마찬가지로 T사의 주가가 현 경영진 하에서 100달러라면 A사에 인수될 경우, 주가는 150달러가 된다. 즉 A사가 인수하게 되면 T사의 가치는 1.5배로 상승한다.

이제 당신은 A사의 이사회로부터 T사 주식의 인수 가격을 결정해달라는 요청을 받았다. 아직 유전 탐사 프로젝트의 결과가 밝혀지지는 않았지만 지금 인수 제안을 해야만 하는 상황이다. 모든 정황으로 볼 때 T사는 A사 이외의 다른 회사에 의한 인수 합병은 피하고 싶다. 그러나 T사는 지금 당신이 인수 제안을 하더라도 거기에 대한 수락 여부를 유전 탐사 프로젝트 결과가 나올 때까지 미루다가 그 결과가 언론에 알려지기 직전에 결정을 내릴 것이다. 결국 A사는 유전 탐사 프로젝트의 결과를 모르고 인수 제안을 해야 하지만, T사는 프로젝트의 결과를 알고 수락 여부를 결정할 수 있는 상황이다. T사는 A사가 제안한 주가가가 현재 경영진 하에서의 주가보다 조금이라도 높으면 그 인수 제안을 받아들일 것으로 예상된다.

이제 당신은 A사의 요청에 따라 인수 가격을 주당 0달러에서 150달러 사이의 어떤 값으로 정해야 할지 숙고 중이다. 얼마를 제안하겠는가?

이 문제에 대해 서울의 한 대학 경영학과 학부생들과 경영 대학원 학생 240명이 응답한 결과는 [그림 7]과 같다.[주]8

[그림 7]을 보면 50퍼센트가 넘는 응답자의 인수 가격이 50달러에서 80달러 사이에 분포함을 알 수 있다. 이 결과는 기존에 시행된 시험 결과[주]9와도 그 분포가 유사하다. 그러나 이 문제의 정답은 '0'으로 T사를 인수하지 않는 것이다. 답을 맞힌 학생의 수는 240명 중 28명에 불과했다.

이 문제를 논리적으로 생각하면 다음과 같다. A사가 T사를 주당 X달러로 인수하겠다고 제안했다고 가정하자. T사가 A사의 그러한 인수 제안을 받아들인다는 것은 T사의 가치가 주당 X달러 이하라는 것이다. 따라서 T사의 기대가치는 일양분포(특정 범위 내에 존재하는 미지의 값들이 발생할 가능성이 동일한 분포)uniform distribution의 기댓값[주]10 논리에 따라 0.5X가 된다.[주]11 이제 A사가 T사를 인수하면 T사의 가치는 현재 가치의 1.5배가 되므로 A사가 인수한 후의 T사의 기대가치는 1.5×(0.5X) = 0.75X가 된다. 따라서 A사는 주당 X달러를 인수했으므로 X가 양(+)의 값일 경우에는 항상 0.25만큼의 손실(0.75X-X)이 기대된다. 결국 문제의 정답은 기댓값을 평가 기준으로 했을 때 A사는 T사를 인수해서는 안 된다는 결론이 나온다.

그러나 이 실험에서 응답자 수의 50퍼센트에 가까운 119명이 실제로 50달러에서 75달러 사이의 인수 가격을 제안했다. 그 이유는 인수하기 전의 T사의 가치의 기댓값은 50달러(0.5×100)이고, A사가 인수한 후의 T사 가치의 기댓값은 75달러(0.5×150)이므로 이 둘 사이의 값을 제안하면 A사나 T사 모두 득이 될 것이라고 섣불리 생각하기 때문이다.

이러한 결론은 정보의 비대칭성(A사와 T사가 가지고 있는 정보의 양과 질이 동일하지 않음)을 고려하지 않은 것으로, T사로서는 유전 탐사 프로젝트의 성공 여부를 보고 자사의 가치를 정확히 평가할 수 있지만, A사의 경우에는 프로젝트의 결과가 나오기 전에 인수 제안을 해야 하는 상황으로 양자가 같은 정보를 가지고 판단하지 않는다는 사실을 간과한 것이다.

승자의 저주는 보통 구매자가 판매자의 관점을 이해하지 못하고, 구매자와 판매자 간 이용할 수 있는 정보의 차이가 있기 때문에 발생한다.[주]12

[주]7. Samuelson, W. and M. Bazerman, "The Winner's Curse in Bilateral Negotiations," ^Research in Experimental Economics^ (1985), Vol. 3, pp. 105~137.

[주]8. 이 실험은 2009년 9월 서강대학교 경영학부 및 경영전문대학언 MBA 과정 학생을 대상으로 이뤄졌으며, 응답 시간은 5분을 주었다.

[주]9. Samuelson, W. and M. Bazerman, 앞의 자료. Ball, S., M. Bazerman, and J. Caroll, "An Evaluation of Learning in the Bilateral Winner's Curse," ^Organizational Behavior and Human Decision Processes^ (1991), Vol. 48, pp.1~22. Grosskoph, B.Y., Bereby-Meyer, and M. Bazerman, "On the Robustness of the Winner's Curse Phenomenon," ^Theory ad Decision^ (2007), Vol. 63, No. 4, pp.389~418.

[주]10. 기댓값은 장기적 관점에서의 평균값을 말한다. 불확실한 변수의 가치를 평가할 때 많이 사용하는 기준이다.

[주]11. T사의 가치를 확률변수 T라고 하자. 그러면 확률변수 T가 a에서 b사이의 값을 갖는 일양분포일 경우, 즉 T~U(a, b)일 경우, 확률변수 T의 기댓값 E(T) = (a + b)/2이다. 이 경우 T~U(0, X)이므로 E(T) = 0.5X이다.

[주]12. Caroll, J., M. Bazerman, and R. Murphy, "Negotiator Cognitions: A Descriptive Approach to Negotiator's Understanding of Their Opponents," ^Organizational Behavior and Human Decision Processes^ (1988), Vol. 41, No. 3, pp. 352~370.  Grosskoph, B.Y., Bereby-Meyer, and M. Bazerman, 앞의 자료.


시세보다 비싼 경매 낙찰가

( ... ... ) 하지만 낙찰 가격은 거의 그 제품의 실제 가치보다 과대평가되었다는 것을 알고 있는가? 특히 해당 제품의 가치가 불확실하고, 많은 사람이 경매에 참여할 때 더욱 그렇다. 경매에 사람이 많이 모이면 해당 제품이 가치 있는 물건이라는 환상에 사로잡히게 되지만 실제로는 그러한 경매 참가자의 수 때문에 과대평가의 폭은 커질 수 있다. ( ... ... )

[그림 8]에서 오른쪽 그래프는 경매 참가자들이 실제로 생각하는 해당 제품의 평가액 분포를 나타내고, 왼쪽의 그래프는 경매 참가자들이 제시한 입찰가의 분포를 나타낸다고 하자.[주]14  그리고 참가들이 생각하는 평가액의 평균은 제품의 실제 가치와 동일하다고 가정하자. 그러면 모든 경매 참가자는 자신의 평가액보다 일정 금액 낮게 입찰가를 책정하므로(경매로부터 이득을 보아야 하므로) 왼쪽 그래프는 오른쪽 그래프를 좌측으로 일정 부분 이동시킨 것이라고 할 수 있다. 그러면 낙찰가는 왼쪽 그래프에서 오른쪽 꼬리 끝에 해당하는 가격이 되는데, 이 입찰가는 제품의 실제 가치(평가액의 평균)보다 높은 것을 알 수 있다.

따라서 경매의 낙찰가는 제품의 실제 가치보다 높은 것이 일반적이며 이에 따라 경매 주선 업체도 어느 정도의 이득을 볼 수 있는 것읻. 경매 시장에서 승자의 저주를 경험하지 않으려면 제품의 가치를 되도록 하향 평가해야 함과 동시에 자신이 생각하는 제품 가치의 평가액보다 훨씬 낮게 입찰가를 불러야 한다. 하지만 제품의 가치가 불확실할 때(이를테면 골동품, 그림 등) 경쟁의 승자가 되기 위해 매우 높은 입찰가를 부르는 경매 참가자가 있게 마련이고, 그 사람은 낙찰의 기쁨을 맛보는 동시에 승자의 저주에 의한 희생자가 된다.

( ... ... )





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