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Second-hand markets have expanded rapidly with the growth of online consumer-to-consumer (C2C) platforms. A key feature of C2C markets is that sellers are typically non-professionals and often face uncertainty about the quality of the goods they sell. This creates scope for platforms to introduce systems that reduce sellers' uncertainty about quality. However, an important question remains: is it socially desirable for sellers to have more precise quality information? We present results showing that while improved information always benefits sellers, it can either benefit or harm buyers. We derive a necessary and sufficient condition under which buyers benefit, and show that this condition holds in many cases, especially when buyers' valuations are not too large relative to sellers' costs. These findings suggest that platforms should consider reducing sellers' uncertainty about quality as a means of improving market efficiency.
E-commerce marketplaces provide business opportunities to millions of sellers worldwide. Some of these sellers have special relationships with the marketplace by virtue of using their subsidiary services (e.g., fulfillment and/or shipping services provided by the marketplace) -- we refer to such sellers collectively as Related Sellers. When multiple sellers offer to sell the same product, the marketplace helps a customer in selecting an offer (by a seller) through (a) a default offer selection algorithm, (b) showing features about each of the offers and the corresponding sellers (price, seller performance metrics, seller's number of ratings etc.), and (c) finally evaluating the sellers along these features. In this paper, we perform an end-to-end investigation into how the above apparatus can nudge customers toward the Related Sellers on Amazon's four different marketplaces in India, USA, Germany and France. We find that given explicit choices, customers' preferred offers and algorithmically selected offers can be significantly different. We highlight that Amazon is adopting different performance metric evaluation policies for different sellers, potentially benefiting Related Selle
Different from traditional Business-to-Consumer e-commerce platforms~(e.g., Amazon), online fleamarket platforms~(e.g., Craigslist) mainly focus on individual sellers who are lack of time investment and business proficiency. Individual sellers often struggle with the bargaining process and thus the deal is unaccomplished. Recent advancements in Large Language Models(LLMs) demonstrate huge potential in various dialogue tasks, but those tasks are mainly in the form of passively following user's instruction. Bargaining, as a form of proactive dialogue task, represents a distinct art of dialogue considering the dynamism of environment and uncertainty of adversary strategies. In this paper, we propose an LLM-empowered bargaining agent designed for online fleamarket platform sellers, named as FishBargain. Specifically, FishBargain understands the chat context and product information, chooses both action and language skill considering possible adversary actions and generates utterances. FishBargain has been tested by thousands of individual sellers on one of the largest online fleamarket platforms~(Xianyu) in China. Both qualitative and quantitative experiments demonstrate that FishBargai
One of the most critical tasks of Microsoft sellers is to meticulously track and nurture potential business opportunities through proactive engagement and tailored solutions. Recommender systems play a central role to help sellers achieve their goals. In this paper, we present a content recommendation model which surfaces various types of content (technical documentation, comparison with competitor products, customer success stories etc.) that sellers can share with their customers or use for their own self-learning. The model operates at the opportunity level which is the lowest possible granularity and the most relevant one for sellers. It is based on semantic matching between metadata from the contents and carefully selected attributes of the opportunities. Considering the volume of seller-managed opportunities in organizations such as Microsoft, we show how to perform efficient semantic matching over a very large number of opportunity-content combinations. The main challenge is to ensure that the top-5 relevant contents for each opportunity are recommended out of a total of $\approx 40,000$ published contents. We achieve this target through an extensive comparison of different
Two sellers compete to sell identical products to a single buyer. Each seller chooses an arbitrary mechanism, possibly involving lotteries, to sell their product. The utility-maximizing buyer can choose to participate in one or both mechanisms, resolving them in either order. Given a common prior over buyer values, how should the sellers design their mechanisms to maximize their respective revenues? We first consider a Stackelberg setting where one seller (Alice) commits to her mechanism and the other seller (Bob) best-responds. We show how to construct a simple and approximately-optimal single-lottery mechanism for Alice that guarantees her a quarter of the optimal monopolist's revenue, for any regular distribution. Along the way we prove a structural result: for any single-lottery mechanism of Alice, there will always be a best response mechanism for Bob consisting of a single take-it-or-leave-it price. We also show that no mechanism (single-lottery or otherwise) can guarantee Alice more than a 1/e fraction of the monopolist revenue. Finally, we show that our approximation result does not extend to Nash equilibrium: there exist instances in which a monopolist could extract full s
In 2007, Andrews and Paule introduced the family of functions $Δ_k(n)$, which enumerate the number of broken $k$-diamond partitions for a fixed positive integer $k$. In 2013, Radu and Sellers completely characterized the parity of $Δ_3(8n+r)$ for certain values of $r$ and proposed a conjecture on congruences modulo powers of $2$ for broken $3$-diamond partitions. In this paper, we employ an unconventional $U$-sequence to resolve the revised conjecture put forward by Radu and Sellers.
Let $a_k(n)$ denote the number of partitions of $n$ wherein even parts come in only one color, while the odd parts may be ``colored" with one of $k$ colors, for fixed $k$. In this note, we find some congruences for $a_k(n)$ in the spirit of Ramanujan's congruences. We prove a number of results for $a_k(n)$ modulo powers of $2$ for infinitely many values of $k$. Our approach is truly elementary, relying on generating function manipulations, theta functions and $q$-dissection techniques. We then close by demonstrating an infinite family of congruences modulo 11 which is proven using a result of Ahlgren.
In 2016, Nath and Sellers proposed a conjecture regarding the precise largest size of ${(s,ms-1,ms+1)}$-core partitions. In this paper, we prove their conjecture. One of the key techniques in our proof is to introduce and study the properties of generalized-$β$-sets, which extend the concept of $β$-sets for core partitions. Our results can be interpreted as a generalization of the well-known result of Yang, Zhong, and Zhou concerning the largest size of $(s,s+1,s+2)$-core partitions.
The existing literature on optimal auctions focuses on optimizing the expected revenue of the seller, and is appropriate for risk-neutral sellers. In this paper, we identify good mechanisms for risk-averse sellers. As is standard in the economics literature, we model the risk-aversion of a seller by endowing the seller with a monotone concave utility function. We then seek robust mechanisms that are approximately optimal for all sellers, no matter what their levels of risk-aversion are. We have two main results for multi-unit auctions with unit-demand bidders whose valuations are drawn i.i.d. from a regular distribution. First, we identify a posted-price mechanism called the Hedge mechanism, which gives a universal constant factor approximation; we also show for the unlimited supply case that this mechanism is in a sense the best possible. Second, we show that the VCG mechanism gives a universal constant factor approximation when the number of bidders is even only a small multiple of the number of items. Along the way we point out that Myerson's characterization of the optimal mechanisms fails to extend to utility-maximization for risk-averse sellers, and establish interesting prop
Let $\bar{p}(n)$ denote the number of overpartitions of $n$. It was conjectured by Hirschhorn and Sellers that $\bar{p}(40n+35)\equiv 0\ ({\rm mod\} 40)$ for $n\geq 0$. Employing 2-dissection formulas of quotients of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for $\bar{p}(40n+35)$ modulo 5. Using the $(p, k)$-parametrization of theta functions given by Alaca, Alaca and Williams, we give a proof of the congruence $\bar{p}(40n+35)\equiv 0\ ({\rm mod\} 5)$. Combining this congruence and the congruence $\bar{p}(4n+3)\equiv 0\ ({\rm mod\} 8)$ obtained by Hirschhorn and Sellers, and Fortin, Jacob and Mathieu, we give a proof of the conjecture of Hirschhorn and Sellers.
We present a simple one-parameter model for spatially localised evolving agents competing for spatially localised resources. The model considers selling agents able to evolve their pricing strategy in competition for a fixed market. Despite its simplicity, the model displays extraordinarily rich behavior. In addition to ``cheap'' sellers pricing to cover their costs, ``expensive'' sellers spontaneously appear to exploit short-term favorable situations. These expensive sellers ``speciate'' into discrete price bands. As well as variety in pricing strategy, the ``cheap'' sellers evolve a strongly correlated spatial structure, which in turn creates niches for their expensive competitors. Thus an entire ecosystem of coexisting, discrete, symmetry-breaking strategies arises.
In this paper, we derive bounds for profit maximizing prior-free procurement auctions where a buyer wishes to procure multiple units of a homogeneous item from n sellers who are strategic about their per unit valuation. The buyer earns the profit by reselling these units in an external consumer market. The paper looks at three scenarios of increasing complexity. First, we look at unit capacity sellers where per unit valuation is private information of each seller and the revenue curve is concave. For this setting, we define two benchmarks. We show that no randomized prior free auction can be constant competitive against any of these two benchmarks. However, for a lightly constrained benchmark we design a prior-free auction PEPA (Profit Extracting Procurement Auction) which is 4-competitive and we show this bound is tight. Second, we study a setting where the sellers have non-unit capacities that are common knowledge and derive similar results. In particular, we propose a prior free auction PEPAC (Profit Extracting Procurement Auction with Capacity) which is truthful for any concave revenue curve. Third, we obtain results in the inherently harder bi-dimensional case where per unit v
Many online marketplaces enjoy great success. Buyers and sellers in successful markets carry out cooperative transactions even if they do not know each other in advance and a moral hazard exists. An indispensable component that enables cooperation in such social dilemma situations is the reputation system. Under the reputation system, a buyer can avoid transacting with a seller with a bad reputation. A transaction in online marketplaces is better modeled by the trust game than other social dilemma games, including the donation game and the prisoner's dilemma. In addition, most individuals participate mostly as buyers or sellers; each individual does not play the two roles with equal probability. Although the reputation mechanism is known to be able to remove the moral hazard in games with asymmetric roles, competition between different strategies and population dynamics of such a game are not sufficiently understood. On the other hand, existing models of reputation-based cooperation, also known as indirect reciprocity, are based on the symmetric donation game. We analyze the trust game with two fixed roles, where trustees (i.e., sellers) but not investors (i.e., buyers) possess rep
We propose a continuum model for the description of buyer and seller dynamics in an Internet market. The relevant variables are the research effort of buyers and the sellers' reputation building process. We show that, if a commercial web-site gives consumers the possibility to rate credibly sellers they bargained with, vendors are forced to be more honest. This leads to mutual beneficial symbiosis between buyers and sellers; the overall enhanced volume of transactions contributes ultimately to the web-site, which facilitates the matchmaking service.
Online market platforms play an increasingly powerful role in the economy. An empirical phenomenon is that platforms, such as Amazon, Apple, and DoorDash, also enter their own marketplaces, imitating successful products developed by third-party sellers. We formulate a Stackelberg model, where the platform acts as the leader by committing to an entry policy: when will it enter and compete on a product? We study this model through a theoretical and computational framework. We begin with a single seller, and consider different kinds of policies for entry. We characterize the seller's optimal explore-exploit strategy via a Gittins-index policy, and give an algorithm to compute the platform's optimal entry policy. We then consider multiple sellers, to account for competition and information spillover. Here, the Gittins-index characterization fails, and we employ deep reinforcement learning to examine seller equilibrium behavior. Our findings highlight the incentives that drive platform entry and seller innovation, consistent with empirical evidence from markets such as Amazon and Google Play, with implications for regulatory efforts to preserve innovation and market diversity.
In recent years, research on the data trading market has been continuously deepened. In the transaction process, there is an information asymmetry process between agents and sellers. For sellers, direct data delivery faces the risk of privacy leakage. At the same time, sellers are not willing to provide data. A reasonable compensation method is needed to encourage sellers to provide data resources. For agents, the quality of data provided by sellers needs to be examined and evaluated. Otherwise, agents may consume too much cost and resources by recruiting sellers with poor data quality. Therefore, it is necessary to build a complete delivery process for the interaction between sellers and agents in the trading market so that the needs of sellers and agents can be met. The federated learning architecture is widely used in the data market due to its good privacy protection. Therefore, in this work, in response to the above challenges, we propose a transaction framework based on the federated learning architecture, and design a seller selection algorithm and incentive compensation mechanism. Specifically, we use gradient similarity and Shapley algorithm to fairly and accurately evalua
We study a recommendation system where sellers compete for visibility by strategically offering commissions to a platform that optimally curates a ranked menu of items and their respective prices for each customer. Customers interact sequentially with the menu following a cascade click model, and their purchase decisions are influenced by price sensitivity and positions of various items in the menu. We model the seller-platform interaction as a Stackelberg game with sellers as leaders and consider two different games depending on whether the prices are set by the platform or prefixed by the sellers. It is complicated to find the optimal policy of the platform in complete generality; hence, we solve the problem in an important asymptotic regime. The core contribution of this paper lies in characterizing the equilibrium structure of the limit game. We show that when sellers are of different strengths, the standard Nash equilibrium does not exist due to discontinuities in utilities. We instead establish the existence of a novel equilibrium solution, namely `$μ$-connected equilibrium cycle' ($μ$-EC), which captures oscillatory strategic responses at the equilibrium. Unlike the (pure) N
Large language model (LLM)-based agents are increasingly expected to negotiate, coordinate, and transact autonomously, yet existing benchmarks lack principled settings for evaluating language-mediated economic interaction among multiple agents. We introduce AgenticPay, a benchmark and simulation framework for multi-agent buyer-seller negotiation driven by natural language. AgenticPay models markets in which buyers and sellers possess private constraints and product-dependent valuations, and must reach agreements through multi-round linguistic negotiation rather than numeric bidding alone. The framework supports a diverse suite of over 110 tasks ranging from bilateral bargaining to many-to-many markets, with structured action extraction and metrics for feasibility, efficiency, and welfare. Benchmarking state-of-the-art proprietary and open-weight LLMs reveals substantial gaps in negotiation performance and highlights challenges in long-horizon strategic reasoning, establishing AgenticPay as a foundation for studying agentic commerce and language-based market interaction. Code and dataset are available at the link: https://github.com/SafeRL-Lab/AgenticPay.
This paper shows how to identify and estimate the seller's risk parameter in an ascending auction. We consider a semiparametric model where the seller has a parametric utility function (such as CARA or CRRA) and the distribution of bidder valuations is modeled flexibly. We provide primitive conditions under which the risk parameter is identified and show that it can be consistently estimated with an asymptotically normal limiting distribution under standard regularity conditions. A Monte Carlo study demonstrates good finite-sample performance of the proposed estimator. We apply our approach to foreclosure real estate auction data from São Paulo. We find evidence that sellers are risk-averse, which leads to a much better fit to the data than a model with risk-neutral sellers, which would substantially underpredict the reserve price relative to what is observed.
In this paper, we design a real-time question-answering system specifically targeted for helping sellers get relevant material/documentation they can share live with their customers or refer to during a call. Taking the Seismic content repository as a relatively large scale example of a diverse dataset of sales material, we demonstrate how LLM embeddings of sellers' queries can be matched with the relevant content. We achieve this by engineering prompts in an elaborate fashion that makes use of the rich set of meta-features available for documents and sellers. Using a bi-encoder with cross-encoder re-ranker architecture, we show how the solution returns the most relevant content recommendations in just a few seconds even for large datasets. Our recommender system is deployed as an AML endpoint for real-time inferencing and has been integrated into a Copilot interface that is now deployed in the production version of the Dynamics CRM, known as MSX, used daily by Microsoft sellers.