Good neighbors are hard to find: computational complexity of network formation

@article{Baron2008GoodNA,
  title={Good neighbors are hard to find: computational complexity of network formation},
  author={Richard Baron and Jacques Durieu and Hans Haller and Rahul Savani and Philippe Solal},
  journal={Review of Economic Design},
  year={2008},
  volume={12},
  pages={1-19}
}
We investigate the computational complexity of several decision problems in a simple strategic game of network formation. We find that deciding if a player has a strategy that guarantees him a certain payoff against a given strategy profile of the other players is an NP-complete problem. Deciding if there exists a strategy profile that guarantees a certain aggregate payoff is also NP-complete. Deciding if there is a Nash equilibrium in pure strategies which guarantees a certain payoff to each… 

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