is stochastic and μ sufficiently large ceteris paribus then an increase in p may favor the non
compliance strategy.
Having characterized the basic properties of the crucial variables θ and ∆∏^, we now
turn to the determination of the equilibrium rate of compliance. We denote G(θ, c) the
joint distribution of the adherence to the norm and the compliance cost, on the product
of their respective supports. We assume that all individuals simultaneously choose between
compliance and non compliance for given parameters (p, μ, f, F, r, δ). If all individuals expect
a compliance rate equal to A, then A must be equal to the population share H(A) that finds
compliance as being optimal. We thus obtain the following result.
Proposition 3 An equilibrium rate of compliance exists and is defined by a fixed point of:
H(A) ≡ J~ dG(θ, c)
(1)
From Lemma 1, it follows that H(.) is a continuous non decreasing function of A, mapping
the interval [0, 1] into itself. Hence, there exists at least one compliance rate satisfying equa-
tion (1) for any policy (p, f, F). This follows from the intermediate value theorem applied to
f (A) = A — H (A) which is a continuous function with f (0) ≤ 0 and f (1) ≥ 0. However, multi-
plicity of equilibria is possible and it is actually a general feature of this class of models with
aggregate externality (see e.g. Weibull and Villa 2005 or Lindbeck et al., 1999). Equilibria
may be stable or unstable.
Given the results contained in Lemma 2, it is not surprising that it is easy to find exemples
where an increase in the audit probability p or in the market loss δ nevertheless induce a
decrease in equilibrium rate of compliance, whether it is stable or not. [to be completed]
4 The role of information
We examine in the following the crucial role of information provided to the market. For
simplicity, we concentrate on the case where social norms are absent and we successively
analyze the impact of self-reporting and public disclosure of information.