On the Foundations of Nash Equilibrium

It is an old ida in game theory that the justification of Nash equilibrium as a prediction of actual play in a game is that each player by imagining himself in the positions of his opponents will be able to figure out what these other players will play, and consequently the player himself will play a best reply to the opponents' actual choices. Since this is true for every single player the collection of strategies played by the players is a Nash equilibrium. We formalize this idea avoiding making an unmotivated uniqueness assumption implicit in it, and expressing explicitly - in plain words - the kind of individual considerations players are assumed to make. As a result we obtain support for Nash equilibrium strategies as the only reasonable conjectures.