Bilateral bargaining. Theory and applications
The book is a monograph on two person bargaining. Roughly half of the book is a useful exposition of selective aspects of bilateral bargaining theory including non-cooperative approaches to bargaining theory as well as models of evolutionary game theory. Aside from staple topics such as Nash's bargaining solution, Kalai-Smorodonsky solution, Rubinstein's alternating offers model and so forth, it also includes an overview of earlier contributions of Edgeworth, Zeuthen and Hicks and concludes with a section on empirical and experimental researches relating to the theory sections. The chapter provides detailed analytical exposition and discusses models and results with an eye to achieving a critical synthesis. The remainder of the book consists of three chapters and an appendix. The material for these chapters are, generally speaking, based on the author's, and co-authors', works in these areas. The first of these chapters is closely related to the expository chapter, building on the ultimatum minigame, dealt with in the section on evolutionary game models in chapter 1. It combines a stochastic evolutionary game setup with satisficing behaviour formulation in a two person bargaining situation. It is an adaptive behaviour type model in which each player satisfices, that is sticks to past action if it has provided a payoff larger than his aspired payoff otherwise there is a positive probability of swiching out of the past action; the probability of sticking to the past action is a decreasing function of the gap between the actual and aspired payoff. The aspiration levels are endogenously determined; they adapt to the gap between realized and aspired levels of payoff; aspiration levels rise if actual payoff exceeds the aspired level and falls, otherwise. In addition, there may be present perturbations or random shifts in the aspiration levels. The stationary distribution of the associated Markov process is investigated. When perturbations occur rarely and aspirations are adapted slowly, the model yields approximately efficient average outcome. The average surplus distribution is shown to depend in general on the supports of the perturbation distributions. The sensitivity of stationary distributions of aspirations and actions, to changes in parameters, are explored using Monte-Carlo simulations, leading to several interesting observations such as ``a player who adapts aspirations more slowly, fares better'' or ``there is a benefit in being capricious in the sense of experiencing big and frequent perturbations in aspirations''. In this sense, the chapter has the novel feature of addressing soft factors of negotiation -- emotional and irrational -- such as persistence, stubbornness or capriciousness. The material of the remaining two chapters are, at best, only tenuously connected to the central theme of bilateral bargaining. Nonetheless, the material of the third chapter is an interesting one. It seeks to refine and improve power indices by introducing the concept of an inferior player. Conventional power indices would attribute positive power to all players in games typified by the presence of one of a kind monopolist facing small traders of another kind who can be `played off' against one another. This is, however, at variance with intuition and analysis of competitive markets, of the core etc. With this as the motivation, the notion of an inferior player is introduced. Loosely speaking, an inferior player is one whose presence or absence in some coalitions may matter, unlike a dummy player (whose presence or absence from any coalition does not affect the outcome for the rest of the coalition materially), however, this power is neutralized by the presence of another player in all of these coalitions who also has the option of participating in a coalition where the inferior player has no effective contribution. Power indices modified to assign zero weight to inferior players just as they do to dummy players. With this modification, the Banzhaf index is studied and possibilities of exploring variations and extensions are discussed. The final chapter is essentially a commentary on some contributions to notions of fairness and justice in the context of bargaining, focusing a good deal on theories of Rawls and Binmore. An appendix provides a summary description of some standard game theory concepts. Despite the somewhat loosely knit character of the monograph, in view of the relation of the last half of the monograph to the first half, the second and third chapters contain interesting material suitable for the reference shelf.
scientific article; zbMATH DE number 1745057