We offer a game-theoretic proof of Hamilton's rule for the spread of altruism. For a simple case of siblings, we show that the rule can be derived as the outcome of a one-shot prisoner's dilemma game between siblings. -- evolution of altruism ; Hamilton's rule ; one-shot prisoner's dilemma game

We demonstrate how altruism can surge in a population of nonaltruists. We assume that each individual plays a one-shot prisoner's dilemma game with his or her sibling, or with a stranger, and that the probability that an individual survives to reproduce is proportional to his or her payoff in...

In a haystack-type representation of a heterogeneous population that is evolving according to a payoff structure of a prisoner's dilemma game, migration is modeled as a process of swapping individuals between heterogeneous groups of constant size after a random allocation fills the haystacks,...

In a haystack-type representation of a heterogeneous population that is evolving according to a payoff structure of a prisoner’s dilemma game, migration is modeled as a process of “swapping” individuals between heterogeneous groups of constant size after a random allocation fills the...

A utilitarian social planner who maximizes social welfare assigns the available income to those who are most efficient in converting income into utility. However, when individuals are concerned about their income falling behind the incomes of others, the optimal income distribution under...

We model group formation as a response to relative deprivation. We employ two measures of relative deprivation. We show that in the case of each of these measures the process of deprivation-induced self-selection into groups reaches a steady state, and that the steady-state distribution differs...

This paper asks whether population growth is conducive to the sustainability of cooperation. A simple model is developed in which farmers who live around a circular lake engage in trade with their adjacent neighbors. The payoffs from this activity are governed by a prisoner's dilemma "rule of...

We calculate the equilibrium fraction of cooperators in a population in which payoffs accrue from playing a single-shot prisoner's dilemma game. Individuals who are hardwired as cooperators or defectors are randomly matched into pairs, and cooperators are able to perfectly find out the type of a...