Abstract
Consider an auction or fair division game where every bidder knows his true value of the single object but is only incompletely informed about the true values of his competitors. By imposing the axiom of envy freeness with respect to stated preferences the set of pricing rules is restricted to the prices between the highest and second highest bid. Whereas for auctions one also can satisfy incentive compatibility, the same is not true for fair division games. We analyse and compare the different pricing rules, partly incentive compatible and partly not, by deriving the optimal bidding strategies. By comparing the payoff expectations induced by the various pricing rules we can prove directly a special equivalence statement saying that expected payoffs do not depend on the pricing rule. It is interesting that in fair division games equivalence of pricing rules is only valid if information is sufficiently incomplete.
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