Question

In: Economics

Suppose a single good is being sold in a sealed-bid auction (no bidder can observe the...

Suppose a single good is being sold in a sealed-bid auction (no bidder can observe the bids of other bidders). The rules of the auction are such that the person who bids the highest value for the good wins, but the winner only has to pay the value of the second-highest bid submitted.

Assume that there are three people bidding for the good (?=1,2,3), and each values the good according to:

  • ?1=$12
  • ?2=$16
  • ?3=$3

where ??v_i is the maximum willingness to pay for the good for player ?i.

What is the Nash equilibrium bid for each player? Who will win the auction? How much will the winner pay?

Solutions

Expert Solution

This is the concept of second-price auction.

Nash equilibrium in this model is that every player bids his/her own value. By doing so s/he is at least as better off as any other strategy. This happens because the winner has to pay the second-highest price. So his utility will be positive if he wins. Now, reducing the amount of bid might make him/her lose the auction. Also bidding any price higher than his own value might lead to a negative payoff.

In this game, player 2 will win the auction, as he will bid 16 and it is the maximum bid among three players.

The winner(player 2) will pay $12 as this is second price auction.

Rahul Sunny answered 2 years ago
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