  Richman games are zero-sum games, where in each turn players bid in order to
determine who will play next [Lazarus et al.'99]. We extend the theory to
impartial general-sum two player games called \emph{bidding games}, showing the
existence of pure subgame-perfect equilibria (PSPE). In particular, we show
that PSPEs form a semilattice, with a unique and natural \emph{Bottom
Equilibrium}.
  Our main result shows that if only two actions available to the players in
each node, then the Bottom Equilibrium has additional properties: (a) utilities
are monotone in budget; (b) every outcome is Pareto-efficient; and (c) any
Pareto-efficient outcome is attained for some budget.
  In the context of combinatorial bargaining, we show that a player with a
fraction of X% of the total budget prefers her allocation to X% of the possible
allocations. In addition, we provide a polynomial-time algorithm to compute the
Bottom Equilibrium of a binary bidding game.
