We study the query complexity of approximate notions of Nash equilibrium in games with large number of players n and constant number of actions m. Our main result states that even for constant {\epsilon}, the query complexity of {\epsilon}-well supported Nash equilibrium is exponential in n.

We consider the situation that two players have cardinal preferences over a finite set of alternatives. These preferences are common knowledge to the players, and they engage in bargaining to choose an alternative. In this they are assisted by an arbitrator (a mechanism) who does not know the...