Worker Runs: Hoffmann & Vladimirov (2025)

What this is. The paper’s core propositions, the model it builds, and the compensation design results: enough to understand what it found and how, without reading all 43 pages. To replicate or extend it, read the full source at the original.

TL;DR

Hoffmann and Vladimirov develop a theory of “worker runs”: because workers privately observe a firm-wide productivity shock, and because a departing skilled worker reduces the value of remaining workers’ output-dependent pay, an initial departure can trigger further departures even from an otherwise healthy firm. The modeling of collective turnover as a coordination failure is similar to the bank-run literature of Diamond and Dybvig (1983) and Goldstein and Pauzner (2005). Unlike bank runs, however, standard remedies such as deposit insurance have no direct labor-market analog, so the paper focuses on compensation design instead. The paper shows that firms can design compensation contracts to prevent such contagious collective turnover at no extra cost relative to a frictionless benchmark. The key instruments are (i) making compensation “dilutable” (promising workers more when others leave) to smooth workers’ expected pay across retention scenarios, and (ii) offering ex-ante identical workers differently structured contracts (asymmetric compensation) to ensure that a critical subset always stays, removing the strategic complementarity for the rest. The asymmetric contracting results extend Winter (2004) and Halac, Kremer, and Winter (2020) by studying differences in compensation structure rather than compensation level. The dilution results build on Oyer (2004)‘s insight that firms optimally match workers’ on-the-job pay to their outside options. The paper characterizes optimal symmetric and asymmetric contracts and derives empirically testable implications for dilution, compensation structure, and worker targeting.

Core results

Propositions and results are as stated in the paper. Locators point into the source PDF.

#	Result	Locator	Content
R1	Dilutable or fixed-wage contracts always resolve the coordination problem at zero extra cost versus the frictionless benchmark	Propositions 2-3, pp. 950-953	Optimal contract sets expected compensation constant in retention level n for each shock realization (W(eps,n) = W(eps,N) for all n), achieved by dilution whenever the output-dependent component is positive
R2	Optimal degree of dilution increases in the equilibrium share of output-dependent pay and in the sensitivity of firm success to retention	Corollaries 1-2, pp. 954-955; Figure 2, p. 955	Dilution through decreasing output-dependent pay (complements case) or decreasing output-independent pay (substitutes case); both w(n) and delta-w(n) move to achieve smoothing
R3	Symmetric contracts conditioning on overall retention n are weakly cheaper than asymmetric contracts that cannot condition on n	Lemma 3, p. 962	Conditioning on n allows off-equilibrium promises to differ from equilibrium pay, fully absorbing coordination costs; asymmetric-only contracts must resolve coordination on-equilibrium, which is costlier
R4	When symmetric contracting entails positive coordination costs, combining asymmetric structure with dilution strictly reduces expected costs	Proposition 7, p. 962	Offering the optimal symmetric contract to N-1 workers and the relaxed-problem contract to worker N halves per-worker coordination cost; generally yields strictly lower total cost
R5	Under optimal asymmetric contracts, higher-ranked workers receive a higher share of output-independent pay and do not necessarily earn more rent	Proposition 5, pp. 959-960	Higher-ranked workers’ decision to stay must be independent of more coworkers, so their output-dependent pay is more mispriced by the coordination friction; firm compensates with safer output-independent pay
R6	Workers retained with higher probability in asymmetric retention policies optimally receive higher output-independent pay when shocks are idiosyncratic; higher output-dependent pay when shocks are systematic with outside options more sensitive than firm output	Internet Appendix Propositions IA.2, IA.5, p. 964	Compensation-type allocation responds to which friction dominates: coordination (pushes toward fixed pay) vs. noncontractibility of the shock (pushes toward output-dependent pay for high-retention workers)

Overall (paper’s conclusion). Mitigating collective contagious turnover poses additional challenges relative to individual turnover and requires different compensation solutions. The tools the paper proposes, making compensation dilutable or offering asymmetric contracts, can be easily implemented with equity-based pay, profit-sharing bonus pools, retention bonuses, and title-linked pay differences that are already common in practice (pp. 970).

Theory / model

The baseline model (Section I, pp. 943-945) has a firm that hires $N \geq 2$ risk-neutral workers at $t = 0$. The firm’s only asset is a project that generates cash flows at $t = 2$: $x > 0$ if the project fails and $x + \Delta x$ with $\Delta x > 0$ if it succeeds. The probability of success at interim date $t = 1$ depends on an exogenous shock $\varepsilon$ (drawn from distribution $G$ with support $[\underline{\varepsilon}, \bar{\varepsilon}]$) and on the number of workers $n$ retained until $t = 2$ (p. 943, eq. 1):

$$p(\varepsilon, n) = \alpha(n) + \beta(\varepsilon)\gamma(n), \tag{1}$$

with $\beta(\varepsilon), \beta'(\varepsilon) > 0$ for all $\varepsilon$ and $\gamma(n) > 0$ for all $n$, so both the shock and retention increase the probability of success. Workers observe the shock $\varepsilon$ privately at $t = 1$ and decide simultaneously whether to stay or take an outside option of value $\underline{w}(\varepsilon) \geq 0$.

Each worker $i$ is offered a compensation contract $C_i = (w_i(n), \Delta w_i(n))_{n=1}^{N}$, which specifies output-independent pay $w_i(n)$ and output-dependent pay $\Delta w_i(n)$ conditional on the number $n$ of workers retained. The firm’s objective is to minimize workers’ expected equilibrium rent (expected compensation minus outside option) subject to achieving full retention as the unique equilibrium at $t = 1$.

The expected surplus of retaining $n$ workers is (p. 944, eq. 2):

$$\Omega(\varepsilon, n) := x + p(\varepsilon, n)\Delta x - n\underline{w}(\varepsilon), \tag{2}$$

which the paper assumes is positive and nondecreasing in $n$ for all $\varepsilon$ (retaining more workers is always efficient).

Worker runs as coordination failure. For symmetric contracts $C_i = C$, workers play a coordination game at $t = 1$. Workers’ expected on-the-job compensation is $W(\varepsilon, n) := w(n) + p(\varepsilon, n)\Delta w(n)$, which increases in $n$ whenever output-dependent pay is positive. This creates strategic complementarities: a worker is more likely to stay if others stay, since the firm’s success probability and thus the value of her equity/bonus increases with retention. Proposition 1 (p. 947) characterizes the resulting equilibrium structure. A worker-run equilibrium, in which all workers leave, exists whenever

$$W(\varepsilon, N) \geq \underline{w}(\varepsilon) > W(\varepsilon, 1), \tag{3}$$

that is, staying is attractive only when all others stay but not when alone. Under condition (3) a full-retention equilibrium also exists, and the worker-run equilibrium is Pareto-dominated by it.

Monotonicity-in-retention constraint (Assumption 1, p. 952): To rule out unrealistic contracts that reward workers for inducing coworkers to leave, the paper imposes that workers’ expected on-the-job pay must be nondecreasing in the number of retained workers: $W_i(\varepsilon, n) \geq W_i(\varepsilon, n-1)$ for all $(\varepsilon, n)$ and $i$. This constraint limits the degree of dilution.

Dilutability (Definition 1, p. 948): Compensation of worker $i$ is dilutable at $(\varepsilon, n)$ if, holding the success probability constant at any $\hat{p} \in [p(\varepsilon, n-1), p(\varepsilon, n)]$, expected compensation $\hat{W}_i(\hat{p}, n) := w_i(n) + \hat{p}\Delta w_i(n)$ decreases in retention (eq. 4):

$$\hat{W}_i(\hat{p}, n) - \hat{W}_i(\hat{p}, n-1) = w_i(n) - w_i(n-1) + \hat{p}[\Delta w_i(n) - \Delta w_i(n-1)] < 0. \tag{4}$$

Equity-based pay exhibits this dilutability because the firm’s equity “pie” is shared among fewer workers when some depart, so each remaining worker’s percentage stake rises even as the total pie shrinks.

Method

This is a contract-theory paper with no econometric estimation. The solution method is backward induction in a three-period ($t = 0, 1, 2$) game with incomplete information (the shock $\varepsilon$ is private), building on principal-agent, repeated-game, and mechanism-design techniques.

The firm’s optimization at $t = 0$ is to design contracts that implement full retention as the unique equilibrium at $t = 1$ at minimum expected compensation cost. For symmetric contracts, this reduces to Problem 1 (p. 950, eqs. 5-6):

$$\min_{C \in \mathbf{C}^f} \int_{\underline{\varepsilon}}^{\bar{\varepsilon}} [w(N) + p(\varepsilon, N)\Delta w(N) - \underline{w}(\varepsilon)] \, dG(\varepsilon) \tag{5}$$ $$\text{subject to} \quad W(\varepsilon, n) = w(n) + p(\varepsilon, n)\Delta w(n) \geq \underline{w}(\varepsilon) \quad \forall (\varepsilon, n). \tag{6}$$

Constraint (6) is the full-retention participation constraint requiring staying to be dominant for all shock realizations and all retention levels. Together with the monotonicity-in-retention constraint (Assumption 1), this implies that optimal contracts satisfy (p. 952, eq. 7):

$$W(\varepsilon, N) \geq \ldots \geq W(\varepsilon, 1) \geq \underline{w}(\varepsilon) \quad \forall (\varepsilon, n). \tag{7}$$

Workers’ equilibrium rent can be decomposed as the sum of incremental rents (p. 952, eq. 8):

$$R(\varepsilon, N) := [W(\varepsilon,N) - W(\varepsilon,N-1)] + \ldots + [W(\varepsilon,1) - \underline{w}(\varepsilon)] \geq 0. \tag{8}$$

The key insight is that minimizing total expected rent pushes as many incremental rents to zero as possible, making expected compensation constant in $n$: $W(\varepsilon, n) = W(\varepsilon, N)$ for all $(\varepsilon, n)$. This requires choosing the output-dependent component $\Delta w(n)$ to offset the retention sensitivity of $p(\varepsilon, n)$ (pp. 952-953, eqs. 9-10):

$$\Delta w(n-1) = \frac{\gamma(n)}{\gamma(n-1)} \Delta w(n), \tag{9}$$ $$w(n-1) = w(n) + \left[\alpha(n) - \alpha(n-1)\frac{\gamma(n)}{\gamma(n-1)}\right] \Delta w(n). \tag{10}$$

For asymmetric contracts (Section IV), each worker $i$ (indexed by rank in the iterative dominance ordering) faces Problem 2 (p. 959, eq. 12):

$$\min_{\{w_i, \Delta w_i\}_{i=1}^{N} \in \mathbf{C}^f} \sum_{i=1}^{N} \int_{\underline{\varepsilon}}^{\bar{\varepsilon}} [W_i(\varepsilon, N) - \underline{w}(\varepsilon)] \, dG(\varepsilon) \quad \text{s.t.} \quad (11) \; \forall i, \tag{12}$$

where the participation constraint for worker $i$ at rank $i$ is (eq. 11):

$$W_i(\varepsilon, i) = w_i + p(\varepsilon, i)\Delta w_i \geq \underline{w}(\varepsilon) \quad \forall \varepsilon. \tag{11}$$

Worker $i$‘s expected rent under idiosyncratic risk is (p. 959, eq. 13):

$$\int_{\underline{\varepsilon}}^{\bar{\varepsilon}} [W_i(\varepsilon, N) - \underline{w}] \, dG(\varepsilon) = \int_{\underline{\varepsilon}}^{\bar{\varepsilon}} (\underline{w} - w_i) \left(\frac{p(\varepsilon, N)}{p(\underline{\varepsilon}, N)} \cdot \frac{p(\underline{\varepsilon}, N)}{p(\underline{\varepsilon}, i)} - 1\right) dG(\varepsilon). \tag{13}$$

The ratio $p(\underline{\varepsilon}, N)/p(\underline{\varepsilon}, i)$ is decreasing in rank $i$, so higher-ranked workers (lower $i$) misprice output-dependent pay more, making output-independent pay relatively cheaper for the firm.

Empirical specifications

This is a theory paper. It has no econometric estimation. Section V (pp. 966-969) translates the propositions into testable cross-sectional implications.

Implication 1 (p. 966): When firms relying on hard-to-replace skilled workers pay with output-dependent compensation, they should make that compensation dilutable. The degree of dilution is higher when (i) firm performance is more sensitive to retention and (ii) the share of output-dependent pay is higher.

Implication 2 (p. 967): Dilution provisions are more likely to be tied to output-dependent pay ($\Delta w(n)$ decreasing in $n$) if technological shocks increase firm productivity more at higher retention levels (complements), and to output-independent pay ($w(n)$ decreasing in $n$) if shocks increase productivity more at lower retention levels (substitutes).

Implication 3 (p. 969): (i) Firms can lower the cost of preventing worker runs by offering identical workers different compensation types, with higher-ranked workers receiving a higher share of output-independent pay and lower-ranked workers a higher share of output-dependent pay. Resource-constrained firms especially benefit. (ii) If firms seek to retain some workers with higher probability, they should optimally pay those workers with a higher share of output-independent pay when shocks are idiosyncratic; with a higher share of dilutable performance/equity-based pay when outside options are more sensitive than firm output to common shocks.

Tests of these implications require identifying sensitivity of workers’ outside options to systematic shocks (proxied by comovement with closely related peer firms, using Hoberg and Phillips (2016) network similarity scores), and the share of output-dependent pay (proxied by proportion of equity-based pay per Bergman and Jenter (2007)). Time-vesting equity implements the dilution pattern of Panel A.3 of Figure 2; equity buyback agreements implement Panel A.1; retention bonuses implement Panels B and C (p. 968).

Datasets used

This is a theoretical paper. No datasets are used for estimation. The paper references management and industry survey evidence to motivate the setting (turnover contagion studies, industry reports on quit rates and replacement costs) but does not analyze microdata.

Dataset / Source	Role	Wiki page
Industry surveys and management studies (cited in motivation)	Motivational evidence on quit rates, contagion, and replacement costs	No page yet

When to read the full paper

Read the original if you are: building a model of collective turnover or contagious labor-market dynamics; designing compensation contracts for teams of skilled workers in startups or professional services; studying the retention properties of equity-based versus fixed pay or bonus pools; or extending the model to richer information structures (global games refinements) and renegotiation environments, which are analyzed in the Internet Appendix.

Attribution and rights

Source: peer-reviewed, The Journal of Finance 80(2), April 2025, pp. 937-979. DOI: 10.1111/jofi.13424.

This distillation was extracted by an LLM on 2026-06-06 and is not human-verified or independently reproduced. The CC BY-NC 4.0 licence permits non-commercial reproduction with attribution; the verbatim PDF is not hosted in this batch.

Attribution (CC BY-NC 4.0). Hoffmann, Florian, and Vladimir Vladimirov. “Worker Runs.” The Journal of Finance 80, no. 2 (April 2025): 937-979. DOI: 10.1111/jofi.13424. (c) 2025 The Author(s). Licensed under CC BY-NC 4.0. This page is an adaptation by the Institute for Automated Research: core results extracted and re-expressed; changes were made.