Definición y tipos de competencias

Let us call the triplet (t, p,f) apolicy, consisting of atax policy tand an enforcement policy (p,f), and remember from above that we assumet ≥p(t+f). Note further, that in a large community the impact of a single individual onnrespectivelyg is negligible. Hence, taking the policy as well as n as given, a player i will choose to contribute iff

ui(1, n)≥ui(0, n). It is easy to show that this holds iff θi ≥θˆ(n) with

ˆ

θ(n) := t−p(t+f)

c(n) . (4)

For agenti, who has internalized the norm to a degree θi ≥θˆ(n), the utility loss from the norm violation would be bigger than (or equal to) the monetary benefits from free- riding.13,14 _{Hence, the player will contribute t to the public good. If the enforcement}

policy gets stricter or if the tax decreases, the monetary incentive to free-ride becomes weaker and ˆθ(n) declines. For the special case of t=p(t+f) we get ˆθ(n) = 0. In this case, law enforcement is strong enough to enforce contributions of all (risk neutral) agents with θi ≥0. As long as the numerator of ˆθ is strictly positive, the law is non- deterrent for agents withθi = 0; i.e., expected monetary sanctions alone do not result

13_{For the case of equality we assume that the player follows the norm.}

14_{We assume here that people rationally solve the trade off between monetary and emotional}

incentives. Empirical support for this assumption is provided by e.g. Bosman and van Winden (2001, 2002), Hopfensitz and van Winden (2005).

in cooperative behavior. However, the (centralized, external) monetary punishment together with the (decentralized, internal) norm-based sanctions may induce public good contributions.

For a given policy and distribution of θ, this model captures three different be- havioral patterns: On the one hand, individuals with θi < θˆ(0) will always free-ride. These players are hardly affected by the social norm and the economic incentive to free-ride is always dominant, even if the whole society would comply with the norm. On the other hand, the action of an individual with ˆθ(0) ≤ θi <θˆ(1) depends on the level of n. Assumption A2 implies that the threshold ˆθ(n) is increasing in n: with a higher share of free-riders, the social norm becomes weaker and it is less costly to deviate from the norm. Hence, an agent might contribute to the public good for low levels of norm-deviations, while he would free-ride if the norm becomes weak. One can characterize such agents as conditional contributors.15 _{(3) Finally, agents with} θi ≥ θˆ(1) act as unconditional contributors: the utility loss from a norm violation always dominates the monetary incentive to free-ride, even for the (hypothetical) case where everybody in society would break the norm. The model therefore explains the typical patterns of individual behavior observed in experimental economic studies of public good games (e.g. Keser and van Winden, 2000; Fischbacher et al., 2001) as well as in field studies (e.g. Croson, 2005; Frey and Meier, 2004a, 2004b). We shall emphasize that here conditional contributors appear in the context of a cooperation norm with an endogenous norm strength. Hence, conditional contributions are not nec- essarily triggered by a ‘norm of conditional cooperation’, as recently proposed by Fehr and Fischbacher (2004a, 2004b). While they consider a norm which commands agents to ‘cooperate in this case’ but ‘free-ride under that conditions’, it has been stressed in the social norms literature (e.g. Elster, 1989a, 1989b), that norms are typically simple moral rules and guidelines. Therefore, our approach seems to be more in line with the standard literature on social norms.

Digression: Congestion in the Detection Technology

Consider the case where the detection technology of the law-enforcing institution de- pends on the frequency of law violations in the society. It seems plausible to assume that, for a given investment into law-enforcement (e.g. a fixed number of policemen), the detection probability is decreasing with the number of illegal actions. Stated differ- ently, there is congestion in the detection technology: If a policeman is busy sanctioning

agenti, it is more likely that the wrongdoing of agent j stays undetect as compared to a situation wherei would comply with the law and the policeman could fully focus on detecting law violations.16

We can easily include this idea into the model, assuming that the detection prob- ability is given by p=π(n) with π0 _{<0. The threshold level for cooperation from (4)}

would then be given by

ˆ

θ(n) := t−π(n) (t+f)

c(n) .

It is straightforward to show, that ˆθ(n) still is increasing inn. As before, the emotional costs of free-riding are decreasing in n. With π0 _{< 0, however, norm violation have}

an additional positive externality on other free-riders: The more people break the law, the lower are the expected monetary sanctions and the temptation to free-ride rises. Hence, the pecuniary incentives related to congestion point into the same direction as the incentives associated with the endogenous norm strength. They both trigger conditional cooperative behavior. As the congestion effect would only change our results quantitatively, we will assumeπ0 _{= 0 in the remainder of this chapter.}

3.3

Social Equilibrium

Let θ be distributed over the interval [0,∞] according to a cumulative distribution function F(θ), which is continuously differentiable and common knowledge. The cor- responding density function f(θ) has full support on the interval [0,∞] and f(θ)>0.

F−1_{(n) denotes the inverse function of F(θ).}