Game theory and the cooperative bargaining model

While exchange theory, including resource and equity theory, sees power as an outcome of an interaction between at least two individuals, researchers often emphasize the analysis of interaction itself for an understanding of power. Scanzoni and Polonko (1980) argue that power should be considered as a process rather than an outcome. Since interacting indi-viduals negotiate their outcomes, power is considered as bargaining power. Like Emerson’s power-dependence relations, bargaining power is dynamic and changes over time. Its defini-tion is similar to that of Thibaut and Kelly (1991): “Bargaining power is simply the capability to bring about modifications in the behavior of Other while at the same time being able to minimize Other’s efforts to bring about modifications in one’s own behavior” (Scanzoni and Polonko, 1980, 42). The one who influences the other within bargaining situations has bar-gaining power. Unlike social exchange theory and resource theory, game theory and

coopera-tive bargaining theory as its derivate stress the dynamic process of long-term interaction and the role of cooperation for relationships. Although so far the focus of this study has been on power imbalances, cooperation between partners should not be disregarded. When we talk about power imbalances, we also have to talk about power balances. Individuals are not fight-ing against each other all the time, nor do they always try to oppress their partner. On the contrary, both cooperation and noncooperation are crucial aspects in long-term relationships in particular.

Among social exchange theorists, it is primarily Thibaut and Kelley who have a dynamic per-spective on power by focusing on the strategies and behavioral influence of two individuals in a bargain. Their theory therefore displays similarities to game theory (Chadwick-Jones, 1976, 26). According to Chadwick-Jones (1976, 26), game theory “is intended to solve the prob-lem of choice between alternative strategies, in favour of the optimal decisions in two-person bargaining situation”. Camerer (2003) defines game theory as “a mathematical derivation of what players with different cognitive capabilities are likely to do in games”. Game theory assesses the strategies individuals apply e.g. to the allocation of welfare. Similarly to ex-change theory, it assumes that individuals act rationally in the way that they try to maximize rewards and minimize costs (Chadwick-Jones, 1976, 26f.). Within interaction, individuals follow their preferences. Individual preferences are expressed through utility functions. An individual prefers one action to another if the expected reward is higher in one action than in the alternative (Chadwick-Jones, 1976, 28). Since the preferences of individuals differ (Ott, 1999, 48), competition takes place. However, game theorists like Emerson do not exclude altruism from bargaining processes.

Since interdependence exists between the players, one player’s rewards depend on the rewards of the other player. Therefore the players are interested in the welfare of the others (Chadwick-Jones, 1976, 50). The individuals will then cooperate – especially in repeated games because, like in exchange relations, interdependence increases with the number of times the individuals bargain. Furthermore, game theorists differentiate between noncooperative and cooperative games. Whereas in cooperative games the players make binding agreements, in noncoopera-tive games players have to guess what the others will do (Camerer, 2003). Hence long-term relationships are repeated cooperative games, in which individuals are able to make binding agreements and increase their welfare through cooperation.

In game theory, cooperation is conceptualized by the “Nash Bargaining Equilibrium”.¹⁶ The Nash equilibrium is reached, when the product of individual gains is maximized, that is when one person cannot increase its gains without reducing the gains of the others – given that bargaining strategies do not change (Ott, 1999, 50).

“Cooperative solution concepts, including the Nash bargaining solution, explicitly as-sume that the equilibrium distribution is Pareto optimal. Cooperative game theory begins

16For the Nash bargaining approach see Lundberg and Pollack (1996, 146).

by assuming that players can communicate freely and make binding, costlessly enforce-able agreements; the analysis focuses on the formation of coalitions [...] and on the distribution of the benefits of cooperation among players” (Lundberg and Pollak, 1994, 133).

The cooperative bargaining model, an application of game theory to the household level, is based on the Nash equilibrium. The interactions between the members of a household can be understood as a repeated game. Sen (1993) points out that since individuals have differ-ent preferences, not only cooperation but also conflicts concerning the allocation of welfare may occur. If conflict occurs, household members will start to bargain. Since cooperation maximizes the welfare of each household member in the long run, everybody is interested in cooperative solutions (Ott, 1999, 49).

Reciprocity is a central norm in long-term bargaining situations where resources are allocated or – to refer again to social exchange theory – exchanged between the members of a house-hold. They pursue reciprocal strategies when negotiating with each other. However, like in exchange theory, bargains might have unreciprocal outcomes. Since cooperation is needed to maximize the welfare in the household, every individual has the potential to threaten with noncooperation (Bahr, 1982, 50). Like in exchange theory, alternative social relations and individual resources play a crucial role. The attractiveness of alternatives outside the family defines the “threat potential” of the partners within the family (Ott, 1997, 50). Ott points out that the utility of the best alternative again depends on the individual’s resources, especially income (Ott, 1997, 51). The partner with the higher threat potential will have a better bargain-ing position and thus the opportunity to change the others’ behaviors in his or her favor. This person has bargaining power.

“The more attractive an individual’s opportunities outside the family, the more strongly that individual’s preferences will be reflected in the intrafamily distribution of resources”

(Lundberg and Pollak, 1993, 992).

The individual’s threat potential involves a threat point. If the individual’s utility reaches or falls below the threat point, they/he or she will leave the relationship. For spouses, this means divorce. In addition to divorce, Lundberg and Pollak (1993) interpret the threat point in an-other way. In their separate sphere bargaining model, they define a noncooperative equilib-rium as a threat point. “Within existing marriage, a noncooperative equilibequilib-rium corresponds to a utility-maximizing strategy in which each spouse takes the other spouse’s strategy as given”

(Lundberg and Pollak, 1993, 993). Such a scenario corresponds to a noncorporative game.

But how can partners maintain welfare production and allocations in a long-term perspective without negotiating? With regard to intra-household production and allocation, they simply do not interact anymore. According to Brines and Joyner (1999) and Lundberg and Pol-lak (1993), the individuals’ specialization in separate spheres replaces bargaining processes within the partnership. These specialization patterns are provided by gender identities and

related gender norms. The traditional division of housework and labor, where he works in the labor market while she maintains the household and cares for the children, makes negotia-tions and bargaining unnecessary. As the partners’ spheres are separate, they never come into conflict which each other. Instead of leading to divorce, the relationship can be maintained.¹⁷ Hence gender identities are crucial guidelines in the noncooperative equilibrium. The separate sphere bargaining model developed by Lundberg and Pollak (1993) can be related to doing gender theory. Women and men choose a position in the household in which they can behave according to their identities as men or women. In their approach the authors integrate gender as a structural category into rational choice theory. However, the noncooperative equilibrium is not the only factor with a gender dimension. Ott (1997) emphasizes that women are often more dependent on their partner since they are generally in charge of child care and therefore reduce their work in the labor market. Her lower income is then related to lower bargain-ing power in the relationship. Recent research has also shown that even if women do not reduce their investment in employment, they are nevertheless in charge of the “second shift”

(Hochschild, 1989), that is housework and child care. Working both in the labor market and at home diminishes the leisure and recreation time of female partners.

Concluding with this last rational choice theory, we have seen that all in all only few ra-tional choice approaches consider the importance of gender for the interaction of individuals.

Thibaut and Kelly (1991) highlight the influence of social norms, and thus gender norms, on individuals’ perception of interaction and exchange outcomes. Brines and Joyner (1999) and Lundberg and Pollak (1993) introduce the role of gender norms and gender identities in non-cooperative games. These theoretical arguments point out that individuals do not interact in a social vacuum but that relationships are embedded in a gendered social structure, which im-plies gender asymmetries. However, rational choice assumptions neglect structural categories such as gender. In order to comprehend partners’ interaction and their arrangements in the household, gender theory therefore has to be considered as well.

The two approaches – rational choice and gender theories – are generally regarded as “mutu-ally exclusive” (Bittman et al., 2003, 187). However, as mentioned above, theoretical work by Thibaut and Kelly (1991), Lundberg and Pollak (1993) and Ott (1997) indicates that the dimension of gender has to be taken into account when dealing with power in couples. By fo-cusing on the emergence of social structure, Blau proposes a link to gender theory and doing gender theory. Gender theory defines gender as a social institution and a baseline category for the organization of social life (Lorber, 2003). The social structure (Risman, 2004) and the physical environment (Goffman, 2001) are gendered. Doing gender theory (West and Zim-mermann, 1991) highlights the everyday reproduction of gender in this gendered setting. Here

17Parsons already emphasized the advantage of the traditional division of labor because of its stabilizing effect on intimate relationships (Hare-Mustin, 1988).

individuals do not only act according to social structure and institutions, but their actions also include a feedback loop on them. The relation between agency and structure can be covered by Giddens (1984) and his structuration theory.

In the following chapter, central assumptions of doing gender theory and gender theory will be presented. Since doing gender theory can be better understood if contrasted with older theoretical approaches to gender, first of all gender role theory will be briefly presented and criticized. Then, doing gender theory and, finally, gender theory will be explained. Following these sections, rational choice theory and gender theory will be brought together.