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Page 18
The notion of a strategic game encompasses situations much more complex than those described in the last five
examples. The following are representatives of three families of games that have been studied extensively:
auctions, games of timing, and location games.
• Example 18.1
(
An auction
) An object is to be assigned to a player in the set {1,.
..,
n
} in exchange for a payment. Player
i
's
valuation of the object is
v
i
, and
v
1
> v
2
> .
.. > v
n
> 0. The mechanism used to assign the object is a (sealedbid)
auction: the players simultaneously submit bids (nonnegative numbers), and the object is given to the player with
the lowest index among those who submit the highest bid, in exchange for a payment.
In
a first price
auction the payment that the winner makes is the price that he bids.
• Exercise 18.2.
Formulate a first price auction as a strategic game and analyze its Nash equilibria. In particular, show that in all
equilibria player I obtains the object.
In a
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 Spring '10
 VINH

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