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Consider this all-pay auction in which it is common knowledge that Bidder 1 has a valuation of 2 and Bidder 2 has a valuation of

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Consider this all-pay auction in which it is common knowledge that Bidder 1 has a valuation of 2 and Bidder 2 has a valuation of 3. The bids must be whole numbers and Bidder 2 wins in the event of tie. Which of the following are Nash equilibria? Bidder 2 0 1 2 3 4 0, 3 0, 2 0, 1 0, 0 0, -1 1, 0 -1, 2 -1, 1 -1, 0 -1, -1 Bidder 1 2 0, 0 0, - 1 -2, 1 -2, 0 -2, -1 3 -1, 0 -1, -1 -1, -2 -3, 0 -3, - 1 -2, 0 -2, - 1 -2, -2 -2, -3 -4, -1 Note: The notation [0], [1], etc. denotes the pure strategies in which the bidder bids 0,1, etc. Mixed strategies are represented by weighted averages of the pure strategies, e.g the mixed strategy in which a bidder bids 1 with a probability of 1/4 and 4 with a probability of 3/4 is written as 1/4 [1] + 3/4 [4]. O (2/3 [0] + 1/3 [1], 1/2 [0] + 1/2 [1]) O ([0], [on) O ([1], [0]) O (5/12 [0] + 1/3 [1] + 1/4 [2], 1/2 [0] + 1/2 [1]) O ([0], [1]) None of these options O ([0], [3])

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