Tian-Ming Bu

Forward looking Nash equilibrium for keyword auction

We introduce the concept of forward looking Nash equilibrium for the position auction (also called the generalized second price auction), a widely studied protocol for Internet advertisement bidding processes. We show that it has a unique solution for the position auction. Most importantly, the cost each bidder pays and the revenue of the auctioneer under the equilibrium are all equal to those under VCG mechanism. As the position auction is not an incentive compatible protocol, the fact that the forward looking Nash equilibrium results in the same payoff for everyone as in the VCG protocol justifies the practical protocol.

On Robustness of Forward-looking in Sponsored Search Auction

We analyze the robustness of pure Nash Equilibria of sponsored search auctions, based on the forward-looking response function. To consider the robustness of such refined solution concept, we first study the convergence property of several adjustment schemes. Especially, we prove that under the randomized scheme, the auction always converges to a unique fixed point with probability one, whose revenue is equal to the celebrated VCG mechanism. Additionally, we study the robustness of such forward-looking strategic heuristic against aggressive selfish strategic heuristic called vindictive bidding. We investigate three types of such bidding strategies and substantiate that the pure Nash equilibrium still exists under two types even if there is an arbitrary portion of vindictive bidders.

Unconditional competitive auctions with copy and budget constraints

This paper investigates a new auction model in which bidders have both copy and budget constraints. The new model has extensive and interesting applications in auctions of online ad-words, software licenses, etc. We consider the following problem: Suppose all the participators are rational, how to allocate the objects at what price so as to guarantee auctioneers high revenue, and how high it is. We introduce a new kind of mechanisms called win-win mechanisms and present the notion of unconditional competitive auctions. A notably interesting property of win-win mechanisms is that each bidders self-interested strategy brings better utility not only to himself but also to the auctioneer. Then we present win-win mechanisms for multi-unit auctions with copy and budget constraints. We prove that these auctions are unconditional competitive under the situation of both limited and unlimited supply.

On discretization methods for approximating optimal paths in regions with direction-dependent costs

The optimal path planning problems are very difficult in the case where the cost metric varies not only in different regions of the space, but also in different directions inside the same region. If the classic discretization approach is adopted to compute an @?-approximation of the optimal path, the size of the discretization (and thus the complexity of the approximation algorithm) is usually dictated by a number of geometric parameters and thus can be very large. In this paper we show a general method for choosing the variables of the discretization to maximally reduce the dependency of the size of the discretization on various geometric parameters. We use this method to improve the previously reported results on two optimal path problems with direction-dependent cost metrics.

Arbitrage opportunities across sponsored search markets

We model and study arbitrage across sponsored search markets, created by search engines. We identify and focus on traffic arbitrage and click arbitrage by auctioneers. We derive and characterize equilibria of such arbitrage behaviors across multiple markets.

Multi-bidding Strategy in Sponsored Keyword Auction

The generalized second price auction has recently become a much studied model for sponsored keyword auctions for Internet advertisement. Though it is known not to be incentive compatible, properties of its pure Nash equilibria have been well characterized under the single bidding strategy of each bidder. In this paper, we study the properties of pure Nash equilibria of the generalized second price auction when each bidder is allowed to submit more than one bid. This multi-bidding strategy is noted to have been adopted by companies for keyword advertisements on search engines. In consideration of the pure Nash equilibria, we completely characterize conditions on the number of selling slots for a pure Nash equilibrium to exist, assuming all the advertisers are allowed to use multi-bidding strategies or only one advertiser will use a multi-bidding strategy. Our findings reveal interesting properties of limitation and potentials of the market place of online advertisement.

Multi-bidding strategy in sponsored search auctions

The generalized second price auction has recently become a much studied model for sponsored search auctions for Internet advertisement. Though it is known not to be incentive compatible, properties of its pure Nash equilibria have been well characterized under the single bidding strategy of each bidder.In this paper, we study the properties of pure Nash equilibria of the generalized second price auction when each bidder is allowed to submit more than one bid. This multi-bidding strategy is noted to have been adopted by companies for keyword advertisements on search engines. In consideration of the pure Nash equilibria, we completely characterize conditions on the number of selling slots for a pure Nash equilibrium to exist, assuming all the advertisers are allowed to use multi-bidding strategies or only one advertiser will use a multi-bidding strategy.Our findings reveal interesting properties of limitations and potentials of the generalized second price auction for the sponsored search market.