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This experiment analyzes multi-offer versions of the signaling and screening litigation games, as well as a bilateral multi-offer litigation game. A plaintiff has either a low or a high claim on an uninformed defendant, and the two negotiate in an attempt to reach a pre-trial settlement. Trial is costly, and settlement generates surplus over which the two parties can bargain. In the signaling game, the defendant has the power to make the offer, while the plaintiff makes the offer in the screening game. Previous experiments on single-offer games find that disputes occur even when offers contain surplus not predicted under the theory, and fairness appears to be important in explaining deviations from theory. This research examines whether renegotiation in the form of successive sequential offers can yield efficiency gains via lower dispute rates. There are four main findings. One, under the one-sided multi-offer structure the excess dispute rate is 23 percentage-points lower in the screening game, and the high-offer dispute rate is 31 percentage-points lower in signaling game. The bilateral game yields an additional 15 percentage-point reduction in the high-offer dispute rate, but excess disputes persist. Two, in these games, proposers take advantage of the multi-offer opportunity and make around three to four offers per negotiation. Three, across games the surplus in a fair offer remains constant at about one-sixth of the surplus, but the empirical benchmark from which this is measured varies according to which player has the power to make the offer. In the one-sided games, the benchmark is the respective zero-surplus endpoint, but in the bilateral game the benchmark is the surplus midpoint. Fourth, dynamic behavior plays an important but complex role in observed outcomes. Multi-offer mechanisms may be alternatives to costly information transmission mechanisms like disclosure or discovery.

This chapter studies the large sample properties of a subclassification-based estimator of the dose–response function under ignorability. Employing standard regularity conditions, it is shown that the estimator is root-n consistent, asymptotically linear, and semiparametric efficient in large samples. A consistent estimator of the standard-error is also developed under the same assumptions. In a Monte Carlo experiment, we investigate the finite sample performance of this simple and intuitive estimator and compare it to others commonly employed in the literature.