Skin in the Game
Page 26
FIGURE 7. The Bob Rubin trade. Payoff in a skewed domain where the benefits are visible (and rewarded with some compensation) and the detriment is rare (and unpunished owing to absence of skin in the game). Can be generalized to politics, anything where the penalty is weak.
A. SKIN IN THE GAME AND TAIL PROBABILITIES
This section will analyze the probabilistic mismatch of tail risks and returns in the presence of a principal-agent problem.
Transfer of Harm: If an agent has the upside of the payoff of the random variable, with no downside, and is judged solely on the basis of past performance, then the incentive is to hide risks in the left tail using a negatively skewed (or more generally, asymmetric) distribution for the performance. This can be generalized to any payoff for which one does not bear the full risks and negative consequences of one’s actions.
Let P(K, M) be the payoff for the operator over M incentive periods:
where i.i.d. random variables representing the distribution of profits over a certain period [t, t + iΔt], i ∈ ℕ, Δt ∈ ℝ+ and K is a “hurdle,” is an indicator of stopping time when past performance conditions are not satisfied (namely, the condition of having a certain performance in a certain number of the previous years, otherwise the stream of payoffs terminates, the game ends and the number of positive incentives stops). The constant