Diminishing paylines reduce investigators' ROIs in a proposal competition.

A: Equilibrium benefit (blue or green) and cost (red) curves for an investigator with a project at the 90th percentile of v in a proposal competition. The blue and green curves show the benefit at a 45% and 15% payline, respectively. Vertical lines show the investigator's equilibrium bid, with solid portions giving the investigator's payoff and dashed portions showing the cost. The corner in the benefit curves appears at the strongest proposal submitted. B: An investigator's ROI (Eq 3) in a proposal competition with 45% (solid line) or 15% (dashed line) paylines, as a function of the quantile of the scientific value of her project, F(v). These curves also give the investigator's ROI in a partial lottery with 45% or 15% lottery lines, and any payline. These results use the baseline parameters. ROI, return on investment.