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This chapter introduces cooperative game theory by examining the axiomatic theory of two-person bargaining problems. The link between cooperative and noncooperative game theory is first explained in terms of the Nash program. The idea of a cooperative payoff region is then developed for use in applied contexts. The Coase theorem is explained for the case of a Nash bargaining problem. A variant of the Nash bargaining solution with both a breakdown point and a deadlock point is described. A proof of Nash's axiomatic bargaining theorem is offered. The Kalai-Smorodinsky bargaining solution and the Walrasian bargaining solution are offered as alternatives to Nash's solution.

This chapter examines noncooperative bargaining models and links them with cooperative bargaining concepts in accordance with the Nash program. Following a discussion of what matters in real-life bargaining, the case in which commitment is possible is studied using the Nash Demand Game. It is shown that a Nash equilibrium of the smoothed version of the Nash Demand Game implements the Nash bargaining solution. Nash threat games are then considered with an application to collusion in Cournot models. The case in which commitment is impossible is considered. Rubinbstein's bargaining model is introduced using one-stage and two-stage Ultimatum Games to set the scene. Rubinstein's theorem that his model has a unique subgame-perfect equilibrium is proved. The outcome is shown to converge on an asymmetric version of the Nash bargaining solution when the time interval between successive proposals becomes sufficiently small. The chapter ends with a discussion of common mistakes in applying the theory.

The movie A Beautiful Mind (2001) portrays the life and work of John F. Nash Jr., who received the Nobel Prize in Economics in 1994. A class of his theories deals with how people should behave in strategic situations that involve what are known as “mixed strategies,” that is, choosing among various possible strategies when no single one is always the best when you face a rational opponent. This chapter uses data from a specific play in soccer (a penalty kick) with professional players to provide the first complete test of a fundamental theorem in game theory: the minimax theorem. The minimax theorem can be regarded as a special case of the more general theory of Nash. It applies only to two-person, zero-sum or constant-sum games, whereas the Nash equilibrium concept can be used with any number of players and any mixture of conflict and common interest in the game.

From the 1930s to the 1950s, scientists, academics, and technologists were portrayed as “heroes” working to make the world a safer, better place. In most recent years, such films have tended to offer a warts-and-all depiction, interweaving the academic prowess of their subjects with complex emotional stories. This chapter examines two films that feature men working in academia during the same period: Alfred Kinsey in Kinsey (2004) and John Nash in A Beautiful Mind (2001). Kinsey focuses on the period leading up to the publication of Kinsey's 1948 study Sexual Behavior in the Human Male, through to his death in 1956. The film covered the darker sides of Kinsey's character, including his bisexuality, masochistic and voyeuristic practices. A Beautiful Mind depicted how Nash dealt with and overcame his schizophrenia.

Scholars have tended to present the 1705 King’s Theatre as part of a newly fashionable area in the developing West End. But a closer examination of the development of London suggests that it was not that ‘newly fashionable’; Henry Jermyn, Earl of St. Albans, had been developing the area of St James’s since the Restoration, and by the time of his death in 1684 the fabric of the area was virtually complete. It was not, then, a great gamble to have sited the King’s Theatre in Haymarket; it placed the fashionable house for the luxury item of opera near the homes of those who could - and did - afford it. But even in the grandeur of the West End, the Opera House originally had little or no front to the street, being surrounded by shops; this was the product of London’s commercially minded developers and theatre promoters. As the 18th century wore on, the theatre began to develop a place in the streetscape, culminating at the end of the 19th century in the construction of a large and pompous building, which nonetheless – as this article argues – remained part of the commercial landscape.

During the postwar era, discussions of conflict and cooperation, altruism and self-interest, war and peace returned consistently to the mathematical idiom of game theory. The famed “prisoner's dilemma” (PD) game, in particular, would prove a constant point of reference in discussions of arms races and international conflict. Yet this fact presents a puzzle given how quickly critiques of game theory's brand of rationality emerged during the 1950s and 1960s. By examining the use of the PD game in three distinct contexts, this chapter sheds light on the remarkable persistence of game theory, even as the theory's empirical adequacy and normative desirability attracted criticism. Whether it was invoked in studies of teamwork and cooperation, the nuclear arms race, or the evolution of reciprocal altruism, PD's characteristic game matrix provided social, behavioral, and biological scientists with a structured language for debating some of the central problems of the day.

This chapter explores the little-studied world of early nineteenth century consumerism. It argues that the West End became productive of new forms of shopping aimed principally at an elite market but one that was increasingly colonized by the growing middle classes. It looks at the development of Regent Street, at the construction of shopping arcades (including the Burlington Arcade on Piccadilly) and bazaars that, it argues, anticipated the department store. The chapter also looks at the development of elite tailoring (Savile Row) and the importance of West End bookshops such as Hatchard’s in the construction of intellectual networks.

This chapter discusses the issues of informed consent and mental capacity as seen in the film A Beautiful Mind (2001). The film tells the story of John Nash Jr. (Russell Crowe), a brilliant, Nobel Prize-winning mathematician who develops schizophrenia. His mind, while still capable of solving even previously insoluble theoretical problems, is not always capable of distinguishing reality from paranoid delusions and visual and auditory hallucinations. Nash is ultimately forced, or at least coerced, into treatment. The film illustrates the problem posed by the multi-tiered concept of informed consent, especially in the context of mental illness, where decision-making capacity and competence are especially hard to isolate and evaluate. One prerequisite for voluntary informed consent is an environment free of a compelling force that will drive the decision in one direction and negate the patient's ability and freedom to choose. Another is the mental capacity to make a reasoned choice. One way to assess this capacity is to establish if the patient has a set of values and goals, if the patient can communicate and understand information, and can reason and deliberate about the choice.