Time-Consistent Solutions for Two-Stage Network Games with Pairwise Interactions
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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).
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