  The solution to a Nash or a nonsymmetric bargaining game is obtained by
maximizing a concave function over a convex set, i.e., it is the solution to a
convex program. We show that each 2-player game whose convex program has linear
constraints, admits a rational solution and such a solution can be found in
polynomial time using only an LP solver. If in addition, the game is succinct,
i.e., the coefficients in its convex program are ``small'', then its solution
can be found in strongly polynomial time. We also give a non-succinct linear
game whose solution can be found in strongly polynomial time.
