Can you find an equilibrium at which every buyer i wins, Game Theory

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Can you find an equilibrium at which every buyer i wins

Consider a sealed-bid second-price auction with n buyers whose private values are independent and uniformly distributed over [0, 1].

Find an asymmetric equilibrium at which every buyer wins with probability 1/n .

Can you find an equilibrium at which every buyer i wins with probability αi, for any collection of nonnegative numbers α₁, α₂,...,α_n whose sum is 1?

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Game Theory: Can you find an equilibrium at which every buyer i wins

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