FAMILY BARGAINING

Bargaining approaches to family decision-making developed in the last two decades of the twentieth century. Because interactions between spouses are simpler than most other family interactions, bargaining approaches have been most fully articulated in the context of marriage. This entry begins by describing pre-bargaining approaches to interactions between spouses and then surveys bargaining approaches. It concludes by discussing briefly the application of bargaining approaches to other interactions within families–between parents and children and between elderly parents and adult children.

Bargaining Approaches and Game Theory

Bargaining approaches are based on game theory and this entry uses the terms bargaining approaches and game-theoretic approaches interchangeably. Within game theory, the threshold distinction is between noncooperative and cooperative games. Cooperative game theory analyzes outcomes or solutions under the assumption that the players can communicate freely and make costlessly-enforceable agreements. Thus, cooperative game theory treats all feasible outcomes as potential equilibria. In contrast, noncooperative game theory treats as potential equilibria only those outcomes that correspond to self-enforcing agreements in the sense that each player's strategy is a best response to the strategies of the others.

Economists say that an equilibrium is "efficient" (or "Pareto efficient" or "Pareto optimal") if no individual can be made better off without someone else being made worse off. Efficiency implies that any division of a cake is efficient provided it leaves none on the plate and none on the floor–thus, a division may be efficient without being fair or equitable. The efficiency of social arrangements and practices is a central concern of economics, yet pre-bargaining models of the family and cooperative bargaining models simply assumed that families are efficient. A major advantage of approaches based on noncooperative game theory is that they do not assume efficiency and thus allow us to investigate the conditions that enable families to achieve and sustain efficient outcomes.

Becker's Altruist Model

Gary Becker, in his work of 1974 and 1981, proposed the first model of family decision-making or household collective choice, his "altruist" model. Three implications of Becker's altruist model deserve attention. First, it implies that family decisions are Pareto efficient. Second, it implies a distribution of the benefits and burdens of family life in which the head of the family–Becker's altruist–attains his most preferred point in the feasible set. Third, it implies that family members pool their resources.

The altruist model is rigged to produce these results, but none of these results–efficiency, the lopsided distribution of benefits and burdens, or pooling of family resources–is an essential feature of bargaining models of family decision-making. Robert A. Pollak in 1985 interprets Becker's altruist model as an "ultimatum game" in which one family member can confront the others with take-it-or-leave-it offers. Without the ultimatum game interpretation, the conclusions of the altruist model and of Becker's so-called Rotten Kid Theorem hold only in a narrow range of environments. This is discussed in Theodore Bergstrom's 1989 article, the introduction to the enlarged edition of Gary Becker's Treatise of the Family published in 1991, and in Robert Pollack's 2003 paper.

Bargaining Models

Cooperative bargaining models of marriage were introduced by Marilyn Manser and Murry Brown in 1980 and Marjorie B. McElroy and Mary J. Horney in 1981 as an alternative to Becker's altruist model. A typical cooperative bargaining model of marriage assumes that if the spouses fail to reach agreement, both husband and wife receive the utilities associated with a default outcome. The utilities associated with the default outcome are usually described as the "threat point." In Manser and Brown and in McElroy and Horney the threat point is interpreted as divorce, while in the "separate spheres" model of Shelley Lundberg and Robert A. Pollak, introduced in their 1993 article, the threat point is interpreted as a noncooperative equilibrium within the marriage.

The Nash bargaining model, developed by John Nash in 1950, provides the leading solution concept in cooperative bargaining models of marriage. The utility received by husband or wife in the Nash bargaining solution depends on the threat point; the higher a spouse's utility at the threat point, the higher the utility that spouse will receive in the Nash bargaining solution. This dependence is the critical empirical implication of Nash bargaining models: the couple's expenditure pattern depends not only on prices and the couple's total income, but also on the threat point.

The income-pooling hypothesis. As the divorce-threat and separate spheres models show, cooperative bargaining does not imply income pooling. If the fraction of the couple's income controlled by each spouse individually affects the threat point, then it will affect the couple's expenditure pattern and the relative well-being of husbands and wives. This dependence implies that public policy, for example, tax and welfare policy, may affect distribution within marriage.

Empirical rejections of family income pooling have been the most influential in weakening economists' attachment to the altruist model. Income pooling implies a restriction on family demand functions that appears simple to test: If family members pool their incomes and allocate the total, then only total income will affect demands. The fraction of family income received or controlled by one family member should not influence those demands. A large number of later empirical studies have rejected pooling, finding instead that earned or unearned income received by the husband or wife significantly affects demand patterns when total income or expenditure is held constant.

For technical reasons discussed in Shelly Lundberg and Robert Pollak's 1996 work, the pooling hypothesis is not simple to test. The ideal test would be based on an experiment in which some husbands and some wives were randomly selected to receive income transfers. A less-than-ideal test could be based on a natural experiment in which some husbands or some wives received an exogenous income change. Lundberg, Pollak, and Terence J. Wales in 1997 examine the effects of such a natural experiment–the policy change in the United Kingdom that transferred substantial resources from husbands to wives in the late 1970s. The policy change involved child allowances, a program of government transfer payments to parents. The child allowance payments were conditioned on the number of children in the family, but not on family income, so that, in welfare-program terminology, the program is not "means tested." Lundberg, Pollak, and Wales find strong evidence that a shift toward relatively greater expenditures on women's goods and children's goods coincided with this income redistribution, and they interpret this finding as a rejection of the pooling hypothesis.

Because efficiency is much more difficult to test than pooling, the discussion of efficiency has focused on theoretical issues. The most convincing rationale for the usual assumption that bargaining in marriage leads to efficient outcomes is the belief that efficiency is likely to emerge from repeated interactions in environments that remain stable or change slowly over time. Most, but not all, marital bargaining involves repeated interactions in stable environments. Lundberg and Pollak in 2001 argue that when a decision affects future bargaining power, inefficient outcomes are plausible. If the spouses could make binding commitments–in effect, commitments to refrain from exploiting future bargaining advantages–then this source of inefficiency would disappear. But spouses seldom can make binding commitments regarding future allocations within marriage. As an example, Lundberg and Pollak consider the location problem of a two-earner couple, where the husband would be advantaged in future bargaining by one location and the wife by the other. Location decisions provide transparent and analytically tractable examples of choices likely to affect future bargaining power, but the logic of the analysis applies to many other decisions. For example, decisions about education, fertility, and labor force participation are also potential sources of inefficiency.

The possibility of divorce (perhaps followed by remarriage) limits the scope for bargaining within marriage by placing bounds on the distributions that can emerge as equilibria. The assumption that individuals are rational implies that no one would accept less than he or she would receive outside the marriage. "Divorce bounds" apply to all bargaining models, cooperative and noncooperative. The divorce bounds depend upon the costs of divorce, including psychic costs, the resources available to divorced individuals, and conditions in the remarriage market. When the divorce bounds are tight, there is little scope for bargaining within marriage. Bargaining models of marriage are motivated by the assumption that, in at least some marriages, the divorce bounds are loose enough that the allocation of the surplus is worth modeling.

Extensions

Bargaining approaches based on game theory provide a framework for analyzing not only interactions between spouses but all strategic interactions involving family members. Yoram Weiss and Robert J. Willis, in their 1985 and 1993 articles, show how the analytical tools of game theory can be used to investigate the distribution of child support responsibilities between ex-spouses. Because bargaining models are most tractable in simple strategic situations–two-person games in relatively stable environments–it is not surprising that bargaining models of marriage are better developed than bargaining models of interactions between parents and children. Nor is it surprising that models of interactions between parents and children are better developed than bargaining models of interactions in blended families or in families that span three or more generations. Nevertheless, bargaining models of marriage are not simple and, in the interest of tractability, analysis usually focuses on relatively stable environments and avoids dynamic ones in which decisions in one period affect bargaining power in the future.

Despite the differences among bargaining models and despite their complexity, bargaining models offer the most promising analytic approach to understanding the formation, dissolution, and functioning of households and families. Although bargaining models are unlikely to lead directly to equations that can be estimated, they are a fruitful source of hypotheses about regularities that may be found in data and of interpretations of such empirical regularities.

See also: Becker, Gary S.; Microeconomics of Demographic Behavior; Partner Choice.

bibliography

Becker, Gary S. 1974. "A Theory of Social Interactions." Journal of Political Economy 82(6): 1063–1094.

——. 1981; enlarged edition, 1991. A Treatise on the Family. Cambridge, MA: Harvard University Press.

Bergstrom, Theodore C. 1989. "A Fresh Look at the Rotten Kid Theorem–and Other Household Mysteries." Journal of Political Economy 97(5):1138–1159.

Lundberg, Shelly, and Robert A. Pollak. 1993. "Separate Spheres Bargaining and the Marriage Market." Journal of Political Economy 101(6): 988–1010.

——. 1996. "Bargaining and Distribution in Marriage." Journal of Economic Perspectives 10(4):139–158.

Lundberg, Shelly, Robert A. Pollak, and Terence J. Wales. 1997. "Do Husbands and Wives Pool Their Resources? Evidence from the U.K. Child Benefit." Journal of Human Resources 32(3):463–480.

Manser, Marilyn, and Murray Brown. 1980. "Marriage and Household Decision-Making: A Bargaining Analysis." International Economic Review. 21(1): 31–44.

McElroy, Marjorie B., and Mary J. Horney. 1981. "Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand." International Economic Review. 22(2):333–349.

Pollak, Robert A. 1985. "A Transaction Cost Approach to Families and Households." Journal of Economic Literature 23(2): 581–608.

——. 2003. "Gary Becker's Contribution to Household and Family Economics." Review of Economics of the Household 1.

Weiss, Yoram, and Robert J. Willis. 1985. "Children as Collective Goods in Divorce Settlements." Journal of Labor Economics 3(3): 268–292.

——. 1993. "Transfers among Divorced Couples: Evidence and Interpretation." Journal of Labor Economics 11(4): 629–679.

Robert A. Pollak