False-name Bids

1. “The effect of false-name bids in combinatorial auctions: new fraud in internet auctions” Makoto Yokoo,Yuko Sakurai, and Shigeo Matsubara False-name Bids

2. Outline • What are false-name bids? • Why are false-name bids a problem? • Making an auction false-name-proof • Collusion in general • Conclusion

3. What are false-name bids? • A bidder submits additional bids under other identities • These are binding bids: the bidder pays the cost for the bid and gets the item if it wins. • Easy to do on the Internet • It's easy to get multiple email addresses. • Paper doesn't mention other ways to prove identity on the Internet.

4. What are false-name bids? • Every agent has a set of identities they can use. • Every agent must use at least one identity (i.e. they must submit at least one bid). • Every identity belongs to exactly one agent. • No one can impersonate another agent. • Auctioneer does not know which agent each identity belongs to, or even how many real agents there are. • No agent knows who an identity belongs to, unless it's their own.

5. What are false-name bids? • The auction: • Feasibility: Cannot allocate an item to multiple identities, even if they belong to the same agent. • Budget: The payment to the auctioneer is equal to the total paid by all the identities. • Non-participation: If an identity makes no bids, then it gets no items and pays nothing. • Almost anonymous: The order of identities does not affect the outcome, except if there is a tie. • If two bids are the same, then v(kidi(θ), θidi) + tidi(θ) = v(kidj(θ), θidj)+ tidj(θ) holds.

6. What are false-name bids? • The auction (continued): • The strategy for an agent is the set of the bids of all their identities. • An agent's utility is the sum of their values for all the items their identities win plus the total payments for their identities. • An agent's strategy is dominant if the agent has no reason to change the bids of any of its identities, regardless of the bids of all other identities.

7. Example: We run a combinatorial auction with a VCG mechanism. There are two items and two bidders. They specify their values as a triple: their values for the two items individually, and then their value for the pair. Their values are as follows: Agent 1: (7, 7, 14) Agent 2: (0, 0, 12) Agent 1 wins both items. Cost: 12 – 0 = 12 Why are false-name bids a problem?

8. But what if agent 1 could make a false-name bid? Agent 1b is agent 1's super-secret identity: Agent 1: (7, 0, 7) Agent 2: (0, 0, 12) Agent 1b: (0, 7, 7) Cost to agent 1: 12 – 7 (utility of agent 1b) = 5 Cost to agent 1b: 12 – 7 (utility of agent 1) = 5 Total cost to agent 1 is 10. Why are false-name bids a problem?

9. What we want is a combinatorial auction that's false-name-proof. False-name-proof: “For all bidder i, s∗(θi, φ(i)) = (θi, 0, . . ., 0) is a dominant strategy.” Why are false-name bids a problem?

10. But, “[i]n combinatorial auctions, there exists no false-name-proof auction protocol that satisfies Pareto efficiency.” :( Satisfies Pareto efficiency: The mechanism distributes the items optimally, maximizing social welfare. Why are false-name bids a problem?

11. Making an auction false-name-proof • Want a sufficient condition condition which makes the VCG mechanism false-name-proof. • Surplus function U: • U(B, Y) = maxk∈KB,YΣ(yi, θyi)∈Yv(kyi, θyi) • The value of the optimal allocation of the items in B to the agents in Y • UA(Y) = U(A, Y), where A contains all the items in the auction.

12. Making an auction false-name-proof • UA(·) is concave over bidders if UA(Z ∪ W) − UA(Z) <=UA(Y ∪ W) − UA(Y) for all sets of bidders Y, Z, and W, where Y is a subset of Z.

13. Making an auction false-name-proof • The VCG mechanism is false-name-proof if: • Θ satisfies that UA(·) is concave for every subset of bidders with types in Θ. • Each declared type is in Θ ∪ {0} • Paper does not claim that this is the only sufficient condition. • Paper does not claim that this condition is necessary to be false-name-proof.

14. Making an auction false-name-proof • Gross substitutes condition: If an item j is demanded at price p, then it will still be demanded at price p if the prices of some other items increase. • No proof given that this condition implies concavity.

15. Making an auction false-name-proof • The gross substitutes condition holds in auctions where marginal utility of each item never increases. • This condition is convenient because auctions that satisfy it have Walrasian equilibria: • No agent has reason to change their bids because they cannot afford any better allocation.

16. Making an auction false-name-proof • U is submodular for all set of bidders X ⊆ N if U(B, X) + U(C, X) >=U(B ∪ C, X) + U(B ∩ C, X) for all B ⊆ A and C ⊆ A. • If U is submodular for all set of bidders X ⊆ N, then UAis concave. • In fact, submodularity is both sufficient necessary for concavity.

17. Making an auction false-name-proof U(B, X) + U(C, X) >=U(B ∪ C, X) + U(B ∩ C, X) • Submodularity has nothing to do with the payments in the auction. • It cannot be achieved by changing the formula for determining payments. • To achieve submodularity, the allowed bids must be restricted.

18. Applying submodularity to our example: U(B, X) + U(C, X) >=U(B ∪ C, X) + U(B ∩ C, X) Let B = {item a}, C = {item b} X = {Agent 1 (7, 0, 7)}: 7 + 0 >= 7 + 0 Ok X = {Agent 2 (0, 0, 12)}: 0 + 0 >= 12 + 0 Contradiction Making an auction false-name-proof

19. Making an auction false-name-proof • Submodularity requires that if any bundle of items is valued: • Each item in the bundle must be valued on its own. • The sum of the values of the items individually must equal or exceed the value for the bundle. • The value for every subset of the bundle must meet these criteria as well.

20. Making an auction false-name-proof • Submodularity eliminates one of the main reasons for using a combinatorial auction in the first place! • Since submodularity is necessary for concavity, any VCG mechanism which uses concavity to ensure it's false-name-proof will also have this problem. • This includes using gross substitution.

21. Making an auction false-name-proof • The submodular restrictions on individual bids are not enough to guarantee concavity. • Also need submodularity among bids from all subsets of agents. • The paper says nothing on how to make an auction submodular.

22. Making an auction false-name-proof • To sum up: • Concavity is sufficient but not necessary for making a VCG mechanism false-name-proof. • Gross substitution implies concavity, and so is also sufficient. • Submodularity is both necessary and sufficient for concavity. • Therefore gross substitution also implies submodularity. • But submodularity does not allow bundles to be valued higher than the sum of their items' values. • Concavity and gross substitution also have this problem.

23. Collusion in general • A mechanism is group-strategy proof if there can be no group of bidders such that: • Every member is untruthful. • Every member obtains at least the same utility as if they told the truth. • Group-strategy-proof as an auction property is independent of false-name-proof.

24. Possible types: (10, 9, 18), (9, 10, 18), (10, 0, 10), (0, 10, 10) All satisfy the gross substitutes condition. This auction is false-name-proof. Agent 1: (10, 9, 18) Agent 2: (9, 10, 18) Agent 1 gets item 1, agent 2 gets item 2, they both pay 8. Collusion in general

25. But if the agents coordinate their strategies: Agent 1: (10, 0, 10) Agent 2: (0, 10, 10) Again agent 1 gets item 1 and agent 2 gets item 2. But the cost to each is 10 – 10 = 0. Therefore this auction is not group-strategy-proof Collusion in general

26. Collusion in general • Group-strategy-proof but not false-name-proof example: • Auction with reserve price p • Auctioneer picks a winner at random. The winner pays p and gets the item.

27. Collusion in general • What if a group of agents can increase their total value by lying, but some agents get lower value? • Payments and exchange of goods afterwards can make every agent come out even or ahead. • If a legitimate bidder has no interest in a set of items, they can “sell” their bid. • In effect, they are selling a false-name bid to another agent. • The two agents can then split the amount the second saves by using the false-name bid.

28. Conclusion • The Internet makes false-name bids feasible because it's hard to prove identity. • No auction can be both Pareto efficient and false-name-proof. • If an auction is submodular, then it is false-name-proof. • False-name-proof is independent of group-strategy-proof.