Bargaining Set Solution Concepts in Dynamic Cooperative Games

Hellman, Ziv (2008): Bargaining Set Solution Concepts in Dynamic Cooperative Games.

Abstract

This paper is concerned with the question of defining the bargaining set, a cooperative game solution, when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face (finite or infinite) sequences of exogenously specified TU-games and receive sequences of imputations against those static cooperative games in each time period. Two alternative definitions of what a ‘sequence of coalitions’ means in such a context are considered, in respect to which the concept of a dynamic game bargaining set may be defined, and existence and non-existence results are studied. A solution concept we term ‘subgame-stable bargaining set sequences’ is also defined, and sufficient conditions are given for the non-emptiness of subgame-stable solutions in the case of a finite number of time periods.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cooperative game; Repeated game; Bargaining set
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

Becker, R., Chakrabarti, S, (1995), ‘The Recursive Core’ Econometrica, 63:401 - 423.

Berden, C. (2007) ‘The Role of Individual Intertemporal Transfers in Dynamic TU-Games’, Unpublished Mimeo.

Gale, D. (1978): ‘The Core of a Monetary Economy without Trust’, Journal of Economic Theory, 19:456-491.

Kranich, L., A. Perea, and H. Peters (2001): ‘Dynamic Cooperative Games’, Unpublished Mimeo.

Kranich, L., A. Perea, and H. Peters (2005): ‘Core Concepts for Dynamic TU Games’ International Game Theory Review, 7:43 - 61.

Oviedo, J. (2000) ‘The Core of a Repeated n-Person Cooperative Game’, European Journal of Operational Research, 127:519 - 524.

Peleg, B. (1963) ‘Bargaining sets of cooperative games without side payments’, Israel Journal of Mathematics, 1:197 - 200.

Predtetchinski, A. (2007): ‘The Strong Sequential Core for Dynamic Cooperative Games,’ Games and Economic Behavior, forthcoming.

Predtetchinski, A., P.J.J. Herings and H. Peters (2004): ‘The Strong Sequential Core in a Dynamic Exchange Economy,’ Economic Theory 24: 147 - 162.

Predtetchinski, A., P.J.J. Herings and H. Peters (2002): ‘The Strong Sequential Core for Two-period Economies,’ Journal of Mathematical Economics 38: 465 - 482.

Predtetchinski, A., P.J.J. Herings and A. Perea (2006): ‘The Weak Sequential Core for Two-period Economies,’ International Journal of Game Theory 34: 55 - 65.