Bargaining and Deadlines

2025-12-15

2026-01-31

Impasse indicator. Unit: pair–round. Definition: 1 if no agreement is reached before the realized deadline; 0 otherwise.

Agreement time Unit: pair–round. Definition: number of seconds between the start of the round and the moment an offer is accepted. For rounds without agreement, we will treat agreement time as missing for primary analyses of timing (and separately analyze censoring).

Opening offer gap. Unit: pair-round. Definition: difference between initial buyer offer and seller demand.

The experiment consists of a laboratory bargaining task in which subjects are randomly assigned to the role of buyer or seller and remain in that role throughout the session. Within each treatment, subjects are placed in fixed matching groups of sixteen participants and engage in twenty rounds of bilateral bargaining, being randomly re-matched with a new partner in every round. In each round, a buyer’s valuation and a seller’s cost are drawn independently from known distributions, and the pair negotiates over the price until either an agreement is reached or the deadline expires. We vary two factors between subjects: whether valuations and costs are private or commonly known, and whether payoffs are discounted continuously over negotiation time. Within each session, we also vary the degree of deadline uncertainty by randomly assigning rounds with different possible realizations of the deadline. All interactions take place through a computer interface, and participants receive monetary payoffs based on their decisions and bargaining outcomes. The design, procedures, and incentives are identical across treatments except for the pre-specified variations described above.

Not available

Subjects are recruited through LINEEX and assigned to sessions by the laboratory using their standard randomized invitation procedure. Once in the lab, all within-experiment randomization—including the draws of valuations and costs, the assignment of deadline-uncertainty conditions across rounds, and the random re-matching of bargaining partners is carried out automatically by the experimental software.

The unit of randomization is the individual subject. Subjects are invited to sessions independently, and all within-experiment randomization—valuations and costs, re-matching of bargaining partners, and the sequence of deadline-uncertainty conditions—is implemented at the individual level by the software.

No

24 matching groups (6 matching groups per treatment, each consisting of 16 subjects).

384 subjects in total (96 subjects per treatment).

96 subjects per treatment arm: 96 in Private Information / No Discount, 96 in Complete Information / No Discount, 96 in Private Information / Discount, and 96 in Complete Information / Discount.

Our power calculations are based on outcome variances estimated from an earlier laboratory experiment in a closely related bargaining environment conducted in the same lab and subject pool (same task without the discounting manipulation). In that study, the impasse rate in surplus-positive rounds was about 25%, implying a standard deviation of roughly 0.43 for the binary impasse indicator, and agreement time had a standard deviation of about 20 seconds. Using these values, assuming cluster-robust inference at the matching-group level (24 matching groups of 16 subjects each) and conventional parameters (α = 0.05, power = 0.80), our design yields a minimum detectable effect size on impasse of roughly 8 percentage points (about 0.20 standard deviations) and a minimum detectable change in agreement time of about 5 seconds (around 0.25 standard deviations) for main treatment contrasts.