# Models of two-person bargaining

##### Alaste, Tomi (2017-06-05)

Alaste, Tomi

T. Alaste

05.06.2017

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**Julkaisun pysyvä osoite on**

https://urn.fi/URN:NBN:fi:oulu-201706062590

##### Tiivistelmä

The purpose of the thesis is to present some theoretical studies on bargaining situations. The thesis concentrates on existing research on the subject, and we do not present any new results. A central aim of the thesis is in describing how different factors present in real life bargaining situations can be taken into account in theoretical models of bargaining. It is our intention to use these models to obtain some information about effects of these factors in bargaining situations. In addition, another central element of the thesis is in describing relationships between different models. The studied models are kept deliberately elementary to provide clear analyses.

We use axiomatic and strategic models to study bargaining situations. Axiomatic method is very general as it does not deal with any particular bargaining process. Instead, these models concentrate solely on the outcome of a bargaining situation. A weakness with axiomatic models is that it might be difficult to evaluate how accurately the assumptions made describe some particular bargaining process. In the thesis, we concentrate mostly on Nash bargaining solution and its properties. Strategic models studied in the thesis include the game of alternating offers and several variations of this game. The main purpose of these variations is to describe what kind of effects different factors present in bargaining situations have on bargaining. The models studied deal with such factors as uncertainty, inside options, outside options, commitment tactics, and incomplete information. We determine the subgame perfect equilibria of models of complete information and sequential equilibria of models of incomplete information.

The most important results of the work are Nash bargaining solution and Rubinstein’s solution to an infinite horizon model of alternating offers. Nash bargaining solution has been extremely important for the development of theoretical research on bargaining, since it is the first systematic study of bargaining situations and has had a significant impact on all later research. This solution is also closely connected to strategic models, as certain limits of solutions of several strategic models are given by Nash solution. This interplay between strategic and axiomatic models is of considerable importance: these models provide information about applicability and limitations of different models and one methods helps to understand the other. Another key result in the thesis is deriving Rubinstein’s solution to an infinite horizon model of the game of alternating offers. This result is also of considerable importance, since this proof involves first determination of subgame perfect equilibrium of an infinite horizon model. Similar arguments have been applied to solve a large number of different models, some of which we also consider in the thesis.

The thesis concentrates on theoretical models of bargaining. We have chosen to deal with elementary models, with an intention to provide clear analysis of these models, instead of general or complex models. In particular, we have chosen the models such that each one of them illustrates some particular element in bargaining situations. This means that all the models treated in the thesis can be generalized, and many interesting models can be generated by combining elements from the models studied. We present some applications of bargaining situations in economics, but the studied models can be applied to a much larger variety of economics problems.

We use axiomatic and strategic models to study bargaining situations. Axiomatic method is very general as it does not deal with any particular bargaining process. Instead, these models concentrate solely on the outcome of a bargaining situation. A weakness with axiomatic models is that it might be difficult to evaluate how accurately the assumptions made describe some particular bargaining process. In the thesis, we concentrate mostly on Nash bargaining solution and its properties. Strategic models studied in the thesis include the game of alternating offers and several variations of this game. The main purpose of these variations is to describe what kind of effects different factors present in bargaining situations have on bargaining. The models studied deal with such factors as uncertainty, inside options, outside options, commitment tactics, and incomplete information. We determine the subgame perfect equilibria of models of complete information and sequential equilibria of models of incomplete information.

The most important results of the work are Nash bargaining solution and Rubinstein’s solution to an infinite horizon model of alternating offers. Nash bargaining solution has been extremely important for the development of theoretical research on bargaining, since it is the first systematic study of bargaining situations and has had a significant impact on all later research. This solution is also closely connected to strategic models, as certain limits of solutions of several strategic models are given by Nash solution. This interplay between strategic and axiomatic models is of considerable importance: these models provide information about applicability and limitations of different models and one methods helps to understand the other. Another key result in the thesis is deriving Rubinstein’s solution to an infinite horizon model of the game of alternating offers. This result is also of considerable importance, since this proof involves first determination of subgame perfect equilibrium of an infinite horizon model. Similar arguments have been applied to solve a large number of different models, some of which we also consider in the thesis.

The thesis concentrates on theoretical models of bargaining. We have chosen to deal with elementary models, with an intention to provide clear analysis of these models, instead of general or complex models. In particular, we have chosen the models such that each one of them illustrates some particular element in bargaining situations. This means that all the models treated in the thesis can be generalized, and many interesting models can be generated by combining elements from the models studied. We present some applications of bargaining situations in economics, but the studied models can be applied to a much larger variety of economics problems.

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