Consider a very simple online auction system that works as follows. There are n bidding agents; agent has a bid b , which is a positive natural number. We will assume that all bids b are distinct from one another. The bidding agents appear in an order chosen uniformly at random, each proposes its bid bi in turn, and at all times the system maintains a variable b* equal to the highest bid seen so far. (Initially b* is set to 0.)
What is the expected number of times that b* is updated when this process is executed, as a function of the parameters in the problem?
Example. Suppose b1 = 20, b2 = 25, and b3 = 10, and the bidders arrive in the order 1, 3, 2. Then b* is updated for 1 and 2, but not for 3.
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