Journal Article The Core when Strategies are Restricted by Law Get access Theodore C. Bergstrom Theodore C. Bergstrom Washington University, St Louis Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 42, Issue 2, April 1975, Pages 249–257, https://doi.org/10.2307/2296532 Published: 01 April 1975

Alice and Bob live in the forest. To sustain themselves, they collect fruits and berries and snare an occasional animal. The nights get cold, but Alice is a skillful fire-builder. Bob has never mastered this art. His fires fizzle and he never seems to collect the right kind of wood. Alice divides her time between collecting food and gathering wood. She does this in such a way that her marginal benefit from time spent collecting food is the same as that from gathering wood. Bob does not attempt to build fires. He spends all of his time gathering food, and every night slinks up and huddles beside Alice’s fire. Bob appreciates the fire’s warmth, but wishes it were larger. Bob has learned to leave morsels of food by the fire for Alice. Warmth and food are both “normal goods ” for Alice. The extra food that Bob leaves induces her to increase her total food consumption, but not by the total amount that Bob leaves for her. She uses some of the time saved by Bob’s gifts to gather more firewood. 1.1 Equilibrium with Unilateral Gifts–An Example Alice’s utility function is U(cA, y) = cAy where cA is the amount of food that she eats and y is the amount of wood on the fire. She has T hours to allocate between collecting food and wood. In an hour, she can collect either one unit of wood or πA units of food. If Bob leaves g units of food by the fire, she maximizes her utility by choosing y = 1

How should benefit-cost analysis account for the value that benevolent individuals place on others' enjoyment of public goods? When adding up the benefits to be compared with costs, should we sum the private valuations, the altruistic valuations, or something else? This paper argues that private valuations are appropriate if concern for the well-being of others respects their private preferences. The discussion has implications for family decision-making, welfare economics, and the design of applied contingent valuation studies.

This paper explores the evolutionary foundations of altruism among siblings and extends the biologists' kin-selection theory to a richer class of games between relatives. It shows that a population will resist invasion by dominant mutant genes if individuals maximize a "semi-Kantian" utility function in games with their siblings. It is shown that a population that resists invasion by dominant mutants may be invaded by recessive mutants. Conditions are found under which a population resists invasion by dominant and also by recessive mutants.

Gary Becker's "rotten kid theorem" asserts that if all family members receive gifts of money income from a benevolent household member, then even if the household head does not precommit to an incentive plan for family members, it will be in the interest of selfish family members to maximize total family income. The author shows by examples that the rotten kid theorem is not true without assuming transferable utility. He finds a simple condition on utility functions that is necessary and sufficient for there to be the kind of transferable utility needed for a rotten kid theorem. While restrictive, these conditions still allow one to apply the strong conclusions of the rotten kid theorem in an interesting class of examples.

Gary Becker's "Rotten Kid theorem" asserts that if all family members receive gifts of money income from a benevolent household member, then even if the household head does not precommit to an incentive plan for family members, it will be in the interest of selfish family members to maximize total family income. I show by examples that the Rotten Kid theorem is not true without assuming transferable utility. I find a simple condition on utility functions that is necessary and sufficient for there to be the kind of transferable utility needed for a Rotten Kid theorem. While restrictive, these conditions still allow one to apply the strong conclusions of the Rotten Kid theorem in an interesting class of examples.

We present some examples of Nash equilibria that are independent of the distribution of some parameter across the economic agents and describe a general theorem that characterizes this phenomenon.

In most times and places, women on average marry older men. We propose a partial explanation for this difference and for why it is diminishing. In a society in which the economic roles of males are more varied than the roles of females, the relative desirability of females as marriage partners may become evident at an earlier age than is the case for males. We study an equilibrium model in which the males who regard their prospects as unusually good choose to wait until their economic success is revealed before choosing a bride. In equilibrium, the most desirable young females choose successful older males. Young males who believe that time will not treat them kindly will offer to marry at a young age. Although they are aware that young males available for marriage are no bargain, the less desirable young females will be offered no better option than the lottery presented by marrying a young male. We show the existence of equilibrium for models of this type and explore the properties of equilibrium.