Profit sharing (with workers) facilitates collusion (among firms).

We show how profit sharing by firms with workers facilitates collusion among firms in a dynamic oligopoly environment with uncertain demand. We first show that firm profits can always be increased by tying wages to market conditions. The optimal agreement takes the form of an option and features partial sharing because increased sharing raises the expected price-wage differential, but reduces price-wage variability. We then show that given any cartel, there exist market conditions such that simply giving some expected profit to workers raises expected firm profits via the transfer's impact on the incentive to cheat on the cartel.

1. Introduction

* This article addresses a basic contracting issue: How does the sharing of profits between a firm and its employees affect the ability of firms to support collusive oligopoly pricing and oligopoly profits? We explore this question in the dynamic oligopoly environment with uncertain demand first characterized by Rotemberg and Saloner (1986).

We obtain a stark answer: Profit sharing between firms and their employees always facilitates collusion between firms in the output market. Indeed, we show that expected profits can be raised by giving workers a share of firm profits, without extracting a corresponding reduction in wages.

It is important to emphasize that our findings do not revolve around either worker moral hazard or insurance explanations. In our bare-bones economy there is no problem eliciting worker effort, so that profit sharing is not required to overcome worker moral hazard. Further, all parties are risk neutral, so there is no role for insurance.

Rather, the driving economic force is that profit sharing between workers and firms favorably alters the strategic interaction of firms in the output market. The economics underlying our results can be gleaned from recalling equilibrium outcomes in Rotemberg and Saloner (1986). There, firms repeatedly interact in an economy with independently and identically distributed demand shocks. Because expected future collusive profits do not depend on the period demand shock, but the gains from cheating on the cartel rise with demand, firms can support monopoly profits only if the demand shock is sufficiently low. If demand is too high, then total industry output is increased beyond the monopoly level until firms just cease to have an incentive to cheat on the cartel.

Now consider the impact of tying worker compensation to market conditions. Tying compensation effectively reduces worker compensation when demand is low and raises worker compensation when demand is high. But in low-demand states, firms do not have an incentive to cheat on the cartel, so the lower worker compensation raises cartel profits in these low-demand states. In contrast, in sufficiently high-demand states, firm profit is completely unaffected by increased worker compensation, as profit is already constrained by the heightened incentive to cheat on the cartel.

The profit-maximizing worker-firm agreement generally features only partial profit sharing so that, along the equilibrium path, net firm profit rises monotonically with the demand realization. This is because while profit sharing increases the expected price-"wage" difference, it also reduces the variance of this difference. Because the period profit function is convex, increased profit sharing eventually reduces this variance by enough that expected firm profits fall (unless monopoly profits cannot be sustained even for the worst demand realization). However, since the variance has only a second-order impact on firm profit, but raising the expected price-"wage" difference has a first-order impact, it follows that some profit sharing is always optimal.

We first consider an environment in which workers' wages can be tied to market conditions in a linear fashion, so that wages are higher when market demand is higher. This framework highlights the tradeoff of increased profit sharing on (i) the expected price-wage difference, and (ii) the variance of the price-wage difference. In this environment, we show that there always exists an incentive-compatible wage agreement that allows firms to capture increased profit. We then relax the restriction that wages be linearly linked to market conditions and require only that the wage be nondecreasing in demand. We show that the resulting profit-maximizing wage-tying agreement takes the form of an option, with wages fixed at a low level unless demand is sufficiently high.

We then explicitly allow for profit sharing, so that employees can receive a share of firm profits. This reveals another benefit of profit sharing: If a firm cheats by increasing output and hence profits, not only must it pay each worker more because its profits are higher, but it must also hire and pay more workers to produce the output. Consequently, an explicit profit-sharing agreement with workers further reduces a firm's incentive to cheat on a cartel. To highlight this, we provide sufficient conditions under which firms can increase expected profits simply by giving employees a share of firm profits, without demanding a lower wage in return. We show that for a cartel of any size, there exist market conditions such that giving workers a share of firm profits raises cartel profits; the reduction in the incentive to cheat on the cartel supported by this transfer to workers supports monopoly pricing in enough additional higher-demand states to more than offset the transfer of surplus to employees.

Our work is related to two research strands. Many, many articles investigate collusion among firms in dynamic oligopoly environments. Haltiwanger and Harrington (1991) explore collusion in a deterministic variant of Rotemberg and Saloner in which demand moves cyclically over time. Green and Porter (1984) and Abreu, Pearce, and Stacchetti (1986, 1990) explore collusion when the realized price depends on both aggregate output and an unobserved shock so that firms cannot unravel from the price realization whether some firm "cheated" on the cartel. Fudenberg, Levine, and Maskin (1994) and Kandori and Matsushima (1998) provide versions of the folk theorem in such environments. Other articles that explore aspects of collusion in environments where firms repeatedly interact include Fershtman and Pakes (2000), Eaton and Eswaran (1997, 2001), and Lambson (1987, 1994).

A second research strand explores how the incentive structures that a firm provides managers affect the strategic interaction of firms in the output market. For example, Fershtman and Judd (1987) and Sklivas (1987) show that if firms compete in quantities, then compensating a manager for sales serves to commit the firm to producing more output, which in turn induces competitors to reduce output. Conversely, if firms compete in prices, then firms can raise profits by designing incentives that discourage undercutting by punishing excessive sales. Reitman (1993) extends their analysis to allow firms to compensate managers with stock options. Basu (1995) also builds on these works, explicitly modelling the decision of whether or not to hire managers. Barcena-Ruiz and Paz Espinosa (1996) investigate the temporal aspect of manager contracts in such a model.

In a similar vein, several articles explore the interaction between product market competition and capital markets. Brander and Lewis (1986, 1988) show how a firm's financial structure affects the nature of competition in output markets. For example, when demand is uncertain, debt commits a firm to producing more output (because firms repay loans only when demand is high). Bolton and Scharfstein (1990), Maksimovic (1998), and Faure-Grimaud (2000) deal with related topics. Maksimovic and Titman (1991) explore financial structure and reputation for product quality.

The focus of this second research strand is very different from ours--addressing in static contexts how managerial incentives or financial structure can be designed to commit the firm to being aggressive or passive in the output market, as desired. In contrast, our focus is on how managerial compensation in the form of profit sharing affects the dynamic incentives of a firm to cheat on a cartel, and hence the ability of the cartel to support more profitable collusion when demand is uncertain.

The article closest in spirit to ours is Spagnolo (2000). He shows that output-deciding managers can collude at higher levels if compensation is given in stocks. However, very different economic forces are at work in his model. Spagnolo studies a market with no uncertainty, and explicitly considers a stock market where the value of a stock is simply its expected sum of discounted payoffs. Therefore, managers' period payoffs are directly tied to the sum of discounted firm profits. Thus, when deviating from collusive strategies, managers incur a period loss through the loss of future profits. In this sense, stock-based compensation directly facilitates collusion.

2. The model

* The basic framework is that of Rotemberg and Saloner (1986): n firms producing a homogeneous good repeatedly interact in an infinite-horizon economy with stochastic demand. Period market demand at time t is given by

[D.sub.t]([[theta].sub.t], [P.sub.t]) = [[theta].sub.t] - [P.sub.t],

where [[theta].sub.t] is an independently and identically distributed demand shock, with distribution function F on its positive support [[[theta].bar], [bar.[theta]]]. (1) The risk-neutral firms share common discount factor [beta] [member of] (0, 1), and they compete in prices in the output market.