Like the durable goods monopolist, the defendant always wins by using an MFN. Spier shows that an MFN implements the full commitment solution (a simple, take-it-or-leave-it offer). When all claimants can settle in both periods, the use of MFN eliminates delay costs that arise in equilibrium without an MFN.
If the defendant refuses the request, the case goes to trial and the first plaintiff is out of the game; the second period begins with no MFN to restrict negotiations. We identify the likely circumstances in which the overall probability of a subsequent case settling increases with the greatest benefit.
Model Structure
An appendix provides proofs of our model's propositions and relevant properties; some derivations are included in the main text for ease of exposition. Note that the monotonicity of the rejection probability implies its continuity, since if there were a jump (which would be upward), the type making the demand just above the jump could make an infinite reduction in demand and enjoy a non- infinite decrease in probability of rejection. However, an upward jump can occur (and sometimes does) for S > SG, since there is no type that would thereby be induced to defect.
If S2 exceeds S1, and if D accepts S2, then D pays S2 P2 and pays S2 - S1 for P1 (if and only if there is an MFN clause in any settlement between D and P1); if D refuses P2's request and goes to trial, then x2 is discovered at trial, D pays x2 to P2 and nothing more to P1, and then P2 and D pay their respective court costs. Finally, plaintiffs are "time inflexible" in that they cannot adjust the timing of their negotiations with D by either delaying or moving earlier. Although each of the bargaining subgames examined in the next two sections differs in some respects, their equilibria have similar attributes.
Equilibrium behavior for a claimant will involve an array demand function that maps the interval of types, [x, xG], into an interval of array demands, [S, SG], with higher types making higher demands. Equilibrium behavior for the defendant will involve a probability of rejection function that is continuous on [S, SG], starts at zero and is strictly increasing up to (at most) one, after which it remains constant at one.6 We will rely on these properties to motivate the derivation of the equilibrium strategies. Equilibrium analysis of the two-stage signaling game when there is no MFN clause, since the levels of expected damages for the claimants, x1 and x2, are independent and.
Equilibrium Analysis of the Two-Stage Signaling Game When There is No MFN Clause Since the levels of expected damages for the plaintiffs, x 1 and x 2 , are independent and
8 For the technical buffs, this equilibrium (and the other equilibria discussed in this article) is the unique Perfect Bayesian equilibrium that survived the D1 refinement of Cho and Kreps (1987). c) r0*(S0*(x)) = 0. Condition (b) states that S0* must maximize P's expected payoff, given D's equilibrium rejection function r0*(S), while condition (c) provides the boundary requirement that D should not reject the lowest rational demand that any P would make (that is, x + kD, which is the minimum that D would pay if he were tried against any type of P). This leads to the following theorem which summarizes the equilibrium strategies for D and P, as well as D's equilibrium beliefs, in the one-stage game (see the Appendix for the proof).8.
For the single-phase signaling game between P and D, the following strategies (r0*(S), S0*(x)) and beliefs b0*(S) provide the unique revealing equilibrium. Thus, in the two-stage game without an MFN, P1 and D play the single-stage game equilibrium strategies as specified above, and either D accepts the demand or D rejects it and P1 and D go to trial; this is followed by P2 and D playing the single-stage game equilibrium strategies specified above, and either D accepts the demand or D rejects it and P2 and D go to trial. Note that this is not to imply that D always settles, but that he pays xi + kD either in settlement or trial against Pi.
Equilibrium analysis of the two-phase signaling game when there is an MFN clause that analyzes the second phase of the signaling game.
Equilibrium Analysis of the Two-Stage Signaling Game When There is an MFN Clause Analyzing the Signaling Game’s Second Stage
In each setting, D is then forced to a point of indifference between accepting the claim or going to court. In this case, claims are rejected with certainty, which means that each type goes to trial and receives their expected compensation less kP. As discussed in the Appendix, there is a trivial manifold of revealing equilibrium claims that are rejected with probability one; those we highlight are the lowest such disclosure requirements, and are the natural extension of those requirements that enjoy a positive probability of acceptance.
If, on the other hand, SG2(S1) < S1 + K, then the revealing demand xG is also less than S1 + K, so that all types have a positive settlement probability. In other words, D is "completely eliminated" with or without the maximum benefit in any agreement entered into in the first stage (or should D go to trial in the first stage). The first term on the top right reflects the possibility that D and P1 go to trial, while the second term on the right reflects the possibility that D and P1 settle and the settlement uses MFN.
This type makes an exposed claim that is just large enough that D rejects it with probability one and that this type (x~2(S1)) is indifferent between settlement and trial. Thus, T(S1) provides a set of types P2 that will yield requests that will (if D accepts) generate a payment based on P1's maximum benefit. In particular, 1 + gN(S1) > 0 means that P1's settlement payoff (S1 + g(S1)) increases in S1, providing the usual incentives for (essentially) all types of P1 to tempt them to inflate their demands, causing D's rejection probability function to increase in S1.
The boundedness of gN(t) ensures that 0 < r1*(S1) < 1, as assumed above; in the appendix, we show that this rejection probability function is the best response for D to P1, revealing the equilibrium requirement. For a first-degree signaling game between P1 and D, the following strategies (r1*(S1), S1*(x)) and beliefs b1*(S1) provide a unique revealing equilibrium when MFN is used. 12 Of course, if inequality (5) does not hold for some x1, this type P1 would not use MFN; again, D would be indifferent to his employment.
Payoffs and Welfare Considerations
Thus, for distributions sufficiently close to uniform (but preferably with fN(C) either positive or negative, or both), P1 always prefers an MFN. On the other hand, P2 is never helped (and sometimes harmed) by the presence of an MFN in the residence between P1 and D, regardless of the distribution of damages. Furthermore, this also means that the expected profit for P2 under an MFN (i.e., taking the expectation of B^P2(x2; x1) with respect to x2) is strictly lower than the expected profit for P2 without MFN.
However, if we consider an alternative measure of welfare, expected trial costs, it is surprising that an MFN can actually reduce expected trial costs for both D and P2. Thus, for an open set of distributions sufficiently close to the uniform, expected trial costs for P2 and D are lowered when an MFN is used. This is possible because an MFN creates both a direct and an indirect (equilibrium) effect on the probability that a later claimant type's claim is rejected.
When an MFN results in a higher probability of rejection for a given claim made by a later claimant (the direct effect), it also moderates the claim made by later claimant types (the indirect or equilibrium effect). We also know that when F(C) is the uniform distribution, r^1(x1) < r^0(x1); that is, P1's expected sample cost is also strictly lower with an MFN. The total expected litigation costs (for all claimants) are thus lower when an MFN is used.
The presence of an MFN makes P2 moderate its demand if x2 > x1; this moderation means that low types of P2 (such that x2 < x1) are unaffected, but high types (x2 > x1) are worse off.
Discussion and Conclusions
The scope of the trial is exactly the same, but there are no late fees; all savings in delay costs accrue to the defendant, making plaintiffs just as good off as without MFN. In contrast, when informed claimants negotiate successively with the same defendant (highlighting the early claimant's ability to take advantage of future settlements), we find that MFN:. 1) does not affect the defendant; (2) it always harms (or leaves unharmed) the later claimant while the early claimant is at least in the same position because it has the option (because the early claimant can choose not to include MFN in its settlement claim); and (3) the overall effect of MFN on settlement scope is indeterminate. Thus, MFN may be introduced by an early claimant to take advantage of a future settlement between the defendant and a later claimant.
Despite this essentially redistributive motive, this use of an MFN can reduce the expected social costs associated with trials. As discussed above, an MFN can reduce the expected trial costs in the second case due to its moderating effect on claims made by P2 that exceed P1's demand. What guidance can these models provide for a judge deciding whether to allow and/or enforce an MFN.
A judge certifying a bilateral settlement in circumstances where there is likely to be further litigation by other parties must be convinced that overall social costs will be sufficiently reduced by the use of an MFN to compensate for likely distributional inequities. Alternatively, when all parties appear to be present, judges should expect the issue of enforcing an MFN to outweigh the benefits of prompt settlement. We argue that when F(C) is the uniform distribution, expected trial costs are lower in both the first and second periods with an MFN.
Perhaps more surprisingly, the expected trial cost in the second period is also lower with MFN when x2 is uniformly distributed. We determine the value of x1 and argue that if x2 is uniformly distributed, the expected trial cost for the second period is lower under MFN. Since this will turn out to be true for all values of x1 (except for x1 = xG, in which case MFN never commits to any x2), the ex ante expected trial cost for the second period is lower under MFN.
