Good neighbors are hard to find: computational complexity of network formation
Résumé
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 player is NP-hard. The problem of deciding if a given strategy profile is a Nash equilibrium is investigated as well.