Question

# Suppose that we have the following auction scheme. There are two bidders, and an item to...

Suppose that we have the following auction scheme. There are two bidders, and an item to be allocated to them. Each bidder submits a bid. The highest bidder gets the good, but both bidders pay their bids. Consider the case in which bidder 1 values the item at 3, while bidder 2 values the item at 5; this is commonly known. Each bidder can only submit one of three bids: 0, 1 or 2. If player i bids more than player j, player i gets the good and both pay. If both players bid the same amount, each gets the item with probability 0.5, but again, both pay. (a) Write down the game in matrix form. Which strategies survive IESDS? (b) Find the NE of the game.

#### Homework Answers

Answer #1

a.Both Player i and Player j should use strictly dominating strategy to Survive IESDS.

b.If two players i and j choose strategies A and B, (A, B) is a Nash equilibrium if i has no other strategy available that does better than A at maximizing her payoff in response to j choosing B, and j has no other strategy available that does better than B at maximizing his payoff in response to i choosing A.

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