bargaining theory the branch of game theory that treats agreements, e.g., wage agreements between labor and management. In the simplest bargaining problems there are two bargainers. They can jointly realize various outcomes, including the outcome that occurs if they fail to reach an agreement. Each bargainer assigns a certain amount of utility to each outcome. The question is, what outcome will they realize if they are rational? Methods of solving bargaining problems are controversial. The best-known proposals are Nash’s and Kalai and Smorodinsky’s. Nash proposes maximizing the product of utility gains with respect to the disagreement point. Kalai and Smorodinsky propose maximizing utility gains with respect to the disagreement point, subject to the constraint that the ratio of utility gains equals the ratio of greatest possible gains. These methods of selecting an outcome have been axiomatically characterized. For each method, there are certain axioms of outcome selection such that that method alone satisfies the axioms. The axioms incorporate principles of rationality from cooperative game theory. They focus on features of outcomes rather than bargaining strategies. For example, one axiom requires that the outcome selected be Pareto-optimal, i.e., be an outcome such that no alternative is better for one of the bargainers and not worse for the other.
Bargaining problems may become more complicated in several ways. First, there may be more than two bargainers. If unanimity is not required for beneficial agreements, splinter groups or coalitions may form. Second, the protocol for offers, counteroffers, etc., may be relevant. Then principles of non-cooperative game theory concerning strategies are needed to justify solutions. Third, the context of a bargaining problem may be relevant. For instance, opportunities for side payments, differences in bargaining power, and interpersonal comparisons of utility may influence the solution. Fourth, simplifying assumptions, such as the assumption that bargainers have complete information about their bargaining situation, may be discarded. Bargaining theory is part of the philosophical study of rationality. It is also important in ethics as a foundation for contractarian theories of morality and for certain theories of distributive justice. See also DECISION THEORY, GAME THEORY. P.We. Barthes, Roland (1915–80), French post-structuralist literary critic and essayist. Born in Cherbourg, he suffered from numerous ailments as a child and spent much of his early life as a semiinvalid. After leaving the military, he took up several positions teaching subjects like classics, grammar, and philology. His interest in linguistics finally drew him to literature, and by the mid-1960s he had already published what would become a classic in structural analysis, The Elements of Semiology. Its principal message is that words are merely one kind of sign whose meaning lies in relations of difference between them. This concept was later amended to include the reading subject, and the structuring effect that the subject has on the literary work – a concept expressed later in his S/Z and The Pleasure of the Text. Barthes’s most mature contributions to the post-structuralist movement were brilliant and witty interpretations of visual, tactile, and aural sign systems, culminating in the publication of several books and essays on photography, advertising, film, and cuisine. See also POSTMODERN , SEMIOSIS , STRUCTURALIS. M.Ro.