The connection between games and no-regret algorithms has been widely studied in the literature. A fundamental result is that when all players play no-regret strategies, this produces a sequence of actions whose time-average is a coarse-correlated equilibrium of the game. However, much less is known about equilibrium selection in the case that multiple equilibria exist.
In this work, we study the convergence of no-regret bidding algorithms in auctions. Besides being of theoretical interest, bidding dynamics in auctions is an important question from a practical viewpoint as well. We study repeated game between bidders in which a single item is sold at each time step and the bidder's value is drawn from an unknown distribution. We show that if the bidders use any mean-based learning rule then the bidders converge with high probability to the truthful pure Nash Equilibrium in a second price auction, in VCG auction in the multi-slot setting and to the Bayesian Nash equilibrium in a first price auction. We note mean-based algorithms cover a wide variety of known no-regret algorithms such as Exp3, UCB, $ε$-Greedy etc. Also, we analyze the convergence of the individual iterates produced by such learning algorithms, as opposed to the time-average of the sequence. Our experiments corroborate our theoretical findings and also find a similar convergence when we use other strategies such as Deep Q-Learning.
Auto-bidding has become one of the main options for bidding in online advertisements, in which advertisers only need to specify high-level objectives and leave the complex task of bidding to auto-bidders. In this paper, we propose a family of auctions with boosts to improve welfare in auto-bidding environments with both return on ad spend constraints and budget constraints. Our empirical results validate our theoretical findings and show that both the welfare and revenue can be improved by selecting the weight of the boosts properly.
This paper describes a study of agent bidding strategies, assuming combinatorial valuations for complementary and substitutable goods, in three auction environments: sequential auctions, simultaneous auctions, and the Trading Agent Competition (TAC) Classic hotel auction design, a hybrid of sequential and simultaneous auctions. The problem of bidding in sequential auctions is formulated as an MDP, and it is argued that expected marginal utility bidding is the optimal bidding policy. The problem of bidding in simultaneous auctions is formulated as a stochastic program, and it is shown by exampl…
Simultaneous ascending auctions present agents with the exposure problem: bidding to acquire a bundle risks the possibility of obtaining an undesired subset of the goods. Auction theory provides little guidance for dealing with this problem. We present a new family of decisiontheoretic bidding strategies that use probabilistic predictions of final prices. We focus on selfconfirming price distribution predictions, which by definition turn out to be correct when all agents bid decision-theoretically based on them. Bidding based on these is provably not optimal in general, but our experimental ev…
In this work we consider selling items using a sequential first price auction mechanism. We generalize the assumption of conservative bidding to extensive form games (henceforth optimistic conservative bidding), and show that for both linear and unit demand valuations, the only pure subgame perfect equilibrium where buyers are bidding in an optimistic conservative manner is the minimal Walrasian equilibrium. In addition, we show examples where without the requirement of conservative bidding, subgame perfect equilibria can admit a variety of unlikely predictions, including high price of anarchy…
Interactions between bids to show ads online can lead to an advertiser's ad being shown to more men than women even when the advertiser does not target towards men. We design bidding strategies that advertisers can use to avoid such emergent discrimination without having to modify the auction mechanism. We mathematically analyze the strategies to determine the additional cost to the advertiser for avoiding discrimination, proving our strategies to be optimal in some settings. We use simulations to understand other settings.
We study a class of manipulations in combinatorial auctions where bidders fundamentally misrepresent what goods they are interested in. Prior work has largely assumed that bidders only submit bids on their bundles of interest, which we call simple bidding: strategizing over the bid amounts, but not the bundle identities. However, we show that there exists an entire class of auction instances for which simple bids are never optimal in Bayes-Nash equilibrium, always being strictly dominated by complex bids (where bidders bid on goods they are not interested in). We show this result for the two m…
Auto-bidding is now widely adopted as an interface between advertisers and internet advertising as it allows advertisers to specify high-level goals, such as maximizing value subject to a value-per-spend constraint. Prior research has mostly focused on auctions which are truthful (such as SPA) since uniform bidding is optimal in such auctions, which makes it manageable to reason about equilibria. A tantalizing question is whether one can obtain more efficient outcomes by leaving the realm of truthful auctions. This is the first paper to study non-truthful auctions in the prior-free auto-biddin…
We perform a simulation-based analysis of keyword auctions modeled as one-shot games of incomplete information to study a series of mechanism design questions. Our first question addresses the degree to which incentive compatibility fails in generalized second-price (GSP) auctions. Our results suggest that sincere bidding in GSP auctions is a strikingly poor strategy and a poor predictor of equilibrium outcomes. We next show that the rank-by-revenue mechanism is welfare optimal, corroborating past results. Finally, we analyze profit as a function of auction mechanism under a series of alternat…
In classic auction theory, reserve prices are known to be effective for improving revenue for the auctioneer against quasi-linear utility maximizing bidders. The introduction of reserve prices, however, usually do not help improve total welfare of the auctioneer and the bidders. In this paper, we focus on value maximizing bidders with return on spend constraints -- a paradigm that has drawn considerable attention recently as more advertisers adopt auto-bidding algorithms in advertising platforms -- and show that the introduction of reserve prices has a novel impact on the market. Namely, by ch…
In this paper, we develop a new method for finding an optimal biddingstrategy in sequential auctions, using a dynamic programming technique. Theexisting method assumes that the utility of a user is represented in anadditive form. Thus, the remaining endowment of money must be explicitlyrepresented in each state, and the calculation of the optimal biddingstrategy becomes time-consuming when the initial endowment of money mbecomes large.In this paper, we develop a new problem formalization that avoids explicitlyrepresenting the remaining endowment, by assuming the utility of a user canbe represe…
Auto-bidding is an area of increasing importance in the domain of online advertising. We study the problem of designing auctions in an auto-bidding setting with the goal of maximizing welfare at system equilibrium. Previous results showed that the price of anarchy (PoA) under VCG is 2 and also that this is tight even with two bidders. This raises an interesting question as to whether VCG yields the best efficiency in this setting, or whether the PoA can be improved upon. We present a prior-free randomized auction in which the PoA is approx. 1.896 for the case of two bidders, proving that one c…
Shill bidding occurs when fake bids are introduced into an auction on the seller's behalf in order to artificially inflate the final price. This is typically achieved by the seller having friends bid in her auctions, or the seller controls multiple fake bidder accounts that are used for the sole purpose of shill bidding. We previously proposed a reputation system referred to as the Shill Score that indicates how likely a bidder is to be engaging in price inflating behaviour with regard to a specific seller's auctions. A potential bidder can observe the other bidders' Shill Scores, and if they …
The simultaneous multiple-round auction (SMRA) and the combinatorial clock auction (CCA) are the two primary mechanisms used to sell bandwidth. Under truthful bidding, the SMRA is known to output a Walrasian equilibrium that maximizes social welfare provided the bidder valuation functions satisfy the gross substitutes property. Recently, it was shown that the combinatorial clock auction (CCA) provides good welfare guarantees for general classes of valuation functions. This motivates the question of whether similar welfare guarantees hold for the SMRA in the case of general valuation functions.…
Advertisers in online ad auctions are increasingly using auto-bidding mechanisms to bid into auctions instead of directly bidding their value manually. One prominent auto-bidding format is the target cost-per-acquisition (tCPA) which maximizes the volume of conversions subject to a return-of-investment constraint. From an auction theoretic perspective however, this trend seems to go against foundational results that postulate that for profit-maximizing bidders, it is optimal to use a classic bidding system like marginal CPA (mCPA) bidding rather than using strategies like tCPA. In this paper w…
We study risk-free bidding strategies in combinatorial auctions with incomplete information. Specifically, what is the maximum profit that a complement-free (subadditive) bidder can guarantee in a multi-item combinatorial auction? Suppose there are $n$ bidders and $B_i$ is the value that bidder $i$ has for the entire set of items. We study the above problem from the perspective of the first bidder, Bidder~1. In this setting, the worst case profit guarantees arise in a duopsony, that is when $n=2$, so this problem then corresponds to playing an auction against a budgeted adversary with budget $…
Small operators who take part in secondary wireless spectrum markets typically have strict budget limits. In this paper, we study the bidding problem of a budget constrained operator in repeated secondary spectrum auctions. In existing truthful auctions, truthful bidding is the optimal strategy of a bidder. However, budget limits impact bidding behaviors and make bidding decisions complicated, since bidders may behave differently to avoid running out of money. We formulate the problem as a dynamic auction game between operators, where knowledge of other operators is limited due to the distribu…
We study two standard multi-unit auction formats for allocating multiple units of a single good to multi-demand bidders. The first one is the Discriminatory Auction, which charges every winner his winning bids. The second is the Uniform Price Auction, which determines a uniform price to be paid per unit. Variants of both formats find applications ranging from the allocation of state bonds to investors, to online sales over the internet, facilitated by popular online brokers. For these formats, we consider two bidding interfaces: (i) standard bidding, which is most prevalent in the scientific l…
This paper considers an electric vehicle charging scheduling setting where vehicle users can reserve charging time in advance at a charging station. In this setting, users are allowed to explicitly express their preferences over different start times and the length of charging periods for charging their vehicles. The goal is to compute optimal charging schedules which maximize the social welfare of all users given their time preferences and the state of charge of their vehicles. Assuming that users are self-interested agents who may behave strategically to advance their own benefits rather tha…
We analyze the problem of how to optimally bid for ad spaces in online ad auctions. For this we consider the general case of multiple ad campaigns with overlapping targeting criteria. In our analysis we first characterize the structure of an optimal bidding strategy. In particular, we show that an optimal bidding strategies decomposes the problem into disjoint sets of campaigns and targeting groups. In addition, we show that pure bidding strategies that use only a single bid value for each campaign are not optimal when the supply curves are not continuous. For this case, we derive a lower-boun…
In an all-pay auction, only one bidder wins but all bidders must pay the auctioneer. All-pay bidding games arise from attaching a similar bidding structure to traditional combinatorial games to determine which player moves next. In contrast to the established theory of single-pay bidding games, optimal play involves choosing bids from some probability distribution that will guarantee a minimum probability of winning. In this manner, all-pay bidding games wed the underlying concepts of economic and combinatorial games. We present several results on the structures of optimal strategies in these …
We address the problem of improving bidders' strategies in prior-dependent revenue-maximizing auctions and introduce a simple and generic method to design novel bidding strategies if the seller uses past bids to optimize her mechanism. We propose a simple and agnostic strategy, independent of the distribution of the competition, that is robust to mechanism changes and local (as opposed to global) optimization of e.g. reserve prices by the seller. This strategy guarantees an increase in utility compared to the truthful strategy for any distribution of the competition. In textbook-style examples…
Many popular search engines run an auction to determine the placement of advertisements next to search results. Current auctions at Google and Yahoo! let advertisers specify a single amount as their bid in the auction. This bid is interpreted as the maximum amount the advertiser is willing to pay per click on its ad. When search queries arrive, the bids are used to rank the ads linearly on the search result page. The advertisers pay for each user who clicks on their ad, and the amount charged depends on the bids of all the advertisers participating in the auction. In order to be effective, adv…
University of Bremen（不来梅大学）；ISL - Institute of Shipping Economics and Logistics（ISL——航运经济与物流研究所）
To support a freight carrier in a combinatorial transport auction, we proposes an exact and two heuristic strategies for bidding on subsets of requests. The exact bidding strategy is based on the concept of elementary request combinations. We show that it is sufficient and necessary for a carrier to bid on each elementary request combination in order to guarantee the same result as bidding on each element of the powerset of the set of tendered requests. Both heuristic bidding strategies identify promising request combinations. For this, pairwise synergies based on saving values as well as the …
Periodic double auctions (PDA) have applications in many areas such as in e-commerce, intra-day equity markets, and day-ahead energy markets in smart-grids. While the trades accomplished using PDAs are worth trillions of dollars, finding a reliable bidding strategy in such auctions is still a challenge as it requires the consideration of future auctions. A participating buyer in a PDA has to design its bidding strategy by planning for current and future auctions. Many equilibrium-based bidding strategies proposed are complex to use in real-time. In the current exposition, we propose a scale-ba…
Cloud computing has been an emerging model which aims at allowing customers to utilize computing resources hosted by Cloud Service Providers (CSPs). More and more consumers rely on CSPs to supply computing and storage service on the one hand, and CSPs try to attract consumers on favorable terms on the other. In such competitive cloud computing markets, pricing policies are critical to market efficiency. While CSPs often publish their prices and charge users according to the amount of resources they consume, auction mechanism is rarely applied. In fact a feasible auction mechanism is the most e…
DeMarzo et al. (2005) consider auctions in which bids are selected from a completely ordered family of securities whose values are tied to the resource being auctioned. The paper defines a notion of relative steepness of families of securities and shows that a steeper family provides greater expected revenue to the seller. Two assumptions are: the buyers are risk-neutral; the random variables through which values and signals of the buyers are realized are affiliated. We show that this revenue ranking holds for the second price auction in the case of risk-aversion. However, it does not hold if …
In this paper, we deal with the uncertainty of bidding for display advertising. Similar to the financial market trading, real-time bidding (RTB) based display advertising employs an auction mechanism to automate the impression level media buying; and running a campaign is no different than an investment of acquiring new customers in return for obtaining additional converted sales. Thus, how to optimally bid on an ad impression to drive the profit and return-on-investment becomes essential. However, the large randomness of the user behaviors and the cost uncertainty caused by the auction compet…
We consider the problem of the optimization of bidding strategies in prior-dependent revenue-maximizing auctions, when the seller fixes the reserve prices based on the bid distributions. Our study is done in the setting where one bidder is strategic. Using a variational approach, we study the complexity of the original objective and we introduce a relaxation of the objective functional in order to use gradient descent methods. Our approach is simple, general and can be applied to various value distributions and revenue-maximizing mechanisms. The new strategies we derive yield massive uplifts c…
We consider the question of whether collusion among bidders (a "bidding ring") can be supported in equilibrium of unrepeated first-price auctions. Unlike previous work on the topic such as that by McAfee and McMillan [1992] and Marshall and Marx [2007], we do not assume that non-colluding agents have perfect knowledge about the number of colluding agents whose bids are suppressed by the bidding ring, and indeed even allow for the existence of multiple cartels. Furthermore, while we treat the association of bidders with bidding rings as exogenous, we allow bidders to make strategic decisions ab…
Artificial Intelligence for Multi-Unit Auction design
RMIT University（皇家墨尔本理工大学）；School of Economics, Finance and Marketing, RMIT University（皇家墨尔本理工大学经济、金融与市场营销学院）；School of Computing Technology, RMIT University（皇家墨尔本理工大学计算技术学院）
As an emerging decentralized secure data management platform, blockchain has gained much popularity recently. To maintain a canonical state of blockchain data record, proof-of-work based consensus protocols provide the nodes, referred to as miners, in the network with incentives for confirming new block of transactions through a process of "block mining" by solving a cryptographic puzzle. Under the circumstance of limited local computing resources, e.g., mobile devices, it is natural for rational miners, i.e., consensus nodes, to offload computational tasks for proof of work to the cloud/fog c…
We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding strategy, we propose a polynomial-time algorithm, inspired by the dynamic programming approach to the knapsack problem. The proposed algorithm, referred to as dynamic programming on discrete set (DPDS), achieves a regret order of $O(\sqrt{T\log{T}})$. By showing that the regret is lower bounded by $Ω(\sqrt{T})$ for any strategy, we conclude tha…
With the advent and increasing consolidation of e-commerce, digital advertising has very recently replaced traditional advertising as the main marketing force in the economy. In the past four years, a particularly important development in the digital advertising industry is the shift from second-price auctions to first-price auctions for online display ads. This shift immediately motivated the intellectually challenging question of how to bid in first-price auctions, because unlike in second-price auctions, bidding one's private value truthfully is no longer optimal. Following a series of rece…
We introduce a new numerical framework to learn optimal bidding strategies in repeated auctions when the seller uses past bids to optimize her mechanism. Crucially, we do not assume that the bidders know what optimization mechanism is used by the seller. We recover essentially all state-of-the-art analytical results for the single-item framework derived previously in the setup where the bidder knows the optimization mechanism used by the seller and extend our approach to multi-item settings, in which no optimal shading strategies were previously known. Our approach yields substantial increases…
In this paper, we consider the problem of optimizing the revenue a web publisher gets through real-time bidding (i.e. from ads sold in real-time auctions) and direct (i.e. from ads sold through contracts agreed in advance). We consider a setting where the publisher is able to bid in the real-time bidding auction for each impression. If it wins the auction, it chooses a direct campaign to deliver and displays the corresponding ad. This paper presents an algorithm to build an optimal strategy for the publisher to deliver its direct campaigns while maximizing its real-time bidding revenue. The op…
We present LADDER, the first deep reinforcement learning agent that can successfully learn control policies for large-scale real-world problems directly from raw inputs composed of high-level semantic information. The agent is based on an asynchronous stochastic variant of DQN (Deep Q Network) named DASQN. The inputs of the agent are plain-text descriptions of states of a game of incomplete information, i.e. real-time large scale online auctions, and the rewards are auction profits of very large scale. We apply the agent to an essential portion of JD's online RTB (real-time bidding) advertisin…
