Theoretical Investigation on the Optimal Contracting for Directors Holding Multiple Directorships
Bibliographic record
Abstract
This paper is the first (to our knowledge) to analytically model the optimal contracting for a member of the board of directors who holds multiple directorships. Prior literature has found conflicting evidence on the overall effect of multiple directorships on shareholder welfare: busy board members are usually detrimental to firm operating performance due to the limited time and effort they are able to devote to each board; however, multiple directorships can be beneficial to firms if the board members gain knowledge and expertise through their multiple appointments. The objective of our study is to expand the research on the effects of multiple directorships on shareholder welfare by modeling the relationship between optimal incentives (pay–performance sensitivity) and the number of directorships. Modeling within the Linear–Exponential–Normal framework, and solving using Subgame-Perfect Nash Equilibrium, we find that this relationship is positive when efforts across directorships are either substitutive or complementary, which highlights another potential significant downside to multiple directorships: companies need to offer high incentive-based pay to compete for directors’ efforts, leading to high-risk premia and welfare loss to shareholders. Our results may be of interest to policy makers considering setting limits on the number of board seats that may be held by directors at public companies, as well as shareholders considering appointing directors with multiple appointments.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.011 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".