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Third-party funding in a sequential litigation process


Third party litigation financing (TPF)—for-profit, nonrecourse funding of litigation by a nonparty—is a new and rapidly developing industry. As a novel phenomenon that involves various normative concerns, TPF has sparked much debate and controversy among scholars and policy-makers, speculating about its potential effects on issues such as the volume of litigation and the quality of claims filed. We develop a game-theoretic model that compares a litigation process with TPF and a “traditional” scheme in which litigation is self-funded. Under the TPF scheme, we decompose the litigation decisions into two parts: the plaintiff is in charge of the legal decisions, while the TPF has the freedom to decide in each stage of the litigation process whether to continue the financial support in the litigation process. Such a setting is characterized by a high level of uncertainty and a degree of asymmetric information between the plaintiff and the TPF. We argue that the divergent interests of the parties to the financing agreement can be aligned by constructing a viable contract that results in the same equilibrium outcome as litigation with no TPF. The contract that achieves these desired results has a few interesting properties. First, it provides a pre-specified remedy to the plaintiff if the TPF funder terminates the financing prior to the conclusion of the litigation process. Second, the contract also specifies the compensation to the TPF funder, which is due upon completion of the litigation process, and it is conditioned upon the awarded verdict.

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Fig. 1


  1. 1.

    Casserleigh v. Wood, 59 P. 1024, 1026 (Colo. App. 1900).

  2. 2.

    For instance, Rt. Hon. Lord Woolf, M.R., Access to Justice: Final Report to the Lord Chancellor on the Civil Justice System in England and Wales (London: HMSO, 1996), available at:

  3. 3.

    For instance, lawyers take the distribution of possible verdicts for a given case as a criterion in settlement negotiations (Schkade et al. 2000); the range of possible verdicts might be taken into account by “an actor contemplating liability for a potentially tortious course of conduct” (Schkade et al. 2000: 24); in litigation insurance it is common for the insurer “to negotiate with the litigant for advances toward legal costs at different stages of the litigation” (Painter 1995: 683)

  4. 4.

    We assume that the number of possible litigation strategies is finite. Therefore, this problem is to choose one option (\(s^{*})\) out of a finite list, thus, ensuring the existence of an optimal litigation strategy. We further assume that if two litigation strategies result in the optimal solution, one is chosen at random.

  5. 5.

    For example, the TPF does not know the exact value of \({\bar{v}}_{s}\), but rather has a signal Y about the value of the case such that \(Y= {\bar{v}}_{s}+\varepsilon \), where \(\varepsilon \) is a zero-mean random variable.

  6. 6.

    We leave the analysis of a risk-averse plaintiff and asymmetric information for future research.


  1. Abramowicz, M. (2013). Litigation finance and the problem of frivolous litigation. DePaul Law Review, 63, 195.

    Google Scholar 

  2. Abramowicz, M., & Alper, O. (2013). Screening legal claims based on third-part litigation finance agreements and other signals of quality. Vand Law Review, 66, 1641.

    Google Scholar 

  3. Abrams, D., & Chen, D. L. (2013). A market for justice: A first empirical look at third party litigation funding. Journal of Business Law, 15(4), 1075.

    Google Scholar 

  4. Avraham, R., & Sebok, A. (2018). An empirical investigation of third party consumer litigant funding. Cornell Law Review, 104, 1133.

    Google Scholar 

  5. Avraham, R., & Wickelgren, A. (2014). Third-party litigation funding-a signaling model. DePaul Law Review, 63(2), 233.

    Google Scholar 

  6. Baik, K. H., & Kim, I. G. (2007). Contingent fees versus legal expenses insurance. International Review of Law and Economics, 27(3), 351–361.

    Article  Google Scholar 

  7. Bar-Gill, O. (2005). Pricing legal options: A behavioral perspective. Review of Law & Economics, 1(2), 204–240.

    Article  Google Scholar 

  8. Barksdale, C. R. (2007). All That Glitters Isn’t Gold: Analyzing the Costs and Benefits of Litigation Finance. Rev. Litig., 26, 707.

  9. Coffee, J. C., Jr. (2010). Litigation governance: Taking accountability seriously. Columbia Law Review, 288–351.

  10. Cornell, B. (1990). The incentive to sue: An option-pricing approach. The Journal of Legal Studies, 19(1), 173–187.

    Article  Google Scholar 

  11. Cotropia, C. A., Kesan, J. P., Rozema, K., & Schwartz, D. L. (2017). Endogenous litigation costs: An empirical analysis of patent disputes. Northwestern Law & Econ Research Paper, 17–01.

  12. Daughety, A. F., & Reinganum, J. F. (2013). Search, bargaining, and signalling in the market for legal services. The RAND Journal of Economics, 44(1), 82–103.

    Article  Google Scholar 

  13. Daughety, A. F., & Reinganum, J. F. (2014). The effect of third-party funding of plaintiffs on settlement. American Economic Review, 104(8), 2552–66.

    Article  Google Scholar 

  14. De Morpurgo, M. (2011). A Comparative Legal and Economic Approach to Third-Party Litigation Funding. Cardozo J. Int’l & Comp. L., 19, 343.

  15. Deffains, B., & Desrieux, C. (2015). To litigate or not to litigate? The impacts of third-party financing on litigation. International Review of Law and Economics, 43, 178–189.

    Article  Google Scholar 

  16. Demougin, D., & Maultzsch, F. (2014). Third-party financing of litigation: Legal approaches and a formal model. CESifo Economic Studies, 60(3), 525–553.

    Article  Google Scholar 

  17. DeStefano, M. M. (2012). Nonlawyers influencing lawyers: Too many cooks in the kitchen or stone soup? Fordham Law Review, 80, 2791.

    Google Scholar 

  18. DeStefano, M. (2013). Claim funders and commercial claim holders: A common interest or a common problem. DePaul Law Review, 63, 305.

    Google Scholar 

  19. Dnes, A., & Rickman, N. (1998). Contracts for legal aid: A critical discussion of government policy proposals. European Journal of Law and Economics, 5(3), 247–265.

    Article  Google Scholar 

  20. Eisenberg, T., & Lanvers, C. (2009). What is the settlement rate and why should we care? Journal of Empirical Legal Studies, 6(1), 111–146.

    Article  Google Scholar 

  21. Estevao, M. J. (2013). The litigation financing industry: Regulation to protect and inform consumers. U Colombia Law Review, 84, 467.

    Google Scholar 

  22. Faure, M., & De Mot, J. (2011). Comparing third-party financing of litigation and legal expenses insurance. JL Econ. & Pol’y, 8, 743.

  23. Fischer, J. M. (2014). Litigation financing: A real or phantom menace to lawyer professional responsibility. Geo J Legal Ethics, 27, 191.

    Google Scholar 

  24. Friehe, T. (2010). Contingent fees and legal expenses insurance: Comparison for varying defendant fault. International Review of Law and Economics, 30(4), 283–290.

    Article  Google Scholar 

  25. Garoupa, N., & Stephen, F. H. (2004). Optimal law enforcement with legal aid. Economica, 71(283), 493–500.

    Article  Google Scholar 

  26. Grous, L. J. (2006). Causes of action for sale: The new trend of legal gambling. U Miami Law Review, 61, 203.

    Google Scholar 

  27. Grundfest, J. A., & Huang, P. H. (2005). The unexpected value of litigation: A real options perspective. Stan Law Review, 58, 1267.

    Google Scholar 

  28. Hashway, J. W. (2012). Litigation loansharks: A history of litigation lending and a proposal to bring litigation advances within the protection of usury laws. Roger Williams U Law Review, 17, 750.

    Google Scholar 

  29. Heyes, A., Rickman, N., & Tzavara, D. (2004). Legal expenses insurance, risk aversion and litigation. International Review of Law and Economics, 24(1), 107–119.

    Article  Google Scholar 

  30. Howlett, M. J. (2013). Consumer litigation financing in Illinois: Seeking security and legitimization through regulation. Loy Consumer Law Review, 26, 140.

    Google Scholar 

  31. Huang, P. H. (2004). Lawsuit abandonment options in possibly frivolous litigation games. Rev Litig, 23, 47.

    Google Scholar 

  32. Hyman, D. A., Black, B., Zeiler, K., Silver, C., & Sage, W. M. (2007). Do defendants pay what juries award? post-verdict haircuts in Texas medical malpractice cases, 1988–2003. Journal of Empirical Legal Studies, 4(1), 3–68.

    Article  Google Scholar 

  33. Kidd, J. (2011). To fund or not to fund: The need for second-best solutions to the litigation finance dilemma. JL Econ. & Pol’y, 8, 613.

  34. Kirstein, R., & Rickman, N. (2004). Third party contingency contracts in settlement and litigation. Journal of Institutional and Theoretical Economics, 160, 555–575.

    Article  Google Scholar 

  35. Lambert, E. A., & Chappe, N. (2014). Litigation with legal aid versus litigation with contingent/conditional fees. Review of Law & Economics, 10(1), 95–115.

    Article  Google Scholar 

  36. Lyon, J. (2010). Revolution in progress: Third-party funding of American litigation. UCLA Law Review, 58, 571.

    Google Scholar 

  37. Lysaught, Geoffrey j.; Hazelgrove, D. Scott. (2011). Economic implications of third-party litigation financing on the US civil justice system. JL Econ. & Pol’y, 8, 645.

  38. Martin, S. L. (2008). Litigation financing: Another subprime industry that has a place in the United States market. Vill Law Review, 53, 83.

    Google Scholar 

  39. McLaughlin, J. H. (2006). Litigation funding: Charting a legal and ethical course. Vt Law Review, 31, 615.

    Google Scholar 

  40. Nichols, S. (2015). Access to cash, access to court: Unlocking the courtroom doors with third-party litigation finance. UC Irvine Law Review, 5, 197.

    Google Scholar 

  41. Painter, R. W. (1995). Litigating on a contingency: A monopoly of champions or a market for champerty. Chi-Kent Law Review, 71, 625.

    Google Scholar 

  42. Perry, R. (2018). Crowdfunding civil justice. BCL Review, 59, 1357.

    Google Scholar 

  43. Puri, P. (1998). Financing of litigation by third-party investors: A share of justice. Osgoode Hall LJ, 36, 515.

    Google Scholar 

  44. Qiao, Y. (2013). Legal effort and optimal legal expenses insurance. Economic Modelling, 32, 179–189.

    Article  Google Scholar 

  45. Rhee, R. J. (2007). The effect of risk on legal valuation. U Colo Law Review, 78, 193.

    Google Scholar 

  46. Richey, J. G. (2013). Tilted scales of justice-The consequences of third-party financing of American litigation. Emory LJ, 63, 489.

    Google Scholar 

  47. Rubin, P. H. (2011). Third-party financing of litigation. N Ky Law Review, 38, 673.

    Google Scholar 

  48. Sahani, V. S. (2016). Judging third-party funding. UCLA Law Review, 63, 388.

    Google Scholar 

  49. Schkade, D., Sunstein, C. R., & Kahneman, D. (2000). Deliberating about dollars: The severity shift, 100 Colum. Law Review, 1139, 1140.

    Google Scholar 

  50. Sebok, A. J. (2013). What do we talk about when we talk about control. Fordham Law Review, 82, 2939.

    Google Scholar 

  51. Shamir, J. (2016). Saving third-party litigation financing. Nw Interdisc Law Review, 9, 141.

    Google Scholar 

  52. Shepherd, J. M., & Stone, J. E. (2015). Economic conundrums in search of a solution: The functions of third-party litigation finance. Ariz St LJ, 47, 919.

    Google Scholar 

  53. Steinitz, M. (2010). Whose claim is this anyway-Third-party litigation funding. Minn Law Review, 95, 1268.

    Google Scholar 

  54. Steinitz, M. (2012). The litigation finance contract. Wm & Mary Law Review, 54, 455.

    Google Scholar 

  55. Steinitz, M. (2013). How much is that lawsuit in the window. Pricing legal claims Vand Law Review, 66, 1889.

    Google Scholar 

  56. Steinitz, M., & Field, A. C. (2014). A model litigation finance contract. Iowa Law Review, 99, 711.

    Google Scholar 

  57. Steinitz, M. (2019). Follow the money? A proposed approach for disclosure of litigation finance agreements. UC Davis Law Review, 53, 1073.

    Google Scholar 

  58. Van Velthoven, B., & Van Wijck, P. (2001). Legal cost insurance and social welfare. Economics Letters, 72(3), 387–396.

    Article  Google Scholar 

  59. Wendel, W. B. (2014). A legal ethics perspective on alternative litigation financing. Can Bus LJ, 55, 133.

    Google Scholar 

  60. Wendel, W. B. (2018). Paying the piper but not calling the tune: Litigation financing and professional independence. Akron Law Review, 52, 1.

    Google Scholar 

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Proof of Proposition 1. The proof uses backward induction. We start with period N. In this case, based on the definition of \(R_{N}={\bar{v}} _{s}\), the plaintiff chooses to execute the final stage only if \(c_{N}\le {\bar{v}}_{s}\), which is indeed the optimal decision.

We now assume that the decision rule is optimal for the case of \(t+1\), and examine the optimality of the decision rule for the case of period t. Note that based on the optimality of period \(t+1\) the profit of plaintiff starting at period \(t+1\) is

$$\begin{aligned} \begin{array}{ll} R_{t+1}(s,{\bar{v}}_{s})-c_{t+1} &{} \,\hbox {if} R_{t+1}(s,{\bar{v}}_{s})\ge c_{t+1}; \\ 0 &{} R_{t+1}(s,{\bar{v}}_{s})<c_{t+1}. \end{array} \end{aligned}$$

and the ex-ante payoff of the plaintiff starting at period \(t+1\) is therefore given by

$$\begin{aligned} E\left[ \left( R_{t+1}(s,{\bar{v}}_{s})-c_{t+1}\right) ^{+}\right] , \end{aligned}$$

which by definition equals \(R_{t}(s,{\bar{v}}_{s})\). Therefore, for a plaintiff observing the litigation cost of \(c_{t}\) it is optimal to continue the process if \(c_{t}\le \) \(R_{t}(s,{\bar{v}}_{s})\). Thus, the Proposition is correct for period t, and by induction it is correct for any period.

Proof of Proposition 2. (a) We first show that under the TC contract, the plaintiff chooses the optimal litigation strategy \(s^{*}\). Note that if the litigation process is terminated during any period \(t<N\), the plaintiff receives the compensation of \(D(s,{\bar{v}}_{s})=\pi (s, {\bar{v}}_{s})\). If the litigation process is completed successfully, the plaintiff receives the reward of \(v_{s}\) minus the payment to the TPF funder. The expected payment to the TPF funder is \(E\left[ P(s,v_{s})\right] ={\bar{v}}_{s}-D(s,{\bar{v}}_{s})={\bar{v}}_{s}-\) \(\pi (s,\bar{ v}_{s})\). Therefore, the expected net payoff to the plaintiff when the litigation process is completed is

$$\begin{aligned} {\bar{v}}_{s}-E\left[ P(s,v_{s})\right] ={\bar{v}}_{s}-\left( {\bar{v}}_{s}-\pi (s,{\bar{v}}_{s})\right) =\pi (s,{\bar{v}}_{s}). \end{aligned}$$

Therefore, according to the TC contract, the plaintiff receives the same expected reward, regardless of the litigation outcome, and this payoff is \( \pi (s,{\bar{v}}_{s})\). When the plaintiff needs to determine the optimal litigation strategy, he maximizes the following objective function of \( \max _{s}\pi (s,{\bar{v}}_{s})\), and by definition \(s^{*}\in \arg \max \pi (s,{\bar{v}}_{s})\).

(b) We next show that TPF funder receives the same decisions as the plaintiff in the benchmark. The proof is conducted by backward induction. For period N, the TPF funder continues the litigation process if

$$\begin{aligned} -D(s,{\bar{v}}_{s})\le E\left[ P(s,v_{s})\right] -c_{N}. \end{aligned}$$

The LHS denotes the compensation that the TPF funder pays the plaintiff if the litigation process is terminated. The RHS is the payoff to the TPF funder if she continues the litigation process. In the latter case, she incurs the cost of \(c_{N}\) and receives the payment of \(P(s,v_{s})\). Note that \(E\left[ P(s,v_{s})\right] ={\bar{v}}_{s}-\) \(D(s,{\bar{v}}_{s})\). Therefore, the TPF funder continues if

$$\begin{aligned} -D(s,{\bar{v}}_{s})\le & {} {\bar{v}}_{s}-D(s,{\bar{v}}_{s})-c_{N} \\ 0\le & {} {\bar{v}}_{s}-c_{N}, \end{aligned}$$

and this is the same decision rule for the plaintiff in the benchmark case.

We next assume that the Proposition holds for period \(t+1\) and examine period t. In period t, a plaintiff in the benchmark case would fund this stage if the following condition is satisfied

$$\begin{aligned} c_{t}\le & {} \underset{*}{\underbrace{\mathop {\displaystyle \prod }\limits _{j=t+1}^{N}\Pr (C_{j}\le R_{j}(s,{\bar{v}}_{s}))}}\left( {\bar{v}} _{s}-\sum _{j=t+1}^{N}E[C_{j}|C_{j}\le R_{j}(s,{\bar{v}}_{s})]\right) \\&-\sum _{j=t+1}^{N}\left[ \underset{**}{\underbrace{ \mathop {\textstyle \prod }\limits _{i=t+1}^{j}\Pr (C_{i}\le R_{i}(s,{\bar{v}}_{s}))\Pr (C_{j}>R_{j}(s,{\bar{v}}_{s}))}}\sum _{i=t+1}^{j-1}E[C_{i}|C_{i}\le R_{i}(s,{\bar{v}}_{s})]\right] . \end{aligned}$$

Under the TPF case, the TPF funder would find it beneficial to continue to the next stage if

$$\begin{aligned} -D(s,{\bar{v}}_{s})\le & {} \underset{***}{\underbrace{ \mathop {\displaystyle \prod }\limits _{j=t+1}^{N}\Pr (\delta _{j}^{TPF}(s,{\bar{v}} _{s},C_{j}|\mathbb {k})=1))}}\left( E\left[ P(s,v_{s})\right] - \sum _{i=t+1}^{N}E[C_{i}|\delta _{i}^{TPF}(s,{\bar{v}}_{s},C_{i}|\mathbb {k})=1)]\right) \nonumber \\&-\sum _{j=t+1}^{N}\left[ \begin{array}{c} \underset{****}{\underbrace{\mathop {\textstyle \prod }\limits _{i=t+1}^{j}\Pr (\delta _{i}^{TPF}(s,{\bar{v}}_{s},C_{i}|\mathbb {k})=1))\Pr ((\delta _{j}^{TPF}(s,{\bar{v}}_{s},C_{j}|\mathbb {k})=0))}} \\ \left( \sum _{i=t+1}^{j-1}E[C_{i}|\delta _{i}^{TPF}(s,{\bar{v}} _{s},C_{t}|\mathbb {k})=1)]+D_{t}(s,{\bar{v}}_{s})\right) \end{array} \right] \nonumber \\&-c_{t}. \end{aligned}$$

Based on the induction assumption that the plaintiff and the TPF funder receive the same funding decisions for any period \(t+1,...,N\), the probability of successfully completing the litigation process or terminating it at a certain point are identical. Also using the fact that \(E\left[ P(s,v_{s})\right] ={\bar{v}}_{s}-D(s,{\bar{v}}_{s})\), we can express Equation (13) in the following way

$$\begin{aligned} -D(s,{\bar{v}}_{s})\le & {} \mathop {\displaystyle \prod }\limits _{j=t+1}^{N}\Pr (\delta _{j}^{TPF}(s,{\bar{v}}_{s},C_{j}|\mathbb {k})=1))\left( {\bar{v}}_{s}-D(s, {\bar{v}}_{s})-\sum _{i=t+1}^{N}E[C_{i}|\delta _{i}^{TPF}(s,v_{s},C_{i}|\mathbb {k})=1)]\right) \\&-\sum _{j=t+1}^{N}\left[ \begin{array}{c} \mathop {\textstyle \prod }\limits _{i=t+1}^{j}\Pr (\delta _{i}^{TPF}(s,{\bar{v}} _{s},C_{i}|\mathbb {k})=1))\Pr ((\delta _{j}^{TPF}(s,{\bar{v}}_{s},C_{j}|\mathbb {k})=0)) \\ \left( \sum _{i=t+1}^{j-1}E[C_{i}|\delta _{i}^{TPF}(s,{\bar{v}} _{s},C_{t}|\mathbb {k})=1)]+D_{t}(s,{\bar{v}}_{s})\right) \end{array} \right] \\&-c_{t} \\= & {} \mathop {\displaystyle \prod }\limits _{j=t+1}^{N}\Pr (\delta _{j}^{TPF}(s,{\bar{v}} _{s},C_{j}|\mathbb {k})=1))\left( {\bar{v}}_{s}-\sum _{i=t+1}^{N}E[C_{i}|\delta _{i}^{TPF}(s,{\bar{v}}_{s},C_{i}|\mathbb {k})=1)]\right) \\&-\sum _{j=t+1}^{N}\left[ \begin{array}{c} \mathop {\textstyle \prod }\limits _{i=t+1}^{j}\Pr (\delta _{i}^{TPF}(s,{\bar{v}} _{s},C_{i}|\mathbb {k})=1))\Pr ((\delta _{j}^{TPF}(s,{\bar{v}}_{s},C_{j}|\mathbb {k})=0)) \\ \left( \sum _{i=t+1}^{j-1}E[C_{i}|\delta _{i}^{TPF}(s,{\bar{v}} _{s},C_{t}|\mathbb {k})=1)]\right) \end{array} \right] \\&-c_{t}-D(s,{\bar{v}}_{s}) \end{aligned}$$

Note that the value of \(-D(s,{\bar{v}}_{s})\) appears on both sides of the inequality, and, thus, cancels. Furthermore, after these manipulations, the decision rule of the plaintiff indeed coincides with the decision rule of the TPF funder. This concludes the proof that the contract satisfies Equation (6). Finally, note that \(\pi (s^{*},v_{s^{*}})>0\) .

Proof of Proposition 3. We denote by \(\pi ^{p}(s,{\bar{v}} _{s},\mathbb {k},{\widetilde{v}}_{s})\) the payoff of the plaintiff when he reports the claim value of \({\widetilde{v}}_{s}\) and by \(\pi ^{p}(s,{\bar{v}} _{s},\mathbb {k},{\bar{v}}_{s})\) when he truthfully reports the claim value of \({\bar{v}}_{s}\). Truthful information sharing is the strategic choice of the plaintiff when

$$\begin{aligned} \pi ^{p}(s,{\bar{v}}_{s},\mathbb {k},{\bar{v}}_{s})-\pi ^{p}(s,{\bar{v}} _{s},\mathbb {k},{\widetilde{v}}_{s})\ge 0\text { for every possible }{\bar{v}} _{s}\text { and }{\widetilde{v}}_{s}. \end{aligned}$$

Recall that \(\pi ^{p}(s,{\bar{v}}_{s},\mathbb {k},{\bar{v}}_{s})=D(s, {\bar{v}}_{s})\). Denote by \(z({\widetilde{v}}_{s})\) the probability to successfully completing all the litigation phases given the announced value of \({\widetilde{v}}_{s}\). Therefore,

$$\begin{aligned} \pi ^{p}(s,{\bar{v}}_{s},\mathbb {k},{\widetilde{v}}_{s})= & {} z({\widetilde{v}} _{s})E\left[ \left( v_{s}-P(s,{\widetilde{v}}_{s}\right) )^{+}\right] +\left( 1-z({\widetilde{v}}_{s})\right) D(s,{\widetilde{v}}_{s}) \\= & {} z({\widetilde{v}}_{s})\left( {\bar{v}}_{s}-{\widetilde{v}}_{s}+D(s, {\widetilde{v}}_{s})\right) +\left( 1-z({\widetilde{v}}_{s})\right) D(s, {\widetilde{v}}_{s}). \end{aligned}$$


$$\begin{aligned} \pi ^{p}(s,{\bar{v}}_{s},\mathbb {k},{\bar{v}}_{s})-\pi ^{p}(s,{\bar{v}} _{s},\mathbb {k},{\widetilde{v}}_{s})= & {} z({\widetilde{v}}_{s})\left( D(s,{\bar{v}} _{s})-{\bar{v}}_{s}+{\widetilde{v}}_{s}-D(s,{\widetilde{v}}_{s})\right) \nonumber \\&+\left( 1-z({\widetilde{v}}_{s})\right) \left( D(s,{\bar{v}}_{s})-D(s, {\widetilde{v}}_{s})\right) \nonumber \\= & {} z({\widetilde{v}}_{s})\left( {\widetilde{v}}_{s}-{\bar{v}}_{s}\right) +D(s, {\bar{v}}_{s})-D(s,{\widetilde{v}}_{s}), \end{aligned}$$

and we need to show that this value is non-negative. Denote the ex-ante expected litigation cost given the claim value of \({\widetilde{v}}_{s}\) by \( E[C|{\widetilde{v}}_{s}]\). Therefore,

$$\begin{aligned} \pi (s,{\widetilde{v}}_{s})= & {} D(s,{\widetilde{v}}_{s})=z({\widetilde{v}}_{s}) {\widetilde{v}}_{s}-E[C|{\widetilde{v}}_{s}]; \\ \pi (s,{\bar{v}}_{s})= & {} D(s,{\bar{v}}_{s})=z({\bar{v}}_{s}) {\bar{v}}_{s}-E[C|{\bar{v}}_{s}], \end{aligned}$$

and note that \(\pi (s,{\bar{v}}_{s})=D(s,{\bar{v}}_{s})=z({\bar{v}} _{s}){\bar{v}}_{s}-E[C|{\bar{v}}_{s}]\ge z({\widetilde{v}} _{s})v_{s}-E[C|{\widetilde{v}}_{s}]=\pi (s,{\widetilde{v}}_{s})\). Therefore,

$$\begin{aligned} D(s,{\widetilde{v}}_{s})-D(s,{\bar{v}}_{s})\le z({\widetilde{v}}_{s})\left( {\widetilde{v}}_{s}-{\bar{v}}_{s}\right) , \end{aligned}$$

which implies that

$$\begin{aligned} \pi ^{p}(s,{\bar{v}}_{s},\mathbb {k},{\bar{v}}_{s})-\pi ^{p}(s,{\bar{v}} _{s},\mathbb {k},{\widetilde{v}}_{s})= & {} z({\widetilde{v}}_{s})\left( {\widetilde{v}} _{s}-{\bar{v}}_{s}\right) -\left( D(s,{\widetilde{v}}_{s})-D(s,{\bar{v}} _{s})\right) \\\ge & {} z({\widetilde{v}}_{s})\left( {\widetilde{v}}_{s}-{\bar{v}}_{s}\right) -z({\widetilde{v}}_{s})\left( {\widetilde{v}}_{s}-{\bar{v}}_{s}\right) =0. \end{aligned}$$

Further note that choosing another strategy \({\widetilde{s}}\) instead of the strategy s cannot improve the situation for the plaintiff since according to the suggested contract the TPF just recovers its costs, and the plaintiff receives the entire surplus from the legal claim - \(\pi (s,{\bar{v}}_{s})\) . Therefore, when choosing the strategy the plaintiff solves for \(max_{s}\pi (s,{\bar{v}}_{s})\), and by definition \(s^{*}\in \arg \max \pi (s, {\bar{v}}_{s})\)

Proof of Proposition 4. Note that for any stage \(\hbox {{ /}{t}}\) in which the litigation process is terminated the plaintiff receives the sum of \(D(s, {\bar{v}}_{s})\). When the litigation process is completed successfully, the plaintiff receives the sum of max(\(v_{s}-P(s,v_{s}),0)\) which according to Proposition 2, its expected value equals \(D(s,{\bar{v}} _{s}). \) Therefore, without a settlement, the plaintiff receives the sum of \( D(s,{\bar{v}}_{s})\) regardless of the outcome of the litigation process. Thus, the plaintiff would agree to any settlement that gives him at least this value.

Under the benchmark case, a plaintiff would agree to a settlement offer of \( o_{t}\) if \(-c_{t}+\) \(R_{t}(s,{\bar{v}}_{s})\le o_{t}\). Based on Proposition 2, we have that \(\underset{*}{\underbrace{-c_{t}+R_{t}(s, {\bar{v}}_{s})=-c_{t}+\pi _{t+1}^{TPF}(s,{\bar{v}}_{s})+D(s,\bar{v }_{s})}}\). Under the TC contract, if a settlement is offered, the TPF funder receives the sum of \(o_{t}-D(s,{\bar{v}}_{s})\); thus she would agree to this settlement offer if

$$\begin{aligned} o_{t}-D(s,{\bar{v}}_{s})\ge -c_{t}+\pi _{t+1}^{TPF}(s,{\bar{v}}_{s}), \end{aligned}$$

where the RHS represents the TPF funder’s payoff from continuing the case and the LHS the payoff from accepting the settlement offer. Using \(*\), this equation can be expressed as

$$\begin{aligned} o_{t}-D(s,{\bar{v}}_{s})\ge & {} -c_{t}+R_{t}(s,{\bar{v}}_{s})-D(s, {\bar{v}}_{s}) \\ o_{t}\ge & {} -c_{t}+R_{t}(s,{\bar{v}}_{s}). \end{aligned}$$

Note that this is the condition that ensures that the plaintiff would agree to accept the settlement offer of \(o_{t}\) under the benchmark case of self-funded litigation process.

Proof of Corollary 1. The results are based on Jensen’s inequality. By Jensen’s Inequality, for a strictly concave utility function, \(E\left[ u(x)\right] <u\left[ E(x)\right] \). A risk neutral TPF funder will fund any claim such that \(E(x)\ge 0\), where x represents the stochastic payoff of the claim. Assume that \(E(x)=0\), then \(E\left[ u(x)\right] <0\), and, thus, a risk-averse plaintiff will not fund this claim under the self-funded litigation setting.

In a similar manner, there exists \(\underline{o}_{t}\), such that \(u( \underline{o}_{t})= E\left[ u(x)\right] \), and, thus, the risk-averse plaintiff will choose to accept any settlement offer with \(o_{t}>\underline{o }_{t}\). However, due to the risk-aversion, we have that \(\underline{o} _{t}<E(x)\).

Proof of Proposition 5. Assume that the TPF funder wishes to negotiate the terms of the contract. The plaintiff would agree only if he receives the amount of x which is higher than what he expects to receive based on the original contract. According to the original contract, the plaintiff receives the amount of \(D(s,{\bar{v}}_{s})\) if the legal process is terminated, and receives the same expected amount if the legal process is completed successfully (see Proposition 2). Therefore, the plaintiff will refuse to any renegotiation offer that results in a lower amount of \(D(s,{\bar{v}}_{s})\). However, the TPF funder cannot do any better if she does not offer the plaintiff a lower amount than \(D(s, {\bar{v}}_{s})\) when the case is completed, and therefore the contract outlined in Proposition 2 is renegotiation-proof. Similar arguments can be made regarding an offer to re-negotiate that comes from the plaintiff.

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Shamir, J., Shamir, N. Third-party funding in a sequential litigation process. Eur J Law Econ 52, 169–202 (2021).

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  • Third party funding
  • Litigation funding
  • Game theory
  • Contract theory

JEL Classification

  • K41
  • L84
  • K20