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Revenue equivalence - Wikipedia

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Revenue equivalence is a concept in auction theory that states that given certain conditions, any mechanism that results in the same outcomes (i.e. allocates items to the same bidders) also has the same expected revenue. There is a set 𝑋 of possible outcomes. There are 𝑛 agents which have different valuations for each outcome. The valuation of agent 𝑖 (also called its "type") is represented as a function: which expresses the value it has for each alternative, in monetary terms. The agents have quasilinear utility functions; this means that, if the outcome is 𝑥 and in addition the agent receives a payment 𝑝 𝑖 (positive or negative), then the total utility of agent 𝑖 is: The vector of all value-functions is denoted by 𝑣 . For every agent 𝑖 , the vector of all value-functions of the other agents is denoted by 𝑣 − 𝑖 . So 𝑣 ≡ ( 𝑣 𝑖 , 𝑣 − 𝑖 ) . A mechanism is a pair of functions: The agents' types are independent identically-distributed random variables. Thus,

Revenue equivalence - Wikipedia Jump to content From Wikipedia, the free encyclopedia Concept in auction theory Part of a series on Auctions Christie's</a>, circa 1808.","txt":"Auction Room, Christie's, circa 1808."}]]}'> Types All-pay Chinese Bidding fee Dollar Amsterdam Anglo-Dutch Barter double Best/not best Brazilian Calcutta Candle Click-box bidding Combinatorial Common value Deferred-acceptance Discriminatory price Double Dutch English Forward French Generalized first-price Generalized second-price Japanese Knapsack Multi-attribute Multiunit No-reserve Rank Reverse Scottish Sealed first-

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