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III.2.2 Migration of Medical Doctors: A Win-Win Framework
First introduced by Aumann (1959, 1960, 1961, 1981, 1985a), cooperative games with
transferable utility has seen many economic applications (see for example, Aumann &
hart, 2007). In the following, we opt for a cooperative game theoretic model with
transferable utility and side payments, as in Sherali & Qing (2000) and Kaneko and
Wooders (2004), for example. An agreement on the distribution of payoffs generates an
accord that is acceptable to all parties involved. Cooperation is beneficial to all.
In what follows, we draw on a framework with “utility transfer” and “side payments” to
formalize the relationship between a sending and a receiving country. The intuition
behind this approach is that a coalition can be formed based on an agreement between for
example, Morocco and one country from the European Union, or between Morocco and
the European Union. This agreement would set the terms of trade between the two
countries in defining the checks and balances for a free circulation of medical doctors.
We develop a framework for collaboration based on the following guiding principles: (i)
Cooperation between sending and receiving countries under the umbrella of the Global
Health system can increase global performance; however (ii) diverting resources for
cooperation may degrade individual performance, that’s why (iii) a natural approach is to
somehow compensate sending countries for their cooperation.
Cooperation in what follows is a coordinated effort between a receiving and a sending
country in order to promote the benefit from cooperation in the medical sector to both
parties in a coalition. The goal of cooperation framework is to form a coalition that will
govern the movement of doctors within the cooperation space under the umbrella of the
global health system. In this framework, we will adopt and heavily borrow from the
structure of a game with transferable utility and side payments described in Kaneko and
Wooders (2004.)
In this model, assumptions are adopted and are related to:
• Logistics such as how countries actually coordinate payoffs and establish checks
and balances to enforce binding agreements will not be taken into consideration.
• Complete information symmetry, in other words, each country participating in
this cooperative game has complete information of the characteristic payoff
functions of the game.
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