X hits on this document

61 views

0 shares

35 / 38

# Distinguishing between equilibria

For each player i the action vi weakly dominates all her other actions

That is: player i can do no better than bid vi no matter what the other players bid.

## Argument:

• If the highest of the other players’ bids is at least vi, then

• if player i bids vi her payoff is 0

• if player i bids x = vi her payoff is either zero or negative.

• If the highest of the other players’ bids is b < vi, then

• if player i bids vi her payoff is vi b (she obtains the object at the price b)

• if player i submits some other bid then she either obtains the good and gets the same payoff, or does not obtain the good and gets the payoff of zero.

# Summary

Second-price auction has many Nash equilibria, but the equilibrium (b1, . . . , bn) = (v1, . . . , vn) is the only one in which every players’ action weakly dominates all her other actions.

35

 Document views 61 Page views 61 Page last viewed Tue Oct 25 03:24:39 UTC 2016 Pages 38 Paragraphs 543 Words 4259