p.595

Straightforwardness of Game Forms with Lotteries as Outcomes

Allan Gibbard

Abstract

Where alternatives, players, and strategies for each player are finitely many, a game form assigns a lottery over alternatives to each configuration of players' strategies. It is straightforward iff it guarantees that each player, whatever his utilities, will have a dominant strategy. It is unilateral iff only one player can influence the outcome, and duple if it restricts the final outcome to a fixed pair of alternatives. Any straightforward game form, it is shown, is, on a domain which gives each player a dominant strategy for each utility scale, a probability mixture of game forms, each unilateral or duple.