Samaritan versus rotten kid: Another look

Abstract

We set up a two-stage game with sequential moves by one altruist and n selfish agents. The Samaritan's dilemma (rotten kid theorem) states that the altruist can only reach her first best when the selfish agents move after (before) the altruist. We find that in general, the altruist can reach her first best when she moves first if and only if a selfish agent's action marginally affects only his own payoff. The altruist can reach her first best when she moves last if and only if a selfish agent cannot manipulate the price of his own payoff.

Gross versus net equalization scheme in a federation with decentralized leadership

“…Our subgame perfect equilibrium under the decentralized leadership thus clearly differs from the Pareto optimum. More generally, for the rotten kid theorem to hold, the prices of the selfish agents' payoffs to the benevolent contributor must be beyond manipulation, as proved by Dijkstra (2007), which is not the case in our paper.…”

Distributional Preferences, Reciprocity-Like Behavior, and Efficiency in Bilateral Exchange

“…Yet, as stated, it raises the question: for what material payoff functions is it satisfied? In a paper about the special case of the rotten kid theorem, Dijkstra (2007, his Lemma 1) answered this question: dp ( a 1 , a 2 ( a 1 )) / da 1 = 0 at SM’s favorite transaction if and only if the material payoff functions are locally conditionally transferable at SM’s favorite transaction, i.e., in a neighborhood of ( a̿ 1 , a̿ 2 ), $\frac{\partial {\pi }_{1}false(a_1,a_{2}false)/\partial a_2}{\partial {\pi }_{2}false(a_1,a_{2}false)/\partial a_2}=-k$ for some constant k > 0. 16 …”

“…Dijkstra’s (2007) result shows that that conjecture was incorrect. Dijkstra’s “Condition 2” characterizes exactly the class of material payoff functions that is locally conditionally transferable at ( a̿ 1 , a̿ 2 ), but the condition is difficult to interpret.…”

Long‐term care policy with lazy rotten kids

“…This in itself is essentially just a different illustration of the well‐known “Samaritan's dilemma” (see, e.g., Bruce & Waldman, ; Dijkstra, ). Children have an incentive to make themselves poorer in order to increase the subsequent bequest.…”