Contracts can be stationary without loss of generality in a sense that for any new match, eort and contingent compensation are constant as long as the relationship re- mains.9 The reason is that it does not matter for an agent whether she is compensated for
her eort immediately (i.e., by the wage paid in the subsequent period) or by a (credible) promise for some future payments (always taking into account the possible termination of the relationship). Each non-stationary contract could thus be replaced by a stationary one, namely by averaging out changes in promised continuation payos.
However, focusing on individually stationary contracts does not automatically imply that stationarity of the whole game can be assumed without loss of generality. Each new contract can depend on the whole turnover history of a principal. This is relevant because market intransparency does not allow a principal to build up an external reputation for keeping his promises, and thus creates an additional commitment problem. The market
8We analyze the case of asymmetric information - the principal cannot observe the agent's eort
choice - later; then, the equilibrium concepts remains the same in a sense that within a relationship, actions only depend on what was observed by both players.
9See Levin (2003) or the Appendix of MacLeod and Malcomson (1998), where the latter considers
reason. Thus, principals are not able to extract the whole feasible surplus, although they are endowed with all the bargaining power. To better understand this point, assume that the maximum feasible surplus is realized (feasible in a sense that it satises all relevant constraints derived below). Furthermore, assume that the principal completely gets this surplus. Then, he would always renege, re an agent at the end of the period instead of oering her a new contract, and employ a new one. Therefore, turnover has to be costly for the principal, where these costs could for example assume some kind of surplus destruction or an upfront payment to new agents (i.e., a payment that cannot be used to give incentives). For convenience, we assume that the principals use the latter tool, and pay new agents a rent.
To simplify the following analysis, we restrict attention to contract-specic strategies in the sense of Board and Meyer-ter-Vehn (2011). This implies that actions of the rm and workers do not depend on the identity of the worker, calendar time, or history outside the current relationship. However, this assumption has only a slight impact on generality in our setup. Not using information outside a current relationship implies that the rm's total turnover history is not part of strategies. Instead, the punishment imposed on a principal when starting a new employment relationship (i.e., the rent going to a new agent) is always the same. Thus, we only have to distinguish between any period in an ongoing and the rst period of a new relationship. In Appendix I, we prove that giving new agents the same rent independent of the whole turnover history is without loss of generality.
Furthermore, conditioning strategies on calendar time could increase a rm's rent. The reason is that future turnover costs are needed to persuade agents today that promises are honored. Thus, turnover costs are only necessary for all periods except for the rst period of the whole game. However, relaxing the assumption of contract-specic strategies and allowing for a dierent countract in the rst period of the game would have no qualitative impact on our results and just slightly increase prots and equilibrium eort levels.
Concluding, the punishment, i.e., the rent going to new agents, will keep the principal from reneging and ring agents in equilibrium. However, he cannot completely prevent this punishment, but will be exposed to it all the time an agent leaves for exogenuous rea- sons and has to be replaced. As these costs must increase with equilibrium compensation,
the principal faces a trade-o between giving optimal incentives and reducing turnover costs, a problem inducing him to voluntarily reduce the feasible eort level and thus the relationship surplus.
2.4 Payos and Constraints
Let us denote the stationary equilibrium eort level e∗, the wage in ongoing relation- shipsw, andU the agent's payo in such an ongoing relationship. Then,U can be dened recursively as
U =w−c(e∗) +δγU (2.1)
The discounted future stream δU only enters with probability γ, since there is a chance that the agent leaves the market for exogenous reasons (happening with probability
(1−γ)), then receiving a payo of zero.
If an agent is on the market and gets a job, her expected payo in the rst period of employment equals
U0 =w0−c(e∗) +δγU
where w0 denotes the wage an agent receives in this rst period of employment.
Finally, an agent currently unemployed but on the market at the beginning of a period receives a job oer with probabilityµ≡ (N−M(1−)+(1γ)M−γ)M = (1N−−γγM)M. Thus, an agent`s
endogenous reservation utility U equals
U =µU0+δ(1−µ)γU
There, note that an agent remains in the market with probability γ, no matter whether she currently is employed or not.
In equilibrium, some constraints have to be satised for each agent who is part of a match. First of all, an agent must prefer to be employed rather than not. This implies
captured by an agent's individual rationality (IRA) constraints, U ≥U
and U0 ≥U
Furthermore, given U, U0 and U, it must be in the interest of an employed agent
to actually choose equilibrium eort e∗, i.e., her incentive compatibility (IC) constraint must be satised. Here, we assume that an agent who does not exert e∗ is red10 and re-enters the job market in the subsequent period. If an agent deviates and chooses eort e 6= e∗, she will obviously set e = 0 (or put dierently: if satised for e = 0, (IC) also
holds for any other eort level). Thus, (IC) equals
c(e∗)≤δγ U −U
A principal's payo starting a new relationship is denoted Π0, while he gets Π in an
ongoing match. These payos can be characterized recursively as well, giving
Π =e∗θ−w+δ[γΠ + (1−γ)Π0]
and Π0 =e∗θ−w0+δ[γΠ + (1−γ)Π0]
Each principal faces some constraints as well. First of all, starting a new employ- ment relationship should be better than shutting down completely, giving the individual rationality (IRP) constraint
Π0 ≥0.
Furthermore, each principal must have an incentive to honor his promises. If he reneges and oers a wage dierent from the one specied in the relational contract, we make the standard assumption that all trust is lost in the specic relationship, the employed agent does not believe the rm`s promises anymore, and thus is not willing to exert positive eort from then on. After a deviation, the principal thus has the choice to either shut down and receive his exogenous reservation utility with a value of zero, or to
employ a new agent. Since either choice must not be optimal, we have two constraints, where the incentive compatibility (ICP) constraint covers the rst case and equals
Π≥0
The second one is denoted the non-reneging (NR) constraint, and characterized by
Π≥Π0
Obviously, (ICP) is automatically satised given (IRP) and (NR), and we can omit it from now on.