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Über dieses Buch

The four volumes of Game Equilibrium Models present applications of non-cooperative game theory. Problems of strategic interaction arising in biology, economics, political science and the social sciences in general are treated in 42 papers on a wide variety of subjects. Internationally known authors with backgrounds in various disciplines have contributed original research. The reader finds innovative modelling combined with advanced methods of analysis. The four volumes are the outcome of a research year at the Center for Interdisciplinary Studies of the University of Bielefeld. The close interaction of an international interdisciplinary group of researchers has produced an unusual collection of remarkable results of great interest for everybody who wants to be informed on the scope, potential, and future direction of work in applied game theory. Volume III Strategic Bargaining contains ten papers on game equilibrium models of bargaining. All these contributions look at bargaining situations as non-cooperative games. General models of two-person and n-person bargaining are explored.



Introduction to the Series “Game Equilibrium Models”

Game equilibrium models are descriptions of interactive decision situations by games in extensive or normal form. The analysis of such models is based on the equilibrium point concept, often refined by additional requirements like subgame perfectness. The series consists of four volumes:
Evolution and Game Dynamics
Methods, Morals and Markets
Strategic Bargaining
Social and Political Interaction.
Reinhard Selten

Introduction to Volume III: “Strategic Bargaining”

A topic that received a lot of attention from the research group throughout the year the group was together at the ZiF was that of strategic bargaining. The inspiration came from papers by Binmore (1985), Rubinstein (1982) and Selten (1981) which were carefully studied and critically discussed at the time the research project started. All the papers collected in this volume, except the one by Selten and Güth, deal with bargaining under conditions of complete information. The papers of Okada and Haller consider bilateral bargaining problems. The Selten/Wooders paper deals with bargaining in a market context in which the number of participants varies over time. The remaining papers consider coalitional bargaining problems with a fixed number of players and they can be viewed as pursuing the “Nash program” of investigating whether concepts from cooperative game theory can be implemented by means of noncooperative bargaining procedures. The Bennett/van Damure paper is restricted to games with transferable utility, while Bennett considers general NTU games. Laing and Albers/Laing consider bargaining in a spatial context where the problem is which location to choose. Laing provides a theoretical analysis whereas Albers/Laing present experimental results obtained in this setting.
Eric van Damme

A Noncooperative Approach to the Nash Bargaining Problem

We present a noncooperative repeated bargaining model for a two-person game in normal form in which the Nash bargaining solution can be implemented as a unique stationary subgame perfect equilibrium point in the limiting case that the discount factor of payoffs goes to 1. Our bargaining game is based on the supergame model in a way that two players are allowed to negotiate for a long-term contract on actions before they select their own actions independently. The disagreement point of the Nash bargaining solution is determined to be a Nash equilibrium point of the normal form game. If short-term contracts only are enforceable, the Nash bargaining solution can not be implemented.
Akira Okada

A Two-Person Repeated Bargaining Game with Long-Term Contracts

Does a noncooperative equilibrium point necessarily lead to a Pareto efficient outcome in a supergame if binding agreements on actions are possible among players? We present a two-person repeated bargaining game in which players can negotiate for a long-term contract on their actions in the supergame model. We show that a subgame perfect equilibrium point of our game necessarily leads to a Pareto efficient outcome if the equilibrium strategies for both players have zero-memory. We also point out that the question above is answered negatively if the equilibrium strategies for players have complete memory.
Akira Okada

Three Approaches to Bargaining in NTU Games

This paper presents a noncooperative model of bargaining in characteristic function games and relates its outcomes to those of a cooperative model and a bargaining theory model. Despite the differences in the approach of these three models and the resulting differences in the nature of their solutions, all three models make similar predictions of bargaining outcomes.
Elaine Bennett

Folk Theorems for the Proposal-Making Model

In the tradition of folk theorems, this paper shows that nearly anything can be a bargaining outcome of the proposal-making model.
Elaine Bennett

A Noncooperative Model of Bargaining in Simple Spatial Games

The bargaining problem facing players who must reach a collective decision can be modeled precisely as a noncooperative game. This essay uses a noncooperative game-th oretic approach to analyze bargaining in a class of games without sidepayments in which a point from a Euclidean set of decision alternatives is to be selected in accordance with a simple collective decision rule (Laing, Nakabayashi, and Slotznick, 1983), such as any weighted or unweighted majority rule. It builds from foundations established in Selten’s (1981) noncooperative analysis of bargaining in zero-normalized, one-stage characteristic function games. It models simple spatial bargaining games, and characterizes noncooperative stationary equilibrium strategies and their relation to demand equilibria (Albers, 1975, 1987).*
James D. Laing

Demand Commitment Bargaining: - The Case Of Apex Games -

An apex game is a bargaining situation in which there is one major (apex) player and n “minor” players. The only profitable coalitions contain either the apex player and any one of the minor players or else all of the minor players. The demand commitment model is a bargaining procedure, i.e. an extensive form game. This paper investigates the payoffs that result (as subgame perfect outcomes) for apex games when players use the demand commitment bargaining procedure. We show that whenever the apex player has the first move he forms a coalition with a minor player and obtains the fraction (n − 1)/n of the coalition’s value while his (minor-player) partner obtains the remaining 1/n. When a minor player has the first move he either forms a coalition with the apex player (and obtains 1/n) or else forms a coalition with all of the remaining minor players. When this minor-player coalition forms there are many subgame perfect payoff distributions. A refinement of subgame perfection is proposed and is shown to select a unique payoff distribution (1/n for each minor player) for the minor-player coalition.
Elaine Bennett, Eric van Damme

Prominence, Competition, Learning, and the Generation of Offers in Computer-Aided Experimental Spatial Games

Collective decision making by people who, as humans, are merely quasirational is subject to influences of substantively irrelevant features of the decision environment. This paper analyzes data from a computer-aided laboratory study of decision making in spatially represented, majority rule games to identify influences of prominent features of the problem environment on the processes and outcomes of decision, and the way in which these influences change through competition and learning.*
Wulf Albers, James D. Laing

Original or Fake — A Bargaining Game with Incomplete Information

We consider a special class of noncooperative bargaining games with incomplete information and two agents who bargain about the price of a given object. The object can be either of high value or of low value. Whereas the seller knows the real value, the buyer is not completely informed in that respect. With probability w he expects that the object is of low value and with the probability 1-w that it is of high value. The parameter w is common knowledge. One can therefore distinguish two types of the seller, namely the one who tries to sell an object of low value and the one who offers the more valuable object. To have something specific in mind, the commodity is assumed to be a work of art which can be either a fake or an original. The two types of the seller are accordingly called fake seller and honest seller. The buyer is of a unique type. Bargaining is supposed to proceed in form of a unanimity game, i.e., the players simultaneously determine their price offers. A contract results only if a seller and the buyer have chosen the same prices. As it is typical for bargaining games, the game has many equilibrium points. We apply the equilibrium selection theory of Harsanyi and Selten to determine a unique solution point for each of the bargaining games.
Reinhard Selten, Werner Güth

Wage Bargaining as a Strategic Game

Wage bargaining between “capital” and “labor” is analyzed as an alternating offer game, where disagreement leads to surplus sharing according to the contractual status quo or to a strike.
Hans Haller

A Game Equilibrium Model of Thin Markets

We consider games of group, or coalition, formation occuring over infinite, discrete time, with new participants becoming active in the game in each period, and with participants that have successfully formed groups leaving the game each period. Markets may be “thin”, in the sense that the number of participants active in the game in any time period is finite and may be small. We construct a subgame perfect equilibrium for an example and show some additional properties of the equilibrium. One property is that, even though markets are thin, the “first mover” within a time period has an advantage (and realizes more than a competitive payoff) only in special circumstances, and, along the equilibrium path, he is the only mover who can have such an advantage. Also, we discuss the limit behavior of the model as costs of waiting (time costs) become small; specifically, the equilibrium payoffs converge to core payoffs of a game with a continuum of players and finite coalitions (f-core payoffs). The static continuum game provides an idealization of the limit of the dynamic games for small waiting costs. Thus our research initiates providing a noncooperative foundation for the core as a solution concept for such games.
Reinhard Selten, Myrna H. Wooders


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