Stochastic policy costs

Updated runs for various norms, added profit plots.

  • L1
  • L2
  • asymmetric: differs on the sign of the asymmetry? Penalty only for decreasing quotas. Penalty only for increasing quotas. check implementation.
  • fixed transaction fee – whoops, fixed cost should still be free when h == h_prev.

We need to determine a the magnitude of penalty coefficient to compare between the different functional forms. For instance, for what value of c is an L2 penalty, $ c ( h_t - h_p )^2 $ comparable to the L1 penalty, $ c (h_t - h_p ) $ ?

I think we decided that we should select this parameter such that the penalty induces the same equilibrium expected profit from fishing (before costs of policy-changes are subtracted) in each functional form. Is this correct?

Consequently we simply calculate this expected-profit-from-fishing under each penalty over a range of c values, and plot a curve for each profit value as a function of c. A horizontal line across this graph at, say, 50% of the adjustment-costs-free (i.e. Reed) profits would intersect each curve at the value of c that corresponded to this common baseline. Was that the agreed upon apples-to-apples strategy?

  • Computing this from the numerics: average over replicates. Provides variance estimates too, but rather noisy. results
  • Computing exactly from the SDP solution – record the equilbrium value-to-go would be before profits have been added. results. Also needs rerunning with corrected fixed-fee model.