VOLUME 6 EJLS ISSUE 2. European Journal of Legal Studies

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1 OUME 6 EJS ISSUE Euroean Journal of egal Stuies Title: Rent Seeking with Asymmetric Players: An Alication to itigation Eenitures Author(s: Svetoslav Salkin Source: Euroean Journal of egal Stuies, olume 6, Issue (Autumn/Winter 013/14, Abstract: This aer uses insights from the literature on rent-seeking contests toanalyze the eeniture ecisions of a Defenant an a Plaintiff in the course of their legal battle. It is shown that the total amount of litigation eenitures is affecte by the sequence of moves (rotocols of interaction, ifferences in stakes, an the effectiveness of the arties (or the strength of their cases an information asymmetries. In articular, it is shown that allowing for ifferent stakes many of the results in the rent-seeking literature may not hol. 157

2 OUME 6 EJS ISSUE RENT SEEKING WIT ASYMMETRIC PAYERS: AN APPICATION TO ITIGATION EXPENDITURES Svetoslav Salkin * TABE OF CONTENTS 1. INTRODUCTION ITIGATION AS A RENT-SEEKING CONTEST A SPECIAIZED MODE Cournot-Nash Protocol of Interaction Stackelberg Protocol of Interaction Rent Seeking with Asymmetric Information Regaring the alue of the Prize Searation SUMMARY OF RESUTS AND CONCUSION * Eurasia Analyst, IS, svetoslavsalkin@gmail.com 158

3 OUME 6 EJS ISSUE 1. INTRODUCTION In this aer I resent a simle moel that can serve as a framework for analyzing litigants outlay ecisions in the rocess of their legal battle. The legal battle is moelle as a rentseeking contest in which layers een resources in orer to increase their robabilities of winning a rize. Thus the aer tries to connect, an heavily borrows from, two fiels of research: the economics of litigation an the theory of contests (initially consiering rentseeking contests only. A traitional question within the economics of litigation is: What affects the ecision of articiants in a legal isute to go to court instea of settling out? 1 The theory of rent seeking, on the other han, tries to etermine the relationshi between the various characteristics of the contest situation an the outlay ecisions of the arties involve. In this aer I analyse these outlay ecisions taken by litigants once they have ecie to go to court. There is a small number of aers that aress this secific question, most notably Katz 3, irshleifer, 4 Farmer an Pecorino, 5 an Kahan an Tuckman, 6 among others. As Katz argues the legal battle itself is analytically rior to the ecision whether to settle or not because this latter ecision is affecte by the eectations of the layers with resect to their future legal eenitures. Several aers analyze relate questions strictly within the contet of rent-seeking contests. Risse analyses the total volume of rent-seeking eenitures for one-stage an two-stage rent-seeking contests involving layers with negatively intereenent references, an conclues that rent issiation is larger for onestage contests. 7 Yates resents a articularly interesting formulation in which the winner in a rent-seeking contest is selecte robabilistically an ays her bi, while the other contestant ays nothing. 8 e also stuies how rivate information regaring the contest s stakes affects the equilibrium outcome. Contests in which only the winner ays her bi, however, o not moel any meaningful kin of litigation contest. Chowhury an Sheremeta use a general rent-seeking contest formulation similar to the one resente in this aer to show that minor changes in the arameters of the contest success function coul result in rather substantial ifferences in rent issiation. 9 The results obtaine in this aer are therefore secial cases of the more general conclusions of Chowhury an Sheremeta. The moel in this aer analyses how litigation eenitures are affecte by ifferences in terms of stakes an effectiveness of the litigants (or merit of their cases, as well as by informational asymmetries regaring the stakes. inster 10 resents a rent-seeking moel in 1 See Thomas J Miceli, Economics of the aw: Torts, Contracts, Proerty, itigation (OUP For a selective survey see Shumel Nitzan, Moelling Rent-Seeking Contests ( Eur J of Political Economy Avery Katz, Juicial Decisionmaking an itigation Eeniture ( Intl Rev of an Economics Jack irshleifer, The Dark Sie of the Force: Economic Founations of Conflict Theory (CUP Amy Farmer an Paul Pecorino, egal Eenitures as a Rent-Seeking Game ( Public Choice Marcel Kahan an Bruce Tuckman, Secial evies on Punitive Damages: Decouling, Agency Problems an itigation Problems ( Intl Rev of an Econmics Sina Risse, Two-Stage Grou Rent-Seeking with Negatively Intereenent Preferences ( Public Choice Anrew J Yates, Winner-Pay Contests ( Public Choice Subhasish Chowhury an Roman Sheremeta, A Generalize Tullock Contest ( Public Choice Bruce G inster, Stackelberg Rent Seeking ( Public Choice

4 OUME 6 EJS ISSUE which layers attach ifferent values to the rize they seek to win, while Kohli 11 an Diit 1 stuy how ifferences in effectiveness affect rent-seeking outlays. Secifically, Kohli an Diit show that the more effective layer commits to higher level rent-seeking outlays. The moel in this aer shows that this result is crucially eenent on the assumtion of equal stakes. Once this assumtion is relae, as in inster s moel, Kohli s result, which he calls the Unerog Theorem, ceases to hol. With regar to asymmetric information, Fu 13 showe that informational asymmetries regaring the value of the rize are welfare enhancing in the contet of sequential rent-seeking rotocols, as they suress the eenitures of the informe contestant. Section 3.3 of this aer shows that Fu s result is vali even when litigants iffer in terms of effectiveness. The net section resents the general setting an relates it to the literature. Section 3 secializes the moel, motivates its assumtions, erives the equilibrium eenitures uner the so calle American rule for allocation of litigation costs for two rotocols of interaction, Cournot-Nash an Stackelberg, an analyzes the effects of informational asymmetries. Section 4 summarizes the results an conclues the aer.. ITIGATION AS A RENT-SEEKING CONTEST The simle worl I envisage consists of a Plaintiff an a Defenant who are risk-neutral an have ecie to go to trial. The economics of litigation literature elains the fact that eole sue each other by referring to ifferences in ercetions regaring the outcome of the trial, ie each litigant is overly otimistic about her chances of winning. 14 Failure to settle, however, might be also ue to attitues towars risk or simly to malevolence. 15 Once at trial, the arties ecie on their litigation eenitures (or legal efforts. The literature offers ifferent interretations here. Katz seaks about search of suorting arguments or favourable facts to be resente to a court, jury or aministrative agency. 16 irshleifer aots a more general interretation which may inclue costs of lawyers, resources evote to factual investigation an legal research, an bribery. 17 The litigation eenitures affect the robabilities of winning. Note that I am ignoring the Princial- Agent roblems that eist between the litigants an their attorneys. It is not imossible, however, to eten the analysis along these lines following Baik an Kim 18 an Schoonebeek. 19 I will use the following notation: - the stakes for the Plaintiff the stakes for the Defenant legal eenitures of Plaintiff legal eeniture of Defenant 11 Inerjit Kohli, Institutional Structure, Strategic Behavior an Rent-Seeking Costs [1994] Working Paer 79, University of California Santa Cruz, Deartment of Economics. 1 Avinash Diit, Strategic Behavior in Contests ( American Economic Rev Qiang Fu, Enogenous Timing of Contests with Asymmetric Information ( Public Choice Miceli (n irshleifer (n ibi. 17 ibi. 18 Kyung wan Baik an In-Gyu Kim, Delegation in Contests ( Eur J of Political Economy ambert Schoonbeek, A Delegate Agent in a Winner-Takes-All Contest (00 9 Alie Economics etters

5 OUME 6 EJS ISSUE ayoff to Plaintiff ayoff to Defenant P robability that Plaintiff wins P robability that Defenant wins Following the stanar setting of the theory of contests, the objective functions of the layers are formalize as follows: The Plaintiff chooses so as to maimize (1 P (, Similarly, the Defenant chooses so as to maimize ( P (, The imortant arts of these eressions are the robabilities of winning P an P. irshleifer calls them contest success functions. 0 The usual assumtions are that each layer s robability of winning is increasing in her own eenitures an ecreasing in the eenitures of her oonent, an that they sum u to one. Tullock s seminal aer offers the classical formulation, which for two layers looks as follows: i (3 Pi (,, i=,, where is a measure of the relative ecisiveness of contest efforts. The intuition behin this game is the following: we assume two arties who are articiating in a lottery uner somewhat unusual rules. Each is ermitte to buy as many lottery tickets as he wishes at one ollar each, the lottery tickets are ut in a rum, one is ulle out, an whoever owns that ticket wins the rize. 1 irshleifer offers two canonical formulations of contest success functions, one in which the relative success eens on the ratios of the resective eenitures (essentially Tullock s formula, an another in which success eens on the ifference between the eenitures. In the contet of litigation eenitures eressions (1 an ( can be etene in orer to analyze the effect of ifferent cost-allocation rules. Shavell 3 iscusses four ossible systems: (i Uner the American system where each arty bears her own costs the objective functions are as above. 0 Jack irshleifer, Conflict an Rent-Seeking Success Functions: Ratio vs. Difference Moels of Relative Success ( Public Choice Goron Tullock, Efficient Rent-Seeking in James M Buchanan, Robert D Tollison an Goron Tullock Towar a Theory of the Rent Seeking Society (A&M Press The ifference formulation, however, is not very convenient as it often requires numerical solutions. 3 Steven Shavell, Suit Settlement an Trial: A Theoretical Analysis Uner Alternative Methos for the Allocation of egal Costs ( J of Stuies

6 OUME 6 EJS ISSUE (ii Uner the British system the losing arty bears all the costs. The objective functions are as follows P (, (, i i i i, (iii Uner the system favoring the Defenant, each arty bears her own costs if the Plaintiff wins, but the Plaintiff bears all the costs if the Defenant wins. The objective functions are P (, ( ; P (, ( (iv Uner the system favoring the Plaintiff, each arty bears her own costs if the Defenant wins, but the Defenant bears all the costs if the Plaintiff wins. The objective functions are P (, ( ; P (, ( Other etensions are also ossible. Miceli iscusses the so-calle Rule 68 of the Feeral Rules of Civil Proceure accoring to which a Plaintiff who refuses a settlement offer ays the Defenant s ost-offer legal costs if the Plaintiff receives a jugement at trial less than the rejecte offer. 4 Daughety an Reinganum 5 consier slit-awar statutes which allocate a ortion of unitive amages awars won by successful laintiffs to the state. 3. A SPECIAIZED MODE In orer to erive analytical solutions, I select a articularly simle variant of contest success function, which nevertheless allows for obtaining non-trivial results. The moel in this section combines an etens the rent-seeking moels of inster 6 an Kohli. 7 Both of these aers kee the sirit of the Tullock s rent-seeking moel, but moify some of his etails. In articular, inster analyze a game where the layers attach ifferent values to the rent they comete for, while Kohli analyze the case where the layers iffer in their effectiveness. ere I allow for both, ie the layers iffer both in their valuations of the stakes ( an in their effectiveness. Differences in stakes are articularly relevant in litigation since this is an emirically confirme fact. From a samle of feeral civil cases from the Southern District of New York (SDNY, file between 1984 an 1987 an terminate by the en of 1998, Walfogel 8 infers that the highest stake asymmetry ertains to intellectual roerty cases. The estimates inicate that Plaintiffs stan to gain 33.6 ercent more than Defenants stan to lose. Secon are contract cases, whereby Plaintiff s stakes are again higher. The lowest stake asymmetry estimate (but still statistically significant ertains to torts, whereby 4 ibi, Anrew F Daughety an Jennifer F Reinganum, Foun Money? Slit-Awar Statutes an Settlement of Punitive Damages Cases (003 5 American an Economics Rev inster (n Kohli (n 11 8 Joel Walfogel, The Selection yothesis an the Relationshi between Trial an Plaintiff ictory ( J of Political Economy

7 OUME 6 EJS ISSUE Defenant s stakes are higher. 9 A ossible elanation is that when a tort Defenant loses she is often eose to otential liability from aitional Plaintiffs. Similarly, a losing intellectual roerty Plaintiff is more likely to become subject of aitional encroachments. 30 The assumtion of ifferences in effectiveness, on the other han, is ifficult to evaluate emirically, but actually has strong intuitive aeal. irshleifer an Osborne 31 seak of one sie or the other being more aet in converting legal effort into esirable outcome. Note, however, that a ifferences in effectiveness arameter can reresent ifferences in the true strength of the cases of the sies (ie one of the litigants having a more meritorious case or the true egree of Defenant s fault. In what follows I will seak of one sie being more effective than the other (although the true egree of Defenant s fault might be more aroriate. A rominent eamle of the ouble asymmetry iscusse in this aer is a lawsuit file by Russian oligarch Boris Berezovsky against his former business artner, Roman Abramovich, in the UK in Both businessmen were very close to former Russian Presient Boris Yeltzin in the 1990s, an use their olitical influence to amass huge fortunes through the Russian government s controversial loans-for-shares rivatization rogramme. Whereas Roman Abramovich remaine close to the Kremlin uring the terms of Presient Putin, who succeee Boris Yeltzin, an Presient Meveev, Boris Berezovsky has been force to flee to the UK in 000 an was later convicte in absentia over allege embezzlement an relate crimes in Russia. In 011, Boris Berezovsky launche what turne out to be one of the most eensive lawsuits in the history of the UK against Roman Abramovich. The litigation eenitures associate with the four-month legal battle eceee 100 million. 33 Boris Berezovsky claime that Roman Abramovich ha use threats an intimiation to make him an Georgian-born businessman Bari Patarkatsishvili sell their stakes in oil firm Sibneft an aluminum roucer RusAl at ecessively low rices. All in all, Boris Berezovsky sought over $5 billion in comensation for the coerce sale of his stake in Sibneft, an over $564 million in comensation for the coerce sale of his stake in RusAl. 34 Roman Abramovich, however, enie that Boris Berezovsky an Bari Patarkatsishvili owne any stakes in Sibneft an RusAl, an allege that he ha ai a total of $.3 billion to Boris Berezovsky in echange for olitical rotection. Inee, Boris Berezovsky faile to resent any ocuments roving his claims. e insiste instea that all agreements regaring ownershi in the two firms ha been mae orally. The court ismisse all claims 9 Walfogel s stuy is much richer than that. In articular, he fins strong suort for the so-calle selection hyothesis accoring to which the samle of trie cases is unreresentative of the oulation of unerlying isutes (see also Miceli (n ibi, Jack irshleifer an Evan W Osborne, Truth, Effort, an the egal Battle ( Public Choice Jane Croft, Abramovich Case Awaits Ruling Financial Times (onon, 8 August 01 <htt:// accesse 3 May Jane Croft an Neil Buckley, Berezovsky oses against Abramovich Financial Times (onon 31 August 01 <htt:// accesse 3 May Eecutive Summary of the Full Jugement of Gloster J in Berezovsky v Abramovich, Action 007 Folio 94 <htt:// accesse 13 May

8 OUME 6 EJS ISSUE mae by Boris Berezovsky. e was escribe by Juge Elisabeth Gloster as an unimressive, an inherently unreliable, witness, who regare truth as a transitory, fleible concet, which coul be moule to suit his current uroses. Some of the evience he gave was escribe as eliberately ishonest. Roman Abramovich s answers, on the other han, were consiere careful an thoughtful. e was furthermore escribe as a truthful, an on the whole reliable witness an frank in making concessions where they were ue. 35 The lawsuit was obviously a eserate move by Boris Berezovsky, who ha allegely lost most of his wealth by the time of the trial. At the same time, Roman Abramovich, with an estimate net worth of aroun $11. billion, was still one of the richest an most influential Russian oligarchs. 36 Therefore, the marginal utility of the $5.564 billion sought by Boris Berezovsky was clearly much larger for Boris Berezovsky himself than it was for Roman Abramovich. Regaring the relative merits of the claims of the litigants, it must have been atently clear to both of them that given the lack of any written evience or witnesses other than Boris Berezovsky, all Roman Abramovich ha to o to win the case was eny anything that Boris Berezovsky claime. With the above remarks an eamle in min, the contest success functions I will use are the following a P (, ; P (, a a here a enotes the relative effectiveness of the Plaintiff. The Plaintiff is more effective when a>1. 37 The major isavantage of such a simle formulation is that it cannot be meaningfully alie to all four cost allocation systems outline in the revious section. Ecet for the American system, it turns out that in equilibrium one of the layers sens an infinite amount of resources in the legal conflict. 38 More comlicate formulations avoi this roblem, the isavantage, however, is that the analysis shoul rocee by calculating numerical solutions (this is actually a roblem in many rent-seeking moels. The resent formulation, however, nicely fits the American rule, thus I consier this system only leaving the other three for further investigation. Uner the American system the objective functions of the Plaintiff an the Defenant resectively are 35 ibi. 36 Forbes (New York, 10 October 010 <htt:// Abramovich_DG3G.html> accesse 5 May If the effectiveness of the layers are measure by ei, i=,, the contest success functions become ei i e e. The above eressions are erive by setting e a. e 38 To rove that this is the case for the British system, note that ifferentiating the Plaintiff s objective function an setting it equal yiels ( 1 a, which is ositive an is ineenent of. The same hols for the Defenant s objective function. 164

9 OUME 6 EJS ISSUE a (4, an a (5. a I eamine two rotocols or interaction, Cournot-Nash, ie when the layers move simultaneously or in ignorance of each other s moves an Stackelberg, when the layers move sequentially. I assume that it is the Plaintiff who moves first an commits to a level of eenitures. irshleifer an Osborne also consier what they call a threat-an romise rotocol in which the Defenant makes the rior commitment. The objective functions consiere in this aer however are symmetric, which makes such an etension unnecessary Cournot-Nash Protocol of Interaction The Cournot-Nash setting reresents a stanar simultaneous move game. Differentiating the objective functions an setting them equal to zero gives the following reaction functions (6 ( a a (7 ( a a At Nash equilibrium the eenitures of the layers are a c (8 a ( a c (9 a ( Thus the total amount of litigation eenitures in equilibrium, ie a ( c (10 C, ( a where the suerscrits c stans for Cournot-Nash. C c is * * Kohli 39 shows that the total level of eenitures (in his terminology, rent-seeking costs is maimize when the layers are equally effective, ie when a=1. The result hols, however, only if the layers attach the same value to the rent they are cometing for (have the same stakes, ie whenever =. To fin the maimization oint uner the current setting, I ifferentiate (10 with resect to a an set it equal to zero. 39 Kohli (n

10 OUME 6 EJS ISSUE c C ( ( a (11 3 a ( a This is equal to zero at a. In other wors, in the Cournot-Nash setting the litigation eenitures are maimize when the relative effectiveness of the layers equals the ratio of their stakes. It is also interesting to fin the equilibrium ayoffs of the layers erive by inster 40 for equally effective layers, an show that they iffer when asymmetric effectiveness is introuce. The eressions are the following (1 (13 a c c c (, 1 a a c c c (, 1 a a, for the Plaintiff, an, for the Defenant. When the layers have equal effectiveness, a is equal to 1 an I obtain inster s result c c c i i (,, for i=,. ( 3.. Stackelberg Protocol of Interaction In this setting the layers move in sequence. Diit 41 analyzes a more general moel than the resent one an ientifies a very interesting result: If re-commitment to effort level (in my case litigation eenitures is allowe, then the favorite in the contest will commit herself to a higher level of effort than woul have been the case if commitment was not allowe, an the unerog will commit herself to a lower level. irshleifer an Osborne reach the same conclusion. 4 Kohli obtains a similar result ineenently an calls it the Unerog Theorem. The interesting imlication for the resent analysis is that the total litigation eenitures uner Stackelberg iffer from Cournot-Nash. The resent section enriches Kohli s formulation by allowing for ifferent stakes. I assume that the Plaintiff moves first. The game is solve along the lines of backwars inuction, ie what I erive is the sub-game erfect equilibrium of the game. Knowing the best resonse function of the Defenant (eression (7, the Plaintiff s objective function becomes a (14 (, ( 40 inster (n Diit (n 1. 4 ibi,

11 OUME 6 EJS ISSUE This is maimize at (15 s a 4 The Defenant s resonse is a a s (16, which is ositive for a /. For a /, however, the Defenant sens zero in equilibrium an the Plaintiff sens / a. It is straightforwar now to resent Diit s over-commitment result for equal stakes. If 1 a (ie the effectiveness of the Plaintiff is higher the Plaintiff s equilibrium eenitures in the Stackelberg rotocol are greater than the resective eenitures in the c s Cournot-Nash setting. The result is obtaine after eamining the inequality. Substituting the resective eressions from (8 an (15 an setting this inequality boils own to a>1, which is true by assumtion. As irshleifer an Osborne ut it merit an effort are comlements. 43 Of course, with asymmetric stakes the result hols only if a /, ie when the relative effectiveness arameter is larger than the ratio of the stakes. I further eamine the total eenitures in the Stackelberg scenario for summing s an s. This results in a /, by (17 C s a (1 a 1, which is maimize at (18 1 a. If the stakes are equal, the result coincies with the one obtaine by Kohli (Proosition - total outlays in the Stackelberg setting are maimize when the Plaintiff s effectiveness is greater, ie at a=3/. The resent formulation shows that this nee not be the case with asymmetric stakes. If, ie the stakes of the Defenant are sufficiently smaller than those of the Plaintiff, the litigation eenitures reach their maimum at a oint where the Defenant is more effective, a<1. This result is erhas best elaine by the fact that stake asymmetries change the relative marginal benefits of litigation eenitures. In other wors, if the stake of the Plaintiff is sufficiently larger than the stake of the Defenant, then the Plaintiff s marginal benefits from an etra unit of eenitures on litigation is too small, an therefore not worth making, if the Plaintiff s effectiveness, or the merit of her case, is sufficiently smaller than the Defenant s effectiveness, of the merit of her case. 43 ibi,

12 OUME 6 EJS ISSUE et us see now the net ayoffs of the layers in the Stackelberg scenario. For the Plaintiff, the net ayoff is (19 (0 a s s s (,, for a /, an 4 a s s s (,, for a /. a The net ayoffs for the Defenant resectively are (1 a s s s (, 1 a, for a /, an 4 ( s s s (, 0, for a /. Now it is ossible to comare the net ayoff of the Plaintiff in the Stackelberg setting with the resective ayoff uner the Cournot-Nash rotocol for a /. The interesting result to note is that the net ayoff of the Plaintiff is always better in the Stackelberg rotocol than on the Cournot-Nash rotocol. This becomes evient when eamining the following inequality s s s c c c (, (,. After substituting with the resective eressions from (19 an (1 an rearranging this eression reuces to 0 ( a, which is obviously true. Uner the resent formulation, however, similar comarisons with resect to the Defenant yiel ambiguous results. Net, for the sake of comleteness, I comare the amount of total litigation eenitures uner the two rotocols of interaction. First, by eamining eressions (10 an (17 it is easy to check that total outlays are equal uner Cournot-Nash an uner Stackelberg if the layers are equally effective an have equal stakes (a=1, =. Similarly, in this case, their net ayoffs are the same (by checking eressions (1, (13, an (19 through (. Secon, with equal stakes, but not necessarily equal effectiveness this no longer hols. For s c == an a<, subtracting C from C results in c s a (3 C C (5 a (1 a. ( a 1 This is ositive for a<1, zero for a=0, an negative for a>1. For a>, the eenitures of the Defenant in the Stackelberg rotocol are zero, an the total amount of eenitures is simly /a. Thus 168

13 OUME 6 EJS ISSUE c s (4 C C ( a a 1. a(1 a This is negative for a 1, an non-negative for a 1. What is the intuition behin these results? The litigation eenitures are lower in the Stackelberg rotocol than in Cournot-Nash for a<1. The Defenant sens less because she is strategically isavantage, while the Plaintiff sens less because she is less effective. If 1 a 1, the eenitures are higher in the Stackelberg rotocol because the leaer sens more to take avantage of her increase effectiveness. For even larger values the Plaintiff is much more effective, the efenant sens zero an the total level of eenitures is again lower. It can be also shown that for a<1 the net ayoff of the Defenant is lower uner Stackelberg than uner Cournot-Nash. aving in min that this is true for the Plaintiff for any a, Kohli s claim (recast in the terminology of this aer is that if the Plaintiff is less effective, the Stackelberg equilibrium is more efficient than the corresoning Cournot-Nash, ie leas to a lower level of eenitures an higher ayoffs for the litigants. Finally, it is ossible to comare the litigation eenitures when the layers are equally effective, a=1, but the stakes are ifferent c s (5 C C ( ( This is ositive for, negative for, an zero for equal stakes. In wors, with equal effectiveness the total level of eenitures is greater in the Cournot-Nash case if the Defenant has larger stake, otherwise the Stackelberg case involves a higher level of eenitures Rent Seeking with Asymmetric Information Regaring the alue of the Prize The last etension of the basic litigation moel consiere in this aer assumes that the two contestants attach the same value to the rize, but one of the contestants has suerior information about that value. The most interesting scenario in this setting occurs when the contestants move sequentially, as this woul have the informe contestant trying to signal her information to the uninforme contestant. A rominent eamle of lawsuits with asymmetric information involves isutes over oil etraction rights. Firms biing for oil rights tyically attach the same value to the rize they bi for. In the terminology of auction theory they have common values Cramton. 44 Once a firm wins the right to search for oil, it quickly uates its estimate for the actual value of the eosit in question. Suose then that one of the losing biers takes the winner to court over allege irregularities uring the biing rocess. If the winner (or Defenant is the first one to choose litigation eenitures, then the interaction has the structure of a signaling game Peter Cramton, ow Best to Auction Oil Rights in Macartan umhreys, Jeffrey D Sachs, an Joseh E Stiglitz (es, Escaing the Resource Curse (Columbia University Press Michael Sence, Job Market Signaling ( Q J of Economics

14 OUME 6 EJS ISSUE Fu, 46 among others, analyze such an etension an reorte the main result obtaine in this subsection, namely that the low value informe contestant woul like to sen less on rent seeking in orer to creibly rove that the rize s value is inee low. ence, in the contet of issiative contests (lobbying, corrution an other rent seeking contests, informational asymmetries are welfare enhancing in that they reuce the total amount of rent-seeking eenitures. In the literature on inustrial organization Gal-Or 47 stuies Cournot s uooly moel when one of the firms is better informe about eman. Tirole 48 rovies an esecially instructive resentation of Gal-Or s moel an the analysis below follows Tirole s eosition. This subsection shows that Fu s result remains vali in the case of ifferences in effectiveness. In other wors, informational asymmetries reuce litigation eenitures even when effectiveness asymmetries are allowe. 49 The remainer of the subsection assumes that the informe contestant moves first in orer to sen a signal regaring the value of the rize. Assume that the Defenant an the Plaintiff attach the same value to a rize, but this value can be of two tyes, an, such that 0 < <. The Defenant learns the rize s tye, which hereafter will be referre to as the Defenant s tye, an chooses her rent seeking eenitures. Thereafter the Plaintiff observes the Defenant s choice, but not her tye, an chooses her rent seeking eenitures. This ens the game. To fin the sequential equilibria of this game, enote the Plaintiff s rior beliefs by ( = q an ( = 1 q. After observing the Defenant s move, the Plaintiff uates her beliefs as follows º( 1 = μ(1 an º( 1 = 1 μ(1 an maimizes her ayoff function given these uate beliefs. Symbolically, the Plaintiff maimizes the following eression (6 1 ence her best resonse function is given by (7 BR 1 Eression (7 is ecreasing in μ(, the belief that the rize is low, therefore, the Defenant will try to convince the Plaintiff that the rize is low in orer to make the Plaintiff evote less resources to rent seeking an thereby increase her (the Defenant s chances of winning. Using incentive comatibility logic, it is straightforwar to show that in any searating equilibrium the Defenant sens more resources on litigation when the rize is high. Denote the otimal choices of the high an the low tye by an, resectively. To ensure that these choices satisfy incentive comatibility, it must be the case that neither 46 Fu (n E Gal-Or, First Mover Disavantages with Private Information ( Rev of Economic Stuies Jean Tirole, The Theory of Inustrial Organization (MIT Press A more comlete treatment woul inclue stake asymmetries as well. owever, such an etension makes the moel technically very ifficult an shoul be treate in a searate aer. 170

15 OUME 6 EJS ISSUE tye has an incentive to select the equilibrium choice of the other tye. In other wors, the following two inequalities shoul be satisfie (8 (9 BR BR BR BR (IC (IC The first inequality is the low tye s incentive comatibility conition an the secon inequality is the high tye s incentive comatibility conition. Subtracting the right han sie of (IC from the left-ha sie of (IC, an subtracting the right-han sie of (IC from the from the left-han sie of (IC yiels (30 BR BR Since <, this eression is equivalent to (31 BR BR From eression (7 it can be shown that the best resonse corresonence BR(. is an increasing concave function, hence the last inequality is true if an only if, which roves the claim that the high-tye Defenant sens more on litigation than the low-tye Defenant. game. The remaining art of this sub-section ientifies the searating equilibria of the 3.4 Searation In a searating equilibrium the tye of the Defenant is reveale. The receing analysis imlies that the high tye lays her full information strategy, 4,, an obtains her full equilibrium ayoff, 4 S. To simlify notation, set. Denote the low tye s searating equilibrium strategy by S. To achieve searation, in equilibrium the beliefs of the layers shoul be confirme. The incentive comatibility constraint for the low tye that sustains such an outcome is the following 4 (3 The incentive comatibility constraint for the high tye is given by 171

16 OUME 6 EJS ISSUE 17 (33 Net, if the low tye is thought to be a high tye an maimizes her ayoff function given that belief, she (the low tye woul obtain (34 BR ma 4 ence, the following rationality conition shoul hol (35 4 This inequality is satisfie for (36 To conclue, the range of searating equilibria is given by (37 S 4 4 Tyically signalling games ehibit a multilicity of both ooling an searating equilibria. Most equilibrium refinements eveloe by game theorists select the least-cost-searating equilibrium, or Riley equilibrium. 50 Following the intuitive criterion roose by Cho an Kres, 51 least-cost searation occurs at the uer boun of the interval in eression (37. (38 CS 4 ence the low tye has an incentive to bi below its equilibrium strategy uner comlete information in orer to creibly rove her knowlege. The eression CS is increasing in an is ecreasing in. 4. SUMMARY OF RESUTS AND CONCUSION Whether Stackelberg or Cournot-Nash is the aroriate rotocol an the etent to which asymmetric information lays a role in the Stackelberg setting is contet-secific an eens very much on the information flows between the layers. Clearly this is a crucial 50 John Riley, Informational Equilibrium ( Econometrica In-Koo Cho an Davi Kres, Signaling Games an Stable Equilibria ( Q J of Economics

17 OUME 6 EJS ISSUE question when it comes to emirical testing. Nevertheless, the resent analysis can be helful in avancing some roositions. Most of the results below are obtaine by others in the literature. Allowing for ifferent stakes, however, leas to a number of moifications. The results in the aer are as follows: 1. In the Cournot-Nash rotocol the level of litigation eenitures is maimize when the relative effectiveness (or the relative merit of the cases of the arties equals the ratio of their stakes. In the Stackelberg rotocol with equal stakes the level of litigation eenitures is maimize when the Plaintiff s effectiveness (merit is sufficiently greater. With unequal stakes, however, this is no longer true. If the stakes of Defenant are sufficiently smaller, the litigation eenitures reach a maimum at a oint where the Defenant is more effective (has stronger case.. In the Stackelberg rotocol the Plaintiff s eenitures are greater than in Cournot-Nash if her effectiveness (merit is higher (but not too high, 1<a<. 3. If the stake of the Plaintiff is sufficiently smaller than the stake of the Defenant, relative to her effectiveness or the merit of her case, the Plaintiff is better off (has higher net ayoff in the Stackelberg rotocol than in Cournot-Nash, ie recommitment is esirable for the Plaintiff. The situation of the Defenant is ambiguous. 4. With equal stakes, if the Plaintiff is less effective (has less merit, the Stackelberg equilibrium is more efficient than the corresoning Cournot-Nash, ie leas to lower legal eenitures an higher ayoffs for the litigants (Kohli s Unerog theorem. Again the result may not hol if the stakes are ifferent. 5. With equal effectiveness, the total level of eenitures is greater in the Cournot- Nash rotocol if the Defenant has a larger stake, otherwise the Stackelberg rotocol involves a higher level of eenitures. 6. Informational asymmetries ten to suress litigation eenitures regarless of ifferences in effectiveness or merit, as the informe arty has an incentive to signal the low value of the rize to the uninforme arty. With asymmetric information total litigation eenitures might be smaller than litigation eenitures in the cases of erfect information or imerfect but symmetric information, ie when both litigants lack information. A number of etensions are ossible. In articular, it is imortant to eamine what haens uner the ifferent cost allocation rules outline in section. Furthermore, a more realistic analysis woul elicate the role of the ecision maker, ie the court or the jury. The analysis of Congelton offers a general framework for aressing this roblem. 5 Finally, the rincial-agent roblems in the relationshis between the litigants an their attorneys shoul be accounte for. 5 Roger D Congelton, Committees an Rent-Seeking Effort ( J of Public Economics