Controlling stochastic externalities with penalty threats: the case of bycatch

Abstract

Previous literature has shown that when there is a deterministic relationship between abatement choices and outcomes, policies with penalty threats can be designed to induce polluting firms to undertake efficient abatement measures voluntarily. We develop a game theoretic model to investigate whether a similar policy can be designed and applied to reduce stochastic bycatch. The policy design would involve a penalty threat that would induce fishers to undertake efficient avoidance measures voluntarily to reduce interactions between fishing vessels and bycatch species. Our findings indicate that both individual and group performance standards (a threshold of allowable bycatch mortalities per fishing season) can be designed such that the penalty threat is sufficient in inducing risk-neutral agents to undertake the first-best level of avoidance activity voluntarily. The optimal threshold depends on the degree of variability in the bycatch level and the discount factor. The net impact of environmental uncertainty on the optimal threshold is ambiguous and depends on the underlying distribution of bycatch mortalities, given the efficient level of avoidance measures. The paper identifies and emphasizes the information requirements that arise when environmental policies involving penalty threats are applied to mitigate stochastic externalities by inducement of efficient (voluntary) abatement behavior.

Appendix

Statement Some free-riding can exist even when the target is met voluntarily

Proof When $a_{jv}$ = 0, there are four possible cases corresponding to the choice of $a_{iv}$:

Given $X = \bar{X}$, $\rho^{**} = d$ and $a_{jv}^{*} = 0$, what is fisher $i$’s best response in the voluntary stage?

Note that if $\frac{{\partial F(\bar{X})}}{\partial a} > 0$ and $a^{*} > 0$, $F(\bar{X}^{**} ,a^{*} ,0) > F(\bar{X}^{**} ,0,0)$ $\forall a$

Because $c(a^{*} ) > c(0)$ and $y(a^{*} ) \ge or \le y(0)$.

$\pi (a^{*} ) \ge or \le \pi (0)$,

when $a_{jv}^{*} = 0,$ there are four possible cases corresponding to the choice of $a_{iv}^{*}$:

• (1) $a_{iv}^{*} = 0$,

• (2) $a_{iv}^{*} \in (0,a^{*} )$,

• (3) $a_{iv}^{*} = a^{*}$,

• (4) $a_{iv}^{*} > a^{*}$.

When $a_{jv}^{*} = 0$, fisher will set $a_{iv}^{*} = a^{*}$ iff $V(a^{*} ,0) > V(a_{v} ,0)$, where $a^{*} \ne a_{v}$, or

$$\frac{{\pi_{v} (a^{*} )}}{{\left[ {1 - \beta F(\bar{X}^{**} ,a^{*} ,0)} \right]}} + \frac{{\beta \left[ {1 - F(\bar{X}^{**} ,a^{*} ,0)} \right]E\left[ {\pi (a^{*} ,a^{*} )} \right]}}{{(1 - \beta )\left[ {1 - \beta F(\bar{X}^{**} ,a^{*} ,0)} \right]}} > \frac{{\pi_{v} (a_{iv} )}}{{\left[ {1 - \beta F(\bar{X}^{**} ,a_{iv} ,0)} \right]}} + \frac{{\beta \left[ {1 - F(\bar{X}^{**} ,a_{iv} ,0)} \right]E\left[ {\pi (a^{*} ,a^{*} )} \right]}}{{(1 - \beta )\left[ {1 - \beta F(\bar{X}^{**} ,a_{iv} ,0)} \right]}}$$

The above expression simplifies to:

$$\frac{{\pi_{v} (a^{*} )}}{{\left[ {1 - \beta F(\bar{X}^{**} ,a^{*} ,0)} \right]}} - \frac{{\pi_{v} (a_{iv} )}}{{\left[ {1 - \beta F(\bar{X}^{**} ,a_{iv} ,0)} \right]}} + \frac{{\beta E\left[ {\pi (a^{*} ,a^{*} )} \right]}}{(1 - \beta )}\left[ {\frac{{\left[ {1 - F(\bar{X}^{**} ,a^{*} ,0)} \right]}}{{\left[ {1 - \beta F(\bar{X}^{**} ,a^{*} ,0)} \right]}} - \frac{{\left[ {1 - F(\bar{X}^{**} ,a_{iv} ,0)} \right]}}{{\left[ {1 - \beta F(\bar{X}^{**} ,a_{iv} ,0)} \right]}}} \right] > 0.$$

Since either terms in the above expression cannot be signed, we cannot claim $V(a^{*} ,0) > V(a_{v} ,0)$ will hold true for all values of $a_{iv}$. Thus, the incentives to free ride in equilibrium are not eliminated with these parameter choices. If all firms choose 0 or any $a < a^{*}$ in the voluntary stage, the target will be met only by pure chance.