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Most contributions in axiomatic bargaining are phrased in the space of utilities. This comes in sharp contrast with standards in most other branches of economic theory. The present paper shows how Nash's original axiomatic system can be rephrased in a natural class of economic environments with lotteries, and how his uniqueness result can be recovered, provided one completes the system with a property of independence with respect to preferences over unfeasible alternatives. A similar result can be derived for the Kalai-Smorodinsky solution if and only if bargaining may involve multiple goods.
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