Siegfried Berninghaus

Evolution, interaction, and Nash equilibria

Abstract The paper analyzes the evolution of strategy profiles in a population of finitely many players where each player interacts only with a subset of the population. Conditions are given which guarantee that the strategy profiles converge globally resp. locally to an equilibrium state. The results, derived by using methods from the theory of iterated discrete functions, are illustrated by several examples, e.g. coordination and hawk-dove games.

The role of the target saving motive in guest worker migration A theoretical study

The return migration decision is modeled as a decision problem under uncertainty. In each period the guest worker has to decide whether to return home and to invest the capital in a small business or to stay in the host country and earn money as a worker for at least one further period. It is shown that the properties of the optimal saving and return migration strategies can be elegantly derived by formulating the migrants decision problem as a Stopped Markovian Decision Process. This framework provides a lot of interesting testable hypotheses concerning remigration behaviour of a target saver.

Temporary vs. permanent migration A decision theoretical approach

The decision problem of the guest worker as a target saver is considered. He plans to accumulate capital in the host country for investment in the home country after return migration. As the worker is supposed to be incompletely informed about the economic variables in the host country he might prolong his stay unexpectedly provided the economic conditions in the host country are unfavourable. Explicit conditions for the economic variables are given such that temporary migration turns into permanent migration.

A temporary equilibrium model for international migration.

This paper is concerned with the existence of temporary equilibria of migration with an overlapping generation structure and analyzes some of its properties. In the first part of the paper sufficient conditions for the existence of a temporary equilibrium of migration (in a given period) are given. In the second part some interesting properties of migration equilibria are analyzed. In particular the effects of differing degrees of information of the individuals on migration equilibria are investigated. Furthermore, it is shown that incomplete information alone suffices to induce migration flows even between countries that can be regarded as “identical” from an economic point of view.

A Microeconomic Model of Migration

In the first part of the paper we give a consistent formal model of migration decision making under incomplete information. It is shown that the migration problem can be regarded as a particular problem in the theory of stochastic dynamic programming. We discuss the Gittins index method as a helpful algorithm in deriving optimal migration decisions. In the second part of the paper we apply our theoretical results to two empirically relevant phenomena. We explain the “attractiveness of city lights” in rural/urban migration as a result of optimal decision making under incomplete information by using arguments that are different from Todaro’s explanation. Further, we give an explanation for the high correlation between inbound and outbound migration that is often observed in particular regions in developing countries.

Migration as a Sequential Decision Problem under Uncertainty

The main subject of the present chapter is the presentation of a logically consistent model for individual migration decision-making. More precisely, we consider the problem of a potential migrant who has the opportunity to move into one of N countries, indexed by j for at least one period. It is natural to assume that the migrant is incompletely informed about the pecuniary and non-pecuniary variables in the countries in question. As the migrant might encounter unexpectedly unfavourable values of these variables, he might decide to leave the country he tried out for at least one period and either move back into his home country or move to a different country. That is, at each decision time point the migrant must be able to revise his decision in face of incoming information.

Temporary vs. Permanent Migration

The following phenomenon has been strongly supported by empirical observations (e.g. Konig (1986), Piore (1979)): a migrant typically is planning only a temporary stay in the host country (3–6 years). But actually he postpones the date of return such that remi-gration becomes less probable after some time. In other words, temporary migration has turned into permanent migration. As well-known empirical examples for this behaviour we can cite here guest-worker migration in Germany (see Konig (1986)) or immigration from Middle- and South-America into the southern part of the United States.

Some Remarks Concerning Econometric Modelling of Informational Aspects in International Migration

It is the purpose of the present chapter to demonstrate how the framework of sequential decision making can be used to specify econometric models which are intended to measure some of the informational aspects in international migration by empirical observations.

Temporary Equilibria of Migration

In contrast to the contents of the previous chapters we will now analyse migration problems in an equilibrium framework. It is intuitively clear that all economic implications concerning aggregate migration behaviour should be based on an underlying equilibrium concept. For let us consider, as a thought experiment, a set of potential migrants who are attracted by a particular country. After a lot of them moved into this country the economic conditions there might change considerably and this might induce the remaining potential migrants no longer to go to this country. To deal with this problem adequately one has to take account not only of migration supply into a country but also of migration demand in a country. Both determine the economic conditions and aggregate immigration streams simultaneously in an equilibrium.