MEGHÍVÓ
Szeretettel meghívjuk Pintér Miklós előadására
az Adatelemzés és Optimalizálás Szeminárium keretében
2025. április 15-én kedden 12:00 órai kezdettel
Az előadás élőben lesz megtartva a H306 teremben.

Előadó:  Pintér Miklós, Corvinus Egyetem

Az előadás címe:  Functional equations in cooperative game theory

Absztrakt: The talk aims to provide a concise introduction to the (potential)
applications of functional equations and inequalities in the theory of
transferable utility (TU) cooperative games (von Neumann and
Morgenstern, 1944). The class of TU-games is a collection of
finite-dimensional vector spaces, and the so-called solutions defined on
this class (or a subclass) of TU-games. A solution is a set-valued
mapping that assigns a ”solution”—a subset of a finite-dimensional
vector space—to each game. In particular, a value is a single-valued
solution. The most well-known solutions include the Shapley value
(Shapley, 1953), the core (Shapley, 1955; Gillies, 1959), and the
nucleolus (Schmeidler, 1969), among others.

To argue for or against a particular solution, the solution is
characterized using so-called axioms. A characterization of a solution
has the form: A FUNCTION defined on a specific SUBCLASS of TU-games is
the SOLUTION if and only if it satisfies a given set of AXIOMS. In such
cases, we say the AXIOMS characterize the SOLUTION on the SUBCLASS.
These axioms take the form of functional equations and inequalities. In
other words, a characterization result asserts that a set of functional
equations and inequalities has a particular unique solution over a given
domain.
For example, the Shapley value, which is a linear function, has numerous
axiomatizations on various subclasses of TU-games. While (almost) each
axiomatization is both interesting and significant, only three are
considered ”fundamentally” distinct: the one employing the linearity
axiom (Shapley, 1953), the one without the linearity axiom (Young,
1985), and a recursive one (Hamiache, 2001).

Minden érdeklődőt szeretettel várunk!

Kovács Edith, Burai Pál