The problem is to determine the appropriate strategies for each player in
terms of how much they should bid, assuming that they want to receive the
maximum payoff, and do not care about the payoff of the other player. It might
be thought that, since there appears to be no dominant strategy, we have to
look for any Nash equilibria. There are then seen to be three of these, (1000, 0),
(500, 500) and (0, 1000). There appears to be no definite conclusion on what
each player should do, since any bid will have some other complementary bid
associated with it in a Nash equilibrium.