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A universal type space of interdependent expected utility preference types is constructed from higher-order preference hierarchies describing an agent's (unconditional) preferences over a lottery space; the agent's preference over Anscombe-Aumann acts conditional on the unconditional preferences; and so on. Two types are said to be strategically indistinguishable if they have an equilibrium action in common in any mechanism that they play. The authors show that two types are strategically indistinguishable if and only if they have the same preference hierarchy. They examine how this result extends to alternative solution concepts and strategic relations between types.
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