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We consider a general non-stochastic online pricing bandit setting in a procurement scenario where a buyer with a budget wants to procure items from a fixed set of sellers to maximize the buyer's reward by dynamically offering purchasing prices to the sellers, where the sellers' costs and values at each time period can change arbitrarily and the sellers determine whether to accept the offered prices to sell the items. This setting models online pricing scenarios of procuring resources or services in multi-agent systems. We first consider the offline setting when sellers' costs and values are known in advance and investigate the best fixed-price policy in hindsight. We show that it has a tight approximation guarantee with respect to the offline optimal solutions. In the general online setting, we propose an online pricing policy, Granularity-based Pricing (GAP), which exploits underlying side-information from the feedback graph when the budget is given as the input. We show that GAP achieves an upper bound of O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln B) on the alpha-regret where n, v_{max}, c_{min}, and B are the number, the maximum value, the minimum cost of sellers, and the budget, respectively. We then extend it to the unknown budget case by developing a variant of GAP, namely Doubling-GAP, and show its alpha-regret is at most O(n{v_{max}}{c_{min}}sqrt{B/c_{min}}ln2 B). We also provide an alpha-regret lower bound Omega(v_{max}sqrt{Bn/c_{min}}) of any online policy that is tight up to sub-linear terms. We conduct simulation experiments to show that the proposed policy outperforms the baseline algorithms. 

We study the k-facility location games with optional preferences on the line. In the games, each strategic agent has a public location preference on the k facility locations and a private optional preference on the preferred/acceptable set of facilities out of the k facilities. Our goal is to design strategyproof mechanisms to elicit agents’ optional preferences and locate k facilities to minimize the social or maximum cost of agents based on their facility preferences and public agent locations. We consider two variants of the facility location games with optional preferences: the Min variant and the Max variant where the agent’s cost is defined as their distance to the closest acceptable facility and the farthest acceptable facility, respectively. For the Min variant, we present two deterministic strategyproof mechanisms to minimize the maximum cost and social cost with k ≥ 3 facilities, achieving approximation ratios of 3 and 2n+1 respectively. We complement the results by establishing lower bounds of 3/2 and n/4 for the approximation ratios achievable by any deterministic strategyproof mechanisms for the maximum cost and social cost, respectively. We then improve our results in a special setting of the Min variant where there are exactly three facilities and present two deterministic strategyproof mechanisms to minimize the maximum cost and social cost. For the Max variant, we present an optimal deterministic strategyproof mechanism for the maximum cost and a k-approximation deterministic strategyproof mechanism for the social cost. 

In recent decades, the design of budget feasible mechanisms for a wide range of procurement auction settings has received significant attention in the Artificial Intelligence (AI) community. These procurement auction settings have practical applications in various domains such as federated learning, crowdsensing, edge computing, and resource allocation. In a basic procurement auction setting of these domains, a buyer with a limited budget is tasked with procuring items (\eg, goods or services) from strategic sellers, who have private information on the true costs of their items and incentives to misrepresent their items' true costs. The primary goal of budget feasible mechanisms is to elicit the true costs from sellers and determine items to procure from sellers to maximize the buyer valuation function for the items and ensure that the total payment to the sellers is no more than the budget. In this survey, we provide a comprehensive overview of key procurement auction settings and results of budget feasible mechanisms. We provide several promising future research directions. 

We study the facility location problems (FLPs) with altruistic agents who act to benefit others in their affiliated groups. Our aim is to design mechanisms that elicit true locations from the agents in different overlapping groups and place a facility to serve agents to approximately optimize a given objective based on agents' costs to the facility. Existing studies of FLPs consider myopic agents who aim to minimize their own costs to the facility. We mainly consider altruistic agents with well-motivated group costs that are defined over costs incurred by all agents in their groups. Accordingly, we define Pareto strategyproofness to account for altruistic agents and their multiple group memberships with incomparable group costs. We consider mechanisms satisfying this strategyproofness under various combinations of the planner's objectives and agents' group costs. For each of these settings, we provide upper and lower bounds of approximation ratios of the mechanisms satisfying Pareto strategyproofness. 

We study the group-fair obnoxious facility location problems from the mechanism design perspective where agents belong to different groups and have private location preferences on the undesirable locations of the facility. Our main goal is to design strategyproof mechanisms that elicit the true location preferences from the agents and determine a facility location that approximately optimizes several group-fair objectives. We first consider the maximum total and average group cost (group-fair) objectives. For these objectives, we propose deterministic mechanisms that achieve 3-approximation ratios and provide matching lower bounds. We then provide the characterization of 2-candidate strategyproof randomized mechanisms. Leveraging the characterization, we design randomized mechanisms with improved approximation ratios of 2 for both objectives. We also provide randomized lower bounds of 5/4 for both objectives. Moreover, we investigate intergroup and intragroup fairness (IIF) objectives, addressing fairness between groups and within each group. We present a mechanism that achieves a 4-approximation for the IIF objectives and provide tight lower bounds. 

We study information design in click-through auctions, in which the bidders/advertisers bid for winning an opportunity to show their ads but only pay for realized clicks. The payment may or may not happen, and its probability is called the click-through rate (CTR). This auction format is widely used in the industry of online advertising. Bidders have private values, whereas the seller has private information about each bidder’s CTRs. We are interested in the seller’s problem of partially revealing CTR information to maximize revenue. Information design in click-through auctions turns out to be intriguingly different from almost all previous studies in this space since any revealed information about CTRs will never affect bidders' bidding behaviors - they will always bid their true value per click - but only affect the auction’s allocation and payment rule. In some sense, this makes information design effectively a constrained mechanism design problem. Our first result is an FPTAS to compute an approximately optimal mechanism under a constant number of bidders. The design of this algorithm leverages Bayesian bidder values which help to "smooth" the seller’s revenue function and lead to better tractability. The design of this FPTAS is complex and primarily algorithmic. Our second main result pursues the design of "simple" mechanisms that are approximately optimal yet more practical. We primarily focus on the two-bidder situation, which is already notoriously challenging as demonstrated in recent works. When bidders' CTR distribution is symmetric, we develop a simple prior-free signaling scheme, whose construction relies on a parameter termed optimal signal ratio. The constructed scheme provably obtains a good approximation as long as the maximum and minimum of bidders' value density functions do not differ much. 

We consider a new problem of selling data to a machine learner who looks to purchase data to train his machine learning model. A key challenge in this setup is that neither the seller nor the machine learner knows the true quality of data. When designing a revenue-maximizing mechanism, a data seller faces the tradeoff between the cost and precision of data quality estimation. To address this challenge, we study a natural class of mechanisms that price data via costly signaling. Motivated by the assumption of i.i.d. data points as in classic machine learning models, we first consider selling homogeneous data and derive an optimal selling mechanism. We then turn to the sale of heterogeneous data, motivated by the sale of multiple data sets, and show that 1) on the negative side, it is NP-hard to approximate the optimal mechanism within a constant ratio e/(e+1) + o(1); while 2) on the positive side, there is a 1/k-approximate algorithm, where k is the number of the machine learner’s private types.