Proposition 6 reveals that expected legal expenses are highest under the British sys-tem and lowest under the Matthew syssys-tem. In fact, Proposition 8 implies that by choosing β arbitrarily large in the Matthew system, one can make total expected legal expenditures arbitrarily small. Thus, one might be tempted to conclude that the Matthew system is the “optimal” litigation system; after all, the judicial outcome is both efficient and just, and furthermore, the system can be devised in a manner that “minimizes” legal expenditures on a per-trial basis. This reasoning is ßawed, however, as the following analysis reveals.
By assumption A3, litigation costs are internalized, so total expected legal ex-penditures equal the total expected utility loss from litigation. Thus, the expected payoffs (denoted EU) of litigants are higher in systems where expected expenditures are lower. It follows from Proposition 8 that
Proposition 9 Under assumptions A1 through A4, the expected payoffs of litigants can be ordered as follows:
EUBritish < EUContinental < EUAmerican =EUM arshall =EUQuayle < EUM atthew More generally, the expected payoffs of the litigants are independent of α and strictly increasing in β.
Together, Propositions 8 and 9 illustrate an important trade-off. On the one hand, legal systems with higherβ’s result in lower expected equilibrium legal expenditures
per trial, and the Matthew system results in the lowest possible expected expenditures per trial. On the other hand, legal systems with higherβ’s result in higher expected payoffs from litigation, thus making it more attractive for parties to bring suits in the Þrst place. Thus, while the Matthew system results in lower expenditures per trial, adopting such a system would maximize the number of cases brought to trial.
Factoring in the increased number of trials, it is not at all clear that a movement to the Matthew system would result in lower social outlays on legal services.
Regardless, the above results do suggest that a movement from the American to the Continental or British systems would reduce the incentives of parties to litigate, while a movement from the American to the Quayle system would have no impact on litigation incentives. Testable implications of Propositions 6 and 9 include the hypotheses that more cases are brought to trial under the American system than under the British or Continental systems, and that less is spent per trial under the American system. We note that Hughes and Snyder (1995) provide empirical evidence that the American system indeed results in fewer trials than the British system. We are unaware of any empirical evidence regarding per-trial expenditures under different legal systems.
To summarize, the effective costs to society of a given legal system depend not only on the expected expenditures per trial under each system, but the number of trials induced by each system. Ceteris paribus, systems that generate lower expected expenditures per trial provide greater expected payoffs from litigation, and therefore
result in more cases being brought to trial.
6 Conclusion
Our auction-theoretic framework considered a symmetric litigation environment in which the legal ownership of the disputed asset is unknown by the court. The court observes only the quality of the case presented by each party, and awards the asset to the party presenting the best case (justice is always served). Litigants can inßuence the quality of their case by hiring skillful attorneys. Even though the parties and the court are asymmetrically informed, in equilibrium the court’s decision is always just and efficient. The class of litigation systems considered includes standard systems (such as the American, British, and Continental systems), as well as more exotic ones (which we call the Quayle, Marshall, and Matthew systems).
Our framework provides a complete ranking of a continuum of different legal systems. Equilibrium legal expenditures per trial are increasing in the proportion of the winner’s attorney fees that must be paid by the loser, while the expected payoffs of the litigants are a decreasing function of this proportion. This results in a trade-off: litigation systems with lower equilibrium legal expenditures per trial (such as the American, Quayle, and Matthew systems) provide a greater incentive for parties to sue than systems that entail higher equilibrium legal expenditures (such as the British and Continental systems). Expected legal expenditures per trial, as well as
litigation incentives, are independent of the proportion of the loser’s legal fees paid by the winner and loser.
Our analysis also reveals that a movement from the American system to the Quayle system would neither reduce expected legal expenditures on a per-trial basis nor reduce the incentives for parties to litigate. To the extent that America’s reputa-tion for being a litigious society is based on the shear number of suits brought to trial in the U.S., a movement toward the Continental or British system might improve matters by reducing the number of suits and the strain on the court system. Unfor-tunately, such a move would result in higher expected legal costs on a per-trial basis.
While our analysis ignores the impact of budget constraints, one undesirable feature of such a move might be to make courts a playing Þeld for only the wealthy. The simple auction-theoretic litigation framework set forth in this paper, coupled with recent work by Che and Gale (1998) on auctions with budget-constrained players, may serve as a useful starting point for a more complete analysis of these issues.
A Appendix
The heuristic argument used to derive the expression in equation (4) assumes that ej(vi) > 0 and e0j(vi) > 0 for vi ∈ (0, v). The following Lemma shows that these conditions are satisÞed by the expression in equation (4).
Lemma 1 e(v)in equation (4) satisÞes the following properties for allv ∈(0, v):
(a) e(v)>0;
(b) e0(v)>0.
Proof.
(a) This part follows from the fact that α(1−F(s)) +βF(s) > 0 for v ∈ (0, v), and (α,β)≥0 with at least one element strictly positive. (b) To see that e0(v)>0, differentiate (4) to obtain
de(v)
dv = f(v)
([α−(α−β)F(v)])3Q(v), where
Q(v) = 2(α−β)
Z v
0
sf(s)[α(1−F(s)) +βF(s)]ds +v[α(1−F(v)) +βF(v)]2.
Evidently, for α ≥ β, Q(v) > 0 and hence e0(v) > 0. When α = 0, Q(v) can be simpliÞed to
Q(v) = −2β
Z v
0 sf(s)βF(s)ds+vβ2F(v)2
= β2
Z v
0
F(s)2ds >0.
Thus if α = 0 and β >0 then e0(v) >0. For the case 0<α <β, we note that the factors with 2αβ can be rewritten as
Z v
Let eA(v), eM(v), and eQ(v) denote the equilibrium expenditures arising under the American, Marshall, and Quayle systems.
Lemma 2 Under assumptions A1 through A4,
vlim→0eA(v) = lim
v→0eQ(v) = lim
v→0eM(v) = 0.
Proof. The Þrst two equalities follow directly, since limv→0eA(v) = lim
For the last equality, use L’Hospital’s rule to obtain
vlim→0eM(v) = lim
Lemma 3 Under assumptions A1 through A4, limv→0
Proof. Note that
Lemma 4 Under assumptions A1 through A4,
vlim→veQ(v)> lim
v→veA(v)>lim
v→veM (v)>0 Proof. The last inequality follows from the fact that
eM(v) ≡ lim
To establish the middle inequality, note that
eA(v) ≡ lim
v→veA(v)
= lim
v→v
Z v
0 sf(s)ds
=
Z v
0 sf(s)ds
> eM(v).
Finally, we establish theÞrst inequality:
eQ(v) ≡ lim
v→veQ(v)
= lim
v→v
Rv
0 sf(s)[2−F(s)]ds (2−F(v))2
=
Z v
0 sf(s)[2−F(s)]ds
= 2eA(v)−eM(v)
> 2eA(v)−eA(v)
= eA(v).
References
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Bücher des Forschungsschwerpunkts Marktprozeß und Unternehmensentwicklung Books of the Research Area Market Processes and Corporate Development
(nur im Buchhandel erhältlich/available through bookstores)
Tobias Miarka
Financial Intermediation and Deregulation:
A Critical Analysis of Japanese Bank-Firm-Relationships
Horst Albach, Ulrike Görtzen, Rita Zobel (Hg.) Information Processing as a Competitive Advantage of Japanese Firms
1999, edition sigma
Dieter Köster
Wettbewerb in Netzproduktmärkten 1999, Deutscher Universitäts-Verlag
Christian Wey
Marktorganisation durch Standardisierung: Ein Beitrag zur Neuen Institutionenökonomik des Marktes
1999, edition sigma
Horst Albach, Meinolf Dierkes, Ariane Berthoin Antal, Kristina Vaillant (Hg.)
Organisationslernen – institutionelle und kulturelle Dimensionen
WZB-Jahrbuch 1998 1998, edition sigma
Lars Bergman, Chris Doyle, Jordi Gual, Lars Hultkrantz, Damien Neven, Lars-Hendrik Röller, Leonard Waverman
Europe’s Network Industries: Conflicting Priorities - Telecommunications
Monitoring European Deregulation 1
1998, Centre for Economic Policy Research
Manfred Fleischer The Inefficiency Trap Strategy Failure in the
German Machine Tool Industry 1997, edition sigma
Christian Göseke
Information Gathering and Dissemination The Contribution of JETRO to
Japanese Competitiveness
1997, Deutscher Universitäts-Verlag
Andreas Schmidt
Flugzeughersteller zwischen globalem Wettbewerb und internationaler Kooperation Der Einfluß von Organisationsstrukturen auf die Wettbewerbsfähigkeit von
Hochtechnologie-Unternehmen 1997, edition sigma
Horst Albach, Jim Y. Jin, Christoph Schenk (eds.) Collusion through Information Sharing?
New Trends in Competition Policy 1996, edition sigma
Stefan O. Georg
Die Leistungsfähigkeit japanischer Banken Eine Strukturanalyse des Bankensystems in Japan
1996, edition sigma
Stephanie Rosenkranz
Cooperation for Product Innovation 1996, edition sigma
Horst Albach, Stephanie Rosenkranz (eds.) Intellectual Property Rights and Global Competition - Towards a New Synthesis 1995, edition sigma.
David B. Audretsch
Innovation and Industry Evolution 1995, The MIT Press.
Julie Ann Elston
US Tax Reform and Investment: Reality and Rhetoric in the 1980s
1995, Avebury
Horst Albach
The Transformation of Firms and Markets:
A Network Approach to Economic
Transformation Processes in East Germany Acta Universitatis Upsaliensis, Studia Oeconomiae Negotiorum, Vol. 34
1994, Almqvist & Wiksell International (Stockholm).
Horst Albach
"Culture and Technical Innovation: A Cross-Cultural Analysis and Policy
Recommendations"
Akademie der Wissenschaften zu Berlin (Hg.) Forschungsbericht 9, S. 1-597
1994, Walter de Gruyter.
DISCUSSION PAPERS 1999
Suchan Chae Bargaining Power of a Coalition in Parallel Bargaining: FS IV 99 - 1 Paul Heidhues Advantage of Multiple Cable System Operators
Christian Wey Compatibility Investments in Duopoly with Demand FS IV 99 - 2 Side Spillovers under Different Degrees of Cooperation
Horst Albach Des paysages florissants? Une contribution FS IV 99 - 3 à la recherche sur la transformation
Jeremy Lever The Development of British Competition Law: FS IV 99 - 4 A Complete Overhaul and Harmonization
Damien J. Neven Union Power and Product Market Competition: FS IV 99 - 5 Lars-Hendrik Röller Evidence from the Airline Industry
Zhentang Zhang
Justus Haucap The Incentives of Employers’ Associations to FS IV 99 - 6 Uwe Pauly Raise Rivals’ Costs in the Presence of
Christian Wey Collective Bargaining
Jianbo Zhang Asymptotic Efficiency in Stackelberg Markets FS IV 99 - 7 Zhentang Zhang with Incomplete Information
Justus Haucap Standortwahl als Franchisingproblem FS IV 99 - 8 Christian Wey
Yasar Barut A Comparison of Multiple-Unit All-Pay and FS IV 99 - 9 Dan Kovenock Winner-Pay Auctions Under Incomplete
Charles Noussair Information
Jim Y. Jin Collusion with Private and Aggregate Information FS IV 99 - 10
Jos Jansen Strategic Information Revelation and Revenue Sharing FS IV 99 - 11 in an R&D Race with Learning Labs
Johan Lagerlöf Incomplete Information in the Samaritan's Dilemma: FS IV 99 - 12 The Dilemma (Almost) Vanishes
Catherine Matraves Market Integration and Market Structure in the FS IV 99 - 13 European Soft Drinks Industry: Always Coca-Cola?
Pinelopi Koujianou Goldberg The Evolution of Price Discrimination in the FS IV 99 - 14 Frank Verboven European Car Market
Olivier Cadot A Political Economy Model of Infrastructure FS IV 99 - 15 Lars-Hendrik Röller Allocation: An Empirical Assessment
Andreas Stephan
Holger Derlien Industriestandort mit Vorbildfunktion? FS IV 99 - 16 Tobias Faupel Das ostdeutsche Chemiedreieck
Christian Nieters
Christine Zulehner Testing Dynamic Oligopolistic Interaction: FS IV 99 - 17 Evidence from the Semiconductor Industry
Johan Lagerlöf Costly Information Acquisition and FS IV 99 - 18 Delegation to a “Liberal” Central Banker
Ralph Siebert New Product Introduction by Incumbent Firms FS IV 99 - 19 Ralph Siebert Credible Vertical Preemption FS IV 99 - 20
Ralph Siebert Multiproduct Competition, Learning by Doing FS IV 99 - 21 and Price-Cost Margins over the Product Life Cycle:
Evidence from the DRAM Industry
Michael Tröge Asymmetric Information Acquisition in Credit Auction FS IV 99 - 22
Michael Tröge The Structure of the Banking Sector, Credit FS IV 99 - 23 Screening and Firm Risk
Michael Tröge Monitored Finance, Usury and Credit Rationing FS IV 99 - 24
Silke Neubauer Multimarket Contact, Collusion and the FS IV 99 - 25 International Structure of Firms
Horst Albach Dokumentation der „Bonner Stichprobe“ – Zur FS IV 99 - 26 Thomas Brandt Datenbank der Jahresabschlüsse deutscher
Holger Jakob Aktiengesellschaften, 1960-1997 M. A. Paradowska-Thimm
Jianping Yang
Tomaso Duso Endogenous Switching Costs and the Incentive FS IV 99 - 29 for High Quality Entry
Jos Jansen Regulating Complementary Input Supply: FS IV 99 - 30 Production Cost Correlation and Limited Liability
Robert Greb Internationalisierung der FuE-Tätigkeit von Unter- FS IV 99 - 34 nehmen der Chemischen Industrie in Deutschland
Suchan Chae The Effects of Downstream Distributor Chains on FS IV 99 - 35 Paul Heidhues Upstream Producer Entry: A Bargaining Perspective
Tobias Miarka The Recent Economic Role of Bank-Firm- FS IV 99 - 36 Relationships in Japan
William Novshek Demand for Customized Products, Production FS IV 99 - 37 Lynda Thoman Flexibility, and Price Competition
DISCUSSION PAPERS 2000
Justus Haucap Collective Wage Setting When Wages Are FS IV 00 - 01 Uwe Pauly Generally Binding: An Antitrust Perspective
Christian Wey
Stephanie Aubert Regionale Infrastrukturpolitik und ihre Auswirkung FS IV 00 - 02 Andreas Stephan auf die Produktivität: Ein Vergleich von
Deutschland und Frankreich
Achim Kemmerling Political Economy of Infrastructure Investment FS IV 00 - 03 Andreas Stephan Allocation: Evidence from a Panel of
Large German Cities
Andreas Blume Security Needs and the Performance FS IV 00 - 04 Asher Tishler of the Defense Industry
Tomaso Duso Who Decides to Regulate? Lobbying FS IV 00 - 05 Activity in the U.S. Cellular Industry
Paul Heidhues Hiding Information in Electoral Competition FS IV 00 - 06 Johan Lagerlöf
Andreas Moerke Grundlegende methodische Überlegungen zur FS IV 00 - 07 Ulrike Görtzen mikroökonomischen Forschung mit japanischen
Rita Zobel Unternehmensdaten
Rabah Amir Market Structure, Scale Economies, and FS IV 00 - 08 Industry Performance
Lars-Hendrik Röller Efficiency Gains from Mergers FS IV 00 - 09
Johan Stennek
Frank Verboven
Horst Albach Documentation of the Kaisha-Database – The FS IV 00 - 10 Ulrike Görtzen Annual Accounts Database of Japanese Stock
Tobias Miarka Companies 1970 – 1999
Andreas Moerke With a detailed Glossary of Japanese Thomas Westphal Accounting Terminology
Rita Zobel
Paul Heidhues Employers’ Associations, Industry-wide Unions, FS IV 00 - 11 and Competition
Roman Inderst Market Structure, Bargaining, and Technology FS IV 00 - 12 Christian Wey Choice
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