Time-Consistent Solutions for Two-Stage Network Games with Pairwise Interactions
- 10 Downloads
In the paper, we consider a cooperative version of a network game with pairwise interactions in which connected players play bimatrix games. For a particular type of a network, a simplified formula for the Shapley value based on a constructed characteristic function is derived. We then show the time inconsistency of classical cooperative solutions — the Shapley value and the core. The findings are applied to two important classes of bimatrix games: prisoner’s dilemma and a coordination game.
KeywordsCooperation Network formation The Shapley value The core Time consistency Prisoner’s dilemma Coordination game
The authors thank two anonymous referees for their comments that have helped in the improvement of the paper. This research was supported by the Russian Science Foundation (grant No. 17-11-01079).
- 2.Aumann R, Myerson R (1988) Endogenous formation of links between players and coalitions: An application of the Shapley value. In: Roth A (ed) The Shapley value: Essays in Honor of Lloyd S. Shapley. Cambridge University Press, Cambridge, pp 175–191Google Scholar
- 4.Bulgakova MA, Petrosyan LA (2016) About strongly time-consistency of core in the network game with pairwise interactions. In: Proceedings of 2016 international conference “Stability and Oscillations of Nonlinear Control Systems”, pp 157–160Google Scholar
- 5.Challita U, Saad W (2017) Network formation in the sky: Unmanned aerial vehicles for multi-hop wireless backhauling. In: Proceedings of the IEEE global communications conference (GLOBECOM), Singapore, 4–8Google Scholar
- 18.Shapley L (1953) A value for n-person games. In: Kuhn H W, Tucker A W (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307–317Google Scholar