Dynamic Stochastic Matching Under Limited Time

Aouad, Ali; Sarıtaç, Ömer

doi:10.2139/ssrn.3497624

Cited by 8 publications

(36 citation statements)

References 40 publications

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“…Our analysis compared to the LP benchmark of [3] gives a simple (1 − 1 /e)-approximation of the optimal online policy, which is tight for their LP. Here, we show that our new PASTA constraint and analysis allow us to break this ubiquitous bound.…”

Section: Our Contributionsmentioning

confidence: 84%

“…For the classic prophet inequality problem, Niazadeh et al [25] show that pricing-based policies yield no better approximation of the optimal online policy than they do of the optimal offline policy. For the stationary prophet inequality problem, the same is not true; while our inapproximability result of Theorem 1.1 implies that no competitive ratio beyond 1 /2 is possible, an algorithm of [3] yields a 1− 1 /e ≈ 0.632 approximation of the optimal online policy. We prove that this latter natural bound, prevalent in the online algorithms literature, is not optimal for our problem, and present a pricing-based policy which breaks this bound.…”

Section: Our Contributionsmentioning

confidence: 89%

“…Collina et al [9] and Aouad and Saritaç [3] present the following LP benchmarks, which upper bound the average gain of any offline or online policy, respectively. Lemma 2.1 ( [3,9]).…”

Section: Prior Lp Benchmarks and A Natural Algorithmmentioning

confidence: 99%

“…A closely related problem of dynamic weighted matching was recently introduced by [3,9]. In their problem, the market is not bipartite, and agents arrive over time and can be matched at any time before their (sudden and unpredictable) departure from the market.…”

Section: Introductionmentioning

confidence: 99%

“…(Our problem is the special case of theirs where buyers' departure rate is infinite.) The authors of [3,9] present algorithms which give 1 4 (1 − 1 /e)-and 1 /8-approximations of the optimal online and offline policies, respectively. For our single-good problem, their approaches yield (1− 1 /e)-and (1− 1 /(e−1)) ≈ 0.418approximations of the optimal online and offline policies, respectively (see Appendix B).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The Stationary Prophet Inequality Problem

Kristen¹,

Saberi²,

Shameli³

et al. 2021

Preprint

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We study a continuous and infinite time horizon counterpart to the classic prophet inequality, which we term the stationary prophet inequality problem. Here, copies of a good arrive and perish according to Poisson point processes. Buyers arrive similarly and make take-it-or-leave-it offers for unsold items. The objective is to maximize the (infinite) time average revenue of the seller.Our main results are pricing-based policies which (i) achieve a 1/2-approximation of the optimal offline policy, which is best possible, and (ii) achieve a better than (1−1/e)-approximation of the optimal online policy. Result (i) improves upon bounds implied by recent work of Collina et al. (WINE'20), and is the first optimal prophet inequality for a stationary problem. Result (ii) improves upon a 1 − 1/e bound implied by recent work of Aouad and Saritaç (EC'20), and shows that this prevalent bound in online algorithms is not optimal for this problem.

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Section: Our Contributionsmentioning

confidence: 84%

Section: Our Contributionsmentioning

confidence: 89%

“…Collina et al [9] and Aouad and Saritaç [3] present the following LP benchmarks, which upper bound the average gain of any offline or online policy, respectively. Lemma 2.1 ( [3,9]).…”

Section: Prior Lp Benchmarks and A Natural Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Stationary Prophet Inequality Problem

Kristen¹,

Saberi²,

Shameli³

et al. 2021

Preprint

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Dynamic competition and market structure for platform‐based products: roles of product quality and indirect network effect

Dou,

Wei,

et al. 2024

Int Trans Operational Res

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We consider dynamic competition between two platform‐based products that exhibit two‐sided network effects, such as game consoles and intelligent hardware. Firms compete in terms of pricing and Research & Development investment, which are driven by consumers’ marginal utility of quality, indirect network effects, and the differentiation between consumers’ preference for the products. We find that with a small marginal utility of consumers, the equilibrium investment of one firm increases first and decreases later with its product quality but is not obviously sensitive to the rival's. In contrast, with a large marginal utility, if the quality of the two products is comparable, the equilibrium investment increases substantially. However, if one product pulls ahead, the other firm will stop investing. Besides, we find that when the intrinsic value and the network value coexist, the market becomes more concentrated, even when consumers’ marginal utility is small. The market concentration increases in both the consumers’ marginal utility and the indirect network effect but decreases in the degree of differentiation between consumers’ preference toward the two products. Interestingly, we show that differentiation plays an important role in shaping the market structure only when the network effect is weak. Counterintuitively, we show that the differentiation corrodes firms’ total profits, which demonstrates that less fierce competition resulting from low substitution leads to a lower profit. Additionally, we reveal that dynamic interaction between quality and installed base motivates firms to improve from a low quality, the first‐mover advantage does not ensure market dominance.

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Fully Online Matching with Stochastic Arrivals and Departures

Wang

Yan

2023

AAAI

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We study a fully online matching problem with stochastic arrivals and departures. In this model, each online arrival follows a known identical and independent distribution over a fixed set of agent types. Its sojourn time is unknown in advance and follows type-specific distributions with known expectations. The goal is to maximize the weighted reward from successful matches. To solve this problem, we first propose a linear program (LP)-based algorithm whose competitive ratio is lower bounded by 0.155 under mild conditions. We further achieve better ratios in some special cases. To demonstrate the challenges of the problem, we further establish several hardness results. In particular, we show that no online algorithm can achieve a competitive ratio better than 2/3 in this model and there is no LP-based algorithm (with respect to our proposed LP) with a competitive ratio better than 1/3. Finally, we demonstrate the effectiveness and efficiency of our algorithm numerically.

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Dynamic Stochastic Matching Under Limited Time

Cited by 8 publications

References 40 publications

The Stationary Prophet Inequality Problem

The Stationary Prophet Inequality Problem

Dynamic competition and market structure for platform‐based products: roles of product quality and indirect network effect

Fully Online Matching with Stochastic Arrivals and Departures

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