A generalization of a classical model in contract theory: The agent behavior

We present a first approximation of agent behaviour in a generalized model in contract theory. This model relaxes some of the the assumptions of one of the classical models allowing to include a broader range of agents. We introduce the motivation for the agent and reinterpret the classical definition of risk perception. Besides, we analyze different scenarios for the relation between the effort exerted by the agent and the probability that he gets an especfic result.

💡 Research Summary

The paper revisits the classic principal‑agent framework in contract theory and proposes a generalized model that relaxes several restrictive assumptions of the traditional approach. In the standard model, the agent’s utility is assumed to be increasing in wage and decreasing in effort, with risk attitudes captured solely by the curvature of the wage‑utility function (the sign of u″). This formulation works well for repetitive, mechanical labor but fails to accommodate agents whose motivation is intrinsic to the act of working (e.g., volunteers, self‑harmers, or “suicide bombers”) or whose effort may generate positive utility in certain ranges.

To broaden the scope, the authors keep the basic two‑player game structure—principal selects a contract w̄ mapping outcomes to wages, the agent chooses an effort level e within a feasible interval, and nature draws an outcome x_i according to a probability distribution p_i(e) that depends on e. The principal’s payoff is B(x−w) and the agent’s payoff is u(w)−v(e). The key innovations are:

1. Generalized effort cost v(e). Instead of treating v(e) as a pure loss, the authors allow it to be negative over some intervals, reflecting situations where exerting effort is itself rewarding. The only restriction retained is convexity (v″>0), ensuring that marginal disutility of effort is non‑decreasing.

2. Risk attitude defined via expected utility over effort. Rather than linking risk aversion to u″ alone, the paper defines the agent’s risk posture through the second derivative of the expected utility Ē_A(e)=∑_i p_i(e)u(w_i)−v(e) with respect to e. Consequently, the same agent can be risk‑averse, risk‑neutral, or risk‑seeking depending on the contract’s wage schedule and the shape of p_i(e).

The agent’s optimization problem becomes max_{e∈