The authors introduce and analyze 'multistage situations, ' which generalize 'multistage games' (which, in turn, generalize 'repeated games'). One reason for this generalization is to avoid the perhaps unrealistic constraints--inherent to noncooperative games--that the set of strategy tuples must be a Cartesian product of the strategy sets of the players. Another reason is that, in most economic and social activities (e.g., in sequential bargaining without a rigid protocol), the 'rules of the game' are rather amorphous; the procedures are rarely pinned down. Such social environments can, however, be represented as multistage situations and be effectively analyzed through the theory of social situations. Copyright 1996 by The Econometric Society.

Consider an environment with a finite number of alternatives, and agents with private values and quasilinear utility functions. A domain of valuation functions for an agent is a monotonicity domain if every finite-valued monotone randomized allocation rule defined on it is implementable in dominant strategies. We fully characterize the set of all monotonicity domains.