What is it about?
When scientists recommend complex alternatives, the choice is hardly easy. The axiomatic approach explains complex concepts in simple terms. Instead of dealing with a difficult formula, we try to understand how solutions deal with simple problems. Ideally, a handful of such choices lead to a single possible way to solve games. When there are different ways to solve games, of course these have different simple choices. This chapter gives an account of these basic principles that have been used to explain solutions. Note that we are staying in the realm of coalitional games with side effects, known as partition function form games.
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Why is it important?
As game theory is more and more driven by applications it becomes a common phenomenon that concepts are used by non-theorists. These people must make decisions about alternative approaches and basic properties known as axioms are their best friend in that.
Perspectives
While the axiomatic approach is very important and works well for some concepts, like the Shapley-value, when the differences between concepts are small, so are the differences between their corresponding axioms. While one concept is explained by simple properties, the principles behind another one may be far more complex and correspondingly less natural. This may be a reason for going for the first one, although the second may have an even more elegant, but so far not known axiomatisation.
Dr László Á Kóczy
Hungarian Academy of Sciences, Centre for Economics and Regional Studies
Read the Original
This page is a summary of: Axioms, January 2018, Springer Science + Business Media,
DOI: 10.1007/978-3-319-69841-0_8.
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