March 26 (Thursday) 10:00-11:00, room C.510 (new building, 5th floor)
Zsófia Dornai (ELTE Centre for Economic and Regional Studies, Budapest)
TU-games with utility functions: the u-τ-value
TU-games with utility functions are generalizations of TU-games. The idea arises from the aim to develop a common framework that unifies several variants of the prenucleolus, including the per capita and the q‑weighted prenucleolus. We achieve this by applying a utility function to the excesses, and then using these u-excesses to compute the u-prenucleolus. This modification not only generalizes the prenucleolus but also enables us to define the u-core, u-least-core, u-anti-prenucleolus, u-anti-core, and the u-balancedness of a game.
A natural question arises: how do utility functions affect other solution concepts of the game, especially those that do not explicitly rely on excesses? Tijs’s τ-value is defined using the utopia payoff vector and the minimal right payoff vector, and it is not immediately clear where excess-related notions enter in this context. We define the u-utopia payoff vector, the u-minimal right payoff vector, and, finally, the u-τ-value. Using the same logic, we define the u-core-cover and show that it has analogous relationships with the u-core and the u-τ-value as the core-cover has with the core and the τ-value in the classical setting.
We also highlight that, in TU-games with utility functions, certain properties of solution concepts must be reconsidered. In particular, we introduce u-rationality and the u-null-player property. This study broadens the theory of TU-games with utility functions and provides deeper insight into what happens when excesses are interpreted through reference dependence. It clarifies how having zero excess serves as an acceptance threshold when the coalition value functions as the reference point for being content across a wide range of solution concepts and their desired properties.
The talk is based on joint work with Miklós Pintér.