Prophet Inequality and Online Auctions

Years and Authors of Summarized Original Work

• 2007; Hajiaghayi, Kleinberg, Sandholm

• 2012; Kleinberg, Weinberg

• 2012; Alaei, Hajiaghayi, Liaghat

• 2015; Esfandiari, Hajiaghayi, Liaghat, Monemizadeh

Problem Definition

The topic of prophet inequality has been studied in optimal stopping theory since the 1970s [7, 9, 10] and more recently in computer science [1, 3, 6, 8]. In the prophet inequality setting, given (not necessary identical) independent distributions D₁, …, D _n , a sequence of random variables x₁, …, x _n where x _i is drawn from D _i , a collection M of feasible subsets of {1, …, n}, an onlooker has to choose from the succession of these values, where x _i is revealed to us at time step i. The onlooker starts with an empty set S = ϕ. Upon the arrival of a value x _i , the onlooker can choose to either add x _i to the set S or discard it permanently. After the arrival of all values, the indices of values in S should form a feasible set in M. The revenue of the onlooker is the total...