arXiv subjects

Nicolas E. Stier-Moses

Publications and source records attributed to Nicolas E. Stier-Moses.

4 recordsLinked to original sources

arXiv2021

Computing large market equilibria using abstractions

Computing market equilibria is an important practical problem for market design, for example in fair division of items. However, computing equilibria requires large amounts of information (typically the valuation of every buyer for every item) and computing power. We consider ameliorating these issues by applying a method used for solving complex games: constructing a coarsened abstraction of a given market, solving for the equilibrium in the abstraction, and lifting the prices and allocations back to the original market. We show how to bound important quantities such as regret, envy, Nash social welfare, Pareto optimality, and maximin share/proportionality when the abstracted prices and allocations are used in place of the real equilibrium. We then study two abstraction methods of interest for practitioners: (1) filling in unknown valuations using techniques from matrix completion, (2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market. We find that in real data allocations/prices that are relatively close to equilibria can be computed from even very coarse abstractions.

cs.GT↗

arXiv2021

Pacing Equilibrium in First-Price Auction Markets

Mature internet advertising platforms offer high-level campaign management tools to help advertisers run their campaigns, often abstracting away the intricacies of how each ad is placed and focusing on aggregate metrics of interest to advertisers. On such platforms, advertisers often participate in auctions through a proxy bidder, so the standard incentive analyses that are common in the literature do not apply directly. In this paper, we take the perspective of a budget management system that surfaces aggregated incentives -- instead of individual auctions -- and compare first and second price auctions. We show that theory offers surprising endorsement for using a first price auction to sell individual impressions. In particular, first price auctions guarantee uniqueness of the steady-state equilibrium of the budget management system, monotonicity, and other desirable properties, as well as efficient computation through the solution to the well-studied Eisenberg-Gale convex program. Contrary to what one can expect from first price auctions, we show that incentives issues are not a barrier that undermines the system. Using realistic instances generated from data collected at real-world auction platforms, we show that bidders have small regret with respect to their optimal ex-post strategy, and they do not have a big incentive to misreport when they can influence equilibria directly by giving inputs strategically. Finally, budget-constrained bidders, who have significant prevalence in real-world platforms, tend to have smaller regrets. Our computations indicate that bidder budgets, pacing multipliers and regrets all have a positive association in statistical terms.

cs.GT↗

arXiv2021

Multiplicative Pacing Equilibria in Auction Markets

Budgets play a significant role in real-world sequential auction markets such as those implemented by internet companies. To maximize the value provided to auction participants, spending is smoothed across auctions so budgets are used for the best opportunities. Motivated by a mechanism used in practice by several companies, this paper considers a smoothing procedure that relies on {\em pacing multipliers}: on behalf of each buyer, the auction market applies a factor between 0 and 1 that uniformly scales the bids across all auctions. Reinterpreting this process as a game between buyers, we introduce the notion of {\em pacing equilibrium}, and prove that they are always guaranteed to exist. We demonstrate through examples that a market can have multiple pacing equilibria with large variations in several natural objectives. We show that pacing equilibria refine another popular solution concept, competitive equilibria, and show further connections between the two solution concepts. Although we show that computing either a social-welfare-maximizing or a revenue-maximizing pacing equilibrium is NP-hard, we present a mixed-integer program (MIP) that can be used to find equilibria optimizing several relevant objectives. We use the MIP to provide evidence that: (1) equilibrium multiplicity occurs very rarely across several families of random instances, (2) static MIP solutions can be used to improve the outcomes achieved by a dynamic pacing algorithm with instances based on a real-world auction market, and (3) for the instances we study, buyers do not have an incentive to misreport bids or budgets provided there are enough participants in the auction.

cs.GT↗

arXiv2015

Asymptotically tight bounds for inefficiency in risk-averse selfish routing

We consider a nonatomic selfish routing model with independent stochastic travel times, represented by mean and variance latency functions for each edge that depend on their flows. In an effort to decouple the effect of risk-averse player preferences from selfish behavior on the degradation of system performance, Nikolova and Stier- Moses [16] defined the concept of the price of risk aversion as the worst-case ratio of the cost of an equilibrium with risk-averse players and that of an equilibrium with risk-neutral users. For risk-averse users who seek to minimize the mean plus variance of travel time on a path, they proved an upper bound on the price of risk aversion, which is independent of the latency functions, and grows linearly with the size of the graph and players' risk-aversion. In this follow-up paper, we provide a matching lower bound for graphs with number of vertices equal to powers of two, via the construction of a graph family inductively generated from the Braess graph. We also provide conceptually different bounds, which we call functional, that depend on the class of mean latency functions and provide characterizations that are independent of the network topology (first derived, in a more complicated way, by Meir and Parkes [10] in a different context with different techniques). We also supplement the upper bound with a new asymptotically-tight lower bound. Our third contribution is a tight bound on the price of risk aversion for a family of graphs that generalize series-parallel graphs which applies to users minimizing the mean plus standard deviation of a path, a much more complex model of risk-aversion due to the cost of a path being non-additive over edge costs. This is a refinement of previous results in [16] that characterized the price of risk-aversion for series-parallel graphs and for the Braess graph.

cs.GT↗