On the gamma-core of asymmetric aggregative games

Stamatopoulos, Giorgos (2018): On the gamma-core of asymmetric aggregative games.

Abstract

This paper analyzes the core of cooperative games generated by asymmetric aggregative normal-form games, i.e., games where the payoff of each player depends on his strategy and the sum of the strategies of all players. We assume that each coalition calculates its worth presuming that the outside players stand alone and select individually optimal strategies (Chander & Tulkens 1997). We show that under some mild monotonicity assumptions on payoffs, the resulting cooperative game is balanced, i.e. it has a non-empty gamma-core. Our paper thus offers an existence result for a core notion that is considered quite often in the theory and applications of cooperative games with externalities.

• Item Type: MPRA Paper
• Language: English
• Keywords: cooperative game; aggregative game; balancedness; core
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

References

1. Aumann R. (1959) Acceptable points in general cooperative n-person games, in: Tucker, Luce (eds.), Contributions to the theory of games IV, Annals of Mathematics Studies 40, Princeton University Press, Princeton.

2. Chander P., H. Tulkens (1997) The core of an economy with multilateral environmental externalities, International Journal of Game Theory 26, 379-401.

3. Chander P. (2007) The gamma-core and coalition formation, International Journal of Game Theory 35, 539-556.

4. Chander P., M. Wooders (2012) Subgame-perfect cooperation in an extensive game, Working Paper.

5. Corchon L. C. (1994) Comparative statics for aggregative games: the strong concavity case, Mathematical Social Sciences 28, 151-165.

6. Currarini S., M. Marini (2003) A sequential approach to the characteristic function and the core in games with externalities, Sertel, M., Kara, A.(eds.), Advances in Economic Design. Springer Verlag, Berlin.

7. Hart S., M. Kurz (1983) Endogenous formation of coalitions, Econometrica 51, 1047-1064.

8. Helm C. (2001) On the existence of a cooperative solution for a cooperative game with externalities, International Journal of Game Theory 30, 141-146.

9. Huang C.Y., T. Sjostrom (2003) Consistent solutions for cooperative games with externalities, Games and Economic Behavior 43, 196-213.

10. Koczy L. (2007) A recursive core for partition function form games, Theory and Decision 63, 41-51.

11. Lardon A. (2012) The $\gamma$-core in Cournot oligopoly TU-games with capacity constraints, Theory and Decision 72, 387-411.

12. Lardon A. (2014) Convexity of Bertrand oligopoly TU-games with differentiated products, Working paper.

13. Lardon A. (2017) Endogenous interval games in oligopolies and the cores, Annals of Operations Research 248, 345-363.

14. Nax, H.H. (2014) A note on the core of TU-cooperative games with multiple membership externalities, Games 5, 191-203.

15. Stamatopoulos G. (2015) The core of aggregative cooperative games with externalities, The B.E. Journal of Theoretical Economics 16, 389-410.

16. Uyanik M. (2015) On the nonemptiness of the $\alpha$-core of discontinuous games: Transferable and nontransferable utilities, Journal of Economic Theory 158, 213-231.

17. Zhao J. (1999) The existence of TU $\alpha$-core in normal form games, International Journal of Game Theory 28, 25-34.