1.suppose that preferences are strongly convex so that the Walrasian correspondence is single-valued,that is ,it is a social function.Is it strategy-proof?if the answer is positive,then give a proof.if the answer is negative,then give a counterexample.
2.Is the uniform rule strategy-proof?if the answer is positive,then give a proof.if the answer is negative,then give a counterexample.
3.Show that the uniform rule satisfies Pareto efficiency and no-envy,if utility function are single-peaked.


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