Advanced Cooperative Games 2024

Basic information

・Friday: 8:50-12:00 (November 1,8, 15, 29; December 6, 13, 20)

・First session: November 1

・Classroom: F304

Overview

In this course, we study advanced topics on cooperative games with transferable utility (TU-games), particularly focusing on TU-games with constraints.

We cover the following three topics:

    ・Basic concepts of TU-games: 1 lecture 

    ・ Axiomatic foundation of solutions by monotonicities: 3 lectures

    ・TU-game with constraints: 3 lectures

The half of the course will consist of lectures by the instructor and the other half will consist of presentations by students/participants. Each student must present at least one paper from the following reading list or a related paper. Presenters should discuss the paper in detail, including key points of the proofs.

・Reading list for the course: PDF (This version, October 17, 2024).

  ・「＊」-marked paper will be discussed in lectures. 

  ・To be updated occasionally.

Schedule 

11/1: 

・Lecture 1, The Core and Shapley value: Slide

     Shapley (1953, 1971), Abe and Nakada (2023, SCW)

・Lecture 2, Monotonic solutions (1): Slide

     Shapley (1953), Young (1985), van den Brink, Funaki, and Ju (2013), Casajus and Huetnner (2014),  Casajus (2015),  Abe and Nakada (2017, 2019)

11/8:

・Lecture 3, Monotonic solutions (2): Slide

      Nakada (2024)

・Lecture 4, Monotonic solutions (3): Slide

     Funaki and Koriyama (2024), Fuanki, Koriyama, and Nakada (2024)

11/15:

・Lecture 5, TU-game with constraints (1): Slide

      Myerson (1977), van den Brink, Khmelnitskaya, and van der Laan (2012), Fuanki, Koriyama, and Nakada (2024)

・Lecture 6, TU-game with constraints (2): Slide

     Aumann and Dr`eze (1974), Owen (1977),  Abe and Nakada (2023, GEB)

11/29:

Lecture 7, TU-game with constraints (3): Slide

Gilles, Owen, and van den Brink (1992), van den Brink and Gilles (1996), Abe, Lowing, and Nakada (2024) 

Student presentations

11/29: 

・Kitano: Casajus and Yokote  (2017)

12/6:

・Kaneko: Algaba , van den Brink, and Dietz (2018)

・Goto: Casajus (2018), Shan, Cui, and Lyu (2023)

12/13:

・Kitano: Ui, Kojima, Kajii (2011)

・Goto (cont):  Shan, Cui, and Lyu (2023)

・Nozawa: Algaba, Bilbao, van den Brink  and Jimenez-Losada (2004)

12/20:

・Yoshimura: Yokote and Funaki (2017)

・Nozawa (cont): Algaba, Bilbao, van den Brink  and Jimenez-Losada (2004)