A look back at the core of games in characteristic function form: some new axiomatization results

In this paper we provide three new results axiomatizing the core of games in characteristic function form (not necessarily having transferable utility) obeying an innocuous condition (that the set of individually rational pay-off vectors is bounded). One novelty of this exercise is that our domain is the {\em entire} class of such games: i.e., restrictions like "non-levelness" or "balancedness" are not required

Single NTU-value solutions

We propose a variation of the Hart and Mas-Colell non-cooperative bargaining model for n-person games in coalitional form. This strategic game implements, in the limit, a new NTU-value for the class of monotonic games. This value coincides with the Maschler and Owen value for hyperplane games, and with the Shapley value for TU games. The main characteristic of this proposal is that always select a unique payoff allocation. This value can also be considered as an extension of the Nash bargaining solution. Variations of this model yield extensions of the Discrete Raiffa solution, and the Kalai-Smorodinsky solution.Shapley value; NTU-value solutions; Nash Bargaining; Raiffa solution; Kali-Smorodinsky solution.

Game theory

game theory

Consistencia en juegos sin utilidad transferible

Programa de Doctorado en Administración y Dirección de EmpresasEsta memoria se centra en el análisis axiomático de algunas de las soluciones para juegos sin utilidad transferibles más referenciadas en la literatura, como son la solución de Harsanyi, la solución Shapley NTU y las soluciones igualitarias. En concreto se caracterizan con diferentes sistemas de axiomas que incluyen el Axioma de Consistencia, determinando dichas soluciones como soluciones consistentes.Universidad Pablo de Olavide. Departamento de Economía, Métodos Cuantitativos e Historia Económic

Duality for General TU-games Redefined

Aslan F, Duman P, Trockel W. Duality for General TU-games Redefined. Center for Mathematical Economics Working Papers. Vol 620. Bielefeld: Center for Mathematical Economics; 2019.We criticize some conceptual weaknesses in the recent literature on coalitional TUgames and propose, based on our critics, a new definition of dual TU-games that coincides with the one in the literature on the class of super-additive games. We justify our new definition in four alternative ways: 1. Via an adequate definition of efficient payoff vectors. 2. Via a modification of the Bondareva-Shapley duality. 3. Via an explicit consideration of \coalition building". 4. Via associating general TU-games to coalition-production economies. Rather than imputations, we base our analysis on a modification of aspirations

Potential Games and Interactive Decisions with Multiple Criteria.

Abstract: Game theory is a mathematical theory for analyzing strategic interaction between decision makers. This thesis covers two game-theoretic topics. The first part of this thesis deals with potential games: noncooperative games in which the information about the goals of the separate players that is required to determine equilibria, can be aggregated into a single function. The structure of different types of potential games is investigated. Congestion problems and the financing of public goods through voluntary contributions are studied in this framework. The second part of the thesis abandons the common assumption that each player is guided by a single goal. It takes into account players who are guided by several, possibly conflicting, objective functions.

Enacting Inquiry Learning in Mathematics through History

International audienceWe explain how history of mathematics can function as a means for enacting inquiry learning activities in mathematics as a scientific subject. It will be discussed how students develop informed conception about i) the epistemology of mathematics, ii) of how mathematicians produce mathematical knowledge, and iii) what kind of questions that drive mathematical research. We give examples from the mathematics education at Roskilde University and we show how (teacher) students from this program are themselves capable of using history to establish inquiry learning environments in mathematics in high school. The realization is argued for in the context of an explicit-reflective framework in the sense of Abd-El-Khalick (2013) and his work in science education