Fisher Market Research Articles

Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements

Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements

Constrained Network Slicing Games: Achieving Service Guarantees and Network Efficiency

Network slicing is a key capability for next generation mobile networks. It enables infrastructure providers to cost effectively customize logical networks over a shared infrastructure. A critical component of network slicing is resource allocation, which needs to ensure that slices receive the resources needed to support their services while optimizing network efficiency. In this paper, we propose a novel approach to slice-based resource allocation named Guaranteed seRvice Efficient nETwork slicing (GREET). The underlying concept is to set up a constrained resource allocation game, where ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$</tex-math> </inline-formula> ) slices unilaterally optimize their allocations to best meet their (dynamic) customer loads, while ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ii$</tex-math> </inline-formula> ) constraints are imposed to guarantee that, if they wish so, slices receive a pre-agreed share of the network resources. The resulting game is a variation of the well-known Fisher market, where slices are provided a budget to contend for network resources (as in a traditional Fisher market), but (unlike a Fisher market) prices are constrained for some resources to ensure that the pre-agreed guarantees are met for each slice. In this way, GREET combines the advantages of a share-based approach (high efficiency by flexible sharing) and reservation-based ones (which provide guarantees by assigning a fixed amount of resources). We characterize the Nash equilibrium, best response dynamics, and propose a practical slice strategy with provable convergence properties. Extensive simulations exhibit substantial improvements over network slicing state-of-the-art benchmarks.

Satiation in Fisher Markets and Approximation of Nash Social Welfare

We study linear Fisher markets with satiation. In these markets, sellers have earning limits, and buyers have utility limits. Beyond applications in economics, they arise in the context of maximizing Nash social welfare when allocating indivisible items to agents. In contrast to markets with either earning or utility limits, markets with both limits have not been studied before. They turn out to have fundamentally different properties. In general, the existence of competitive equilibria is not guaranteed. We identify a natural property of markets (termed money clearing) that implies existence. We show that the set of equilibria is not always convex, answering a question posed in the literature. We design an FPTAS to compute an approximate equilibrium and prove that the problem of computing an exact equilibrium lies in the complexity class continuous local search ([Formula: see text]; i.e., the intersection of polynomial local search ([Formula: see text]) and polynomial parity arguments on directed graphs ([Formula: see text])). For a constant number of buyers or goods, we give a polynomial-time algorithm to compute an exact equilibrium. We show how (approximate) equilibria can be rounded and provide the first constant-factor approximation algorithm (with a factor of 2.404) for maximizing Nash social welfare when agents have capped linear (also known as budget-additive) valuations. Finally, we significantly improve the approximation hardness for additive valuations to [Formula: see text]. Funding: J. Garg was supported by the National Science Foundation [Grant CCF-1942321 (CAREER)]. M. Hoefer was supported by Deutsche Forschungsgemeinschaft [Grants Ho 3831/5-1, Ho 3831/6-1, and Ho 3831/7-1].

Fisher markets with linear constraints: Equilibrium properties and efficient distributed algorithms

The Fisher market is one of the most fundamental models for resource allocation. However, Fisher markets are less amenable for resource allocation settings when agents have additional linear constraints beyond the budget constraints of buyers and the capacity constraints of goods. Thus, in this work, we introduce a modified Fisher market, where agents may have additional linear constraints, and study the properties of the resulting equilibria. To set equilibrium prices, we introduce a budget-adjusted social optimization problem (BA-SOP), whose optimal dual variables correspond to the equilibrium prices. Since solving BA-SOP can be computationally intensive and requires centralized knowledge of all agents' utilities, we propose a new class of distributed algorithms based on the Alternating Direction Method of Multipliers (ADMM) to compute equilibrium prices. Our ADMM approach has strong convergence guarantees and provides a general-purpose method for computing market equilibria for Fisher markets with homogeneous linear constraints and classical Fisher markets.

Fisher Markets with Social Influence

A Fisher market is an economic model of buyer and seller interactions in which each buyer’s utility depends only on the bundle of goods she obtains. Many people’s interests, however, are affected by their social interactions with others. In this paper, we introduce a generalization of Fisher markets, namely influence Fisher markets, which captures the impact of social influence on buyers’ utilities. We show that competitive equilibria in influence Fisher markets correspond to generalized Nash equilibria in an associated pseudo-game, which implies the existence of competitive equilibria in all influence Fisher markets with continuous and concave utility functions. We then construct a monotone pseudo-game, whose variational equilibria and their duals together characterize competitive equilibria in influence Fisher markets with continuous, jointly concave, and homogeneous utility functions. This observation implies that competitive equilibria in these markets can be computed in polynomial time under standard smoothness assumptions on the utility functions. The dual of this second pseudo-game enables us to interpret the competitive equilibria of influence CCH Fisher markets as the solutions to a system of simultaneous Stackelberg games. Finally, we derive a novel first-order method that solves this Stackelberg system in polynomial time, prove that it is equivalent to computing competitive equilibrium prices via tâtonnement, and run experiments that confirm our theoretical results.

Fast and Interpretable Dynamics for Fisher Markets via Block-Coordinate Updates

We consider the problem of large-scale Fisher market equilibrium computation through scalable first-order optimization methods. It is well-known that market equilibria can be captured using structured convex programs such as the Eisenberg-Gale and Shmyrev convex programs. Highly performant deterministic full-gradient first-order methods have been developed for these programs. In this paper, we develop new block-coordinate first-order methods for computing Fisher market equilibria, and show that these methods have interpretations as tâtonnement-style or proportional response-style dynamics where either buyers or items show up one at a time. We reformulate these convex programs and solve them using proximal block coordinate descent methods, a class of methods that update only a small number of coordinates of the decision variable in each iteration. Leveraging recent advances in the convergence analysis of these methods and structures of the equilibrium-capturing convex programs, we establish fast convergence rates of these methods.

The new full-Newton step interior-point algorithm for the Fisher market equilibrium problems based on a kernel function

In this paper, we propose a full-Newton step interior-point method for the weighted linear complementarity problem (wLCP) model of the Fisher market equilibrium problem. The weighted complementarity problem (wCP) is a generalization of the complementarity problem (CP) with the nonnegative weight vector, where the zero on the right-hand side is replaced by the nonnegative weight vector. The importance of a wCP lies in the fact that many equilibrium problems in science, engineering, and economics can be reformulated as wCPs, which lead to the development of highly efficient algorithms. We extend a full-Newton step interior-point method (IPM) to the wLCP model of the Fisher problem. New search directions are obtained by using a kernel function in the scaled Newton system. The algorithm takes only full-Newton steps, thus, avoiding the calculation of the step size which is computationally advantageous. Under the suitable assumptions, the algorithm is shown to have global convergence and polynomial complexity. Some numerical results indicate the efficiency of the algorithm. To the best of our knowledge, this is the first full-Newton step IPM for Fisher problems, which uses the kernel function to obtain new search directions.

Infinite-Dimensional Fisher Markets and Tractable Fair Division

Fisher market equilibrium models have long been a central topic in economics and computation. Recently, they have been widely used in the design and implementation of Internet marketplaces. Although the classical models are well studied and can be solved via tractable optimization characterizations, they only allow a finite number of items and thus face scalability issues when the item space is huge or even continuous. In “Infinite-Dimensional Fisher Markets and Tractable Fair Division,” Gao and Kroer propose infinite-dimensional convex programs and show that they capture market equilibria for infinite and possibly continuous item spaces, extending the classical Eisenberg-Gale framework. Using these results, the authors show that a challenging cake-cutting problem for piecewise linear agent valuations is equivalent to finding a market equilibrium and admits a tractable convex optimization characterization. Thus, it can be solved in polynomial time in theory and highly efficiently by numerical optimization software.

Market efficiency as indicators of fish market along the middle stretch of River Ganga, India

AbstractThe fish market in the state of Uttar Pradesh, India, is not formally organised. Rather, it permeates from a direct fisher market to a wholesale market. Fish caught from the River Ganga are distributed through many intermediaries and are transported to farther regions like Guwahati and Kolkata in the east. The objective of the study is to assess market efficiency and, with this assessment, make recommendations that can be used to improve the livelihoods of the fishers. We accomplish this by investigating market efficiency indicators including production capacity of the area, Percent Share of Fisher in the Consumer's Money, and price stability of fish markets in different districts (including Bulandshahr, Farrukhabad, Kanpur, Fatehpur, Prayagraj and Varanasi). These are the districts that are located on the bank of the River Ganga in the state of Uttar Pradesh. The study consists of interviews with fishers, wholesalers, vendors, auctioneers, and consumers. The study examines 9 wholesalers, 9 retail markets and 1 direct fisher market. The demographic variables of fish sellers viz. age, education, caste, family size, experience and occupation are also studied. Descriptive statistics and cross-tabulation are used for nominal variables to measure and test conceptions and misconceptions of the fish market. Fish selling is carried out through fish market channels including 220 middlemen, 249 retailers, 48 wholesalers, and 72 auctioneers. Together, these individuals make up the channel structure, channel strategy, and channel performance. The high number of middlemen demonstrates that the market structure is inefficient. Higher Percent Share of Fisher in the Consumer's Money was observed for fishes like Labeo rohita (65.8%), Cirrhinus Mrigala (64%), and Labeo Calbasu (64.3%). The average Percent Share of Fisher in the Consumer's Money is 54% and shows the fishers earn little more than half of the revenue generated. The study shows that high-value fish have less price stability and low-value fish have high price stability across the fish market channel, respectively. Our investigation recommends reducing the number of market channels with the application of modern infrastructure in order to increase the quality of products received by the consumer and to increase fisher share in consumer's money.

Incentive ratio: A game theoretical analysis of market equilibria

In a Fisher market, the market maker sells m products to n potential agents. The agents submit their utility functions and money endowments to the market maker, who, upon receiving submitted information, derives market equilibrium prices and allocations of the products. Agents are self-interested entities who wish to maximize their utility, and they may misreport their private information for this purpose. The incentive ratio characterizes the extent to which strategic plays can increase an agent's utility. While agents do benefit by misreporting their private information, we show that the ratio of improvement by a unilateral strategic play is no more than two in markets with gross substitute utilities for the agents. Moreover, it can be pinned down to e1/e≈1.445 in Cobb-Douglas markets. For the Leontief markets in which products are complementary, we show that the incentive ratio is at most two as well.

A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem

&lt;p style='text-indent:20px;'&gt;The weighted complementarity problem (wCP) can be applied to a large variety of equilibrium problems in science, economics and engineering. Since formulating an equilibrium problem as a wCP may lead to highly efficient algorithms for its numerical solution, wCP is a nontrivial generalization of the complementarity problem. In this paper we consider a special weighted linear complementarity problem (wLCP), which is the more general optimization of the Fisher market equilibrium problem. A full-modified-Newton infeasible interior-point method (IIPM) for the special wLCP is proposed. The algorithm reformulates the central path of the perturbed problem as an equivalent system of equations, and uses only full-Newton steps at each iteration, so-called a feasibility step (i.e., a full-modified-Newton step) and several usual centering steps. The polynomial complexity of the algorithm is as good as the best known iteration bound for these types of IIPMs in linear optimization.&lt;/p&gt;

Fair Resource Allocation in a Volatile Marketplace

In settings where a platform must allocate finite supplies of goods to buyers, balancing overall platform revenues with the fairness of the individual allocations to platform participants is paramount to the well-functioning of the platform. This is made even more difficult by the fact that the supply of goods is in practice stochastic and difficult to forecast, such as in the case of online ad allocation, where the platform manages a supply of impressions that varies over time. In this paper, we design a fair allocation scheme that works in the presence of supply uncertainty. Algorithmically, the scheme repeatedly solves for Fisher market equilibria in a model predictive control fashion and is proved to admit constant factor guarantees versus the offline optimal. In addition, the scheme is tested on a sequence of real ad datasets, showing strong empirical performance.

Reef Conservation off the Hook: Can Market Interventions Make Coral Reef Fisheries More Sustainable?

The overexploitation of coral reef fisheries threatens the persistence of reef ecosystems and the livelihoods and food security of millions of people. Market-based initiatives to increase fisheries sustainability have been widely implemented in industrialized commodity fisheries, but the suitability of these initiatives for coral reef fisheries has not been systematically investigated. Here, we present a typology of market-based interventions and coral reef fisheries sectors and identity promising approaches for each fishery archetype. For high value, export-oriented reef fisheries that are highly unsustainable (live reef food fish and dried sea cucumbers), traditional regulatory efforts including trade restrictions will be most effective. For high-value, export-oriented fisheries for highly fecund invertebrates (lobsters and mollusks), certification and ratings efforts, fishery improvement projects, and sustainable purchasing commitments can improve fishing practices and increase fisher market access and revenue. For lower-value fisheries targeting species for domestic or regional consumption, sustainable purchasing commitments among local buyers, consumer awareness campaigns, and local certification and ratings schemes hold promise for shifting attitudes toward sustainability and increasing food security for local communities. Finally, fisher empowerment efforts including direct access to local markets and market information, training on improved post-harvest methods, and formation of fisher associations hold promise for increasing fisher incomes, reducing wasteful catch, increasing food security, and de-incentivizing unsustainable practices. Despite the potential of market-based interventions, specific approaches must be carefully tailored to the ecological and social reality of these systems, including the inherent unsustainability of commercial coral reef fisheries, the limited capacity for fisheries governance, the limited financial support of market-based initiatives, and the threatened status of coral reef ecosystems globally.

An Alternating Algorithm for Finding Linear Arrow-Debreu Market Equilibria

Motivated by the convergence result of mirror-descent algorithms to market equilibria in linear Fisher markets, it is natural for one to consider designing dynamics (specifically, iterative algorithms) for agents to arrive at linear Arrow-Debreu market equilibria. Jain (SIAM J. Comput. 37(1), 303–318, 2007) reduced equilibrium computation in linear Arrow-Debreu markets to the equilibrium computation in bijective markets, where everyone is a seller of only one good and a buyer for a bundle of goods. In this paper, we design an algorithm for computing linear bijective market equilibrium, based on solving the rational convex program formulated by Devanur et al. The algorithm repeatedly alternates between a step of gradient-descent-like updates and a distributed step of optimization exploiting the property of such convex program. Convergence can be ensured by a new analysis different from the analysis for linear Fisher market equilibria.

Infinite-Dimensional Fisher Markets: Equilibrium, Duality and Optimization

This paper considers a linear Fisher market with n buyers and a continuum of items. In order to compute market equilibria, we introduce (infinite-dimensional) convex programs over Banach spaces, thereby generalizing the Eisenberg-Gale convex program and its dual. Regarding the new convex programs, we establish existence of optimal solutions, KKT conditions, as well as strong duality. All these properties are established via non-standard arguments, which circumvent the limitations of duality theory in optimization over infinite-dimensional vector spaces. Furthermore, we show that there exists a pure equilibrium allocation, i.e., a division of the item space. Similar to the finite-dimensional case, a market equilibrium under the infinite-dimensional Fisher market is Pareto optimal, envy-free and proportional. We also show how to obtain the (a.e. unique) equilibrium prices and a pure equilibrium allocation from the (unique) equilibrium utility prices. When the item space is the unit interval [0,1] and buyers have piecewise linear utilities, we show that approximate equilibrium prices can be computed in polynomial time. This is achieved by solving a finite-dimensional convex program using the ellipsoid method. To this end, we give nontrivial and efficient subgradient and separation oracles. For general buyer valuations, we propose computing market equilibrium using stochastic dual averaging, which finds approximate equilibrium prices with high probability.

Markets for public decision-making

A public decision-making problem consists of a set of issues, each with multiple possible alternatives, and a set of competing agents, each with a preferred alternative for each issue. We study adaptations of market economies to this setting, focusing on binary issues. Issues have prices, and each agent is endowed with artificial currency that she can use to purchase probability for her preferred alternatives (we allow randomized outcomes). We first show that when each issue has a single price that is common to all agents, market equilibria can be arbitrarily bad. This negative result motivates a different approach. We present a novel technique called pairwise issue expansion, which transforms any public decision-making instance into an equivalent Fisher market, the simplest type of private goods market. This is done by expanding each issue into many goods: one for each pair of agents who disagree on that issue. We show that the equilibrium prices in the constructed Fisher market yield a pairwise pricing equilibrium in the original public decision-making problem which maximizes Nash welfare. More broadly, pairwise issue expansion uncovers a powerful connection between the public decision-making and private goods settings; this immediately yields several interesting results about public decisions markets, and furthers the hope that we will be able to find a simple iterative voting protocol that leads to near-optimum decisions.

Competitive equilibrium based personal data market model

Background/Objectives: In a digital economy, with the increasing commercial value, personal data is viewed as a commodity to be bought and sold. Data owners expect an appropriate compensation for trading off their privacy depending on how they value their privacy. Simultaneously, data consumers want to maximize their utility which is dependent on the value derived from the data. Consequently, a data market model that optimally recompenses data owners and maximizes the profits of data consumers is required. Methods: In this study, a data market model and pricing mechanism based on Fisher market model and competitive equilibrium are presented where the value derived from the data is calculated from information entropy. The proposed data model and the pricing mechanism jointly and simultaneously maximize the profit of data owners and the utility of data buyers. Findings: Experiments are conducted on adult data set to validate the efficacy of the proposed approach. Data owners are classified as risk averse, risk neutral, risk taking and privacy regarders. Subsequently, prices of data samples are adjusted to reach equilibrium as defined by the Fisher market model maximizing simultaneously and jointly the profit of data owners and the utility of data buyers. Applications: The proposed competitive equilibrium based personal data market model can be used to find equilibrium prices and bundles of data samples for each data buyer at these prices maximizing the utility of data buyer subject to his budgetary constraints and data requirements, and data owners\' privacy preferences. Keywords: Personal data; Competitive equilibrium; Fisher market; Information entropy; Data buyers; Data owners; Data market

Market Clearing–based Dynamic Multi-agent Task Allocation

Realistic multi-agent team applications often feature dynamic environments with soft deadlines that penalize late execution of tasks. This puts a premium on quickly allocating tasks to agents. However, when such problems include temporal and spatial constraints that require tasks to be executed sequentially by agents, they are NP-hard, and thus are commonly solved using general and specifically designed incomplete heuristic algorithms. We propose FMC_TA, a novel such incomplete task allocation algorithm that allows tasks to be easily sequenced to yield high-quality solutions. FMC_TA first finds allocations that are fair (envy-free), balancing the load and sharing important tasks among agents, and efficient (Pareto optimal) in a simplified version of the problem. It computes such allocations in polynomial or pseudo-polynomial time (centrally or distributedly, respectively) using a Fisher market with agents as buyers and tasks as goods. It then heuristically schedules the allocations, taking into account inter-agent constraints on shared tasks. We empirically compare our algorithm to state-of-the-art incomplete methods, both centralized and distributed, on law enforcement problems inspired by real police logs. We present a novel formalization of the law enforcement problem, which we use to perform our empirical study. The results show a clear advantage for FMC_TA in total utility and in measures in which law enforcement authorities measure their own performance. Besides problems with realistic properties, the algorithms were compared on synthetic problems in which we increased the size of different elements of the problem to investigate the algorithm’s behavior when the problem scales. The domination of the proposed algorithm was found to be consistent.

On the Proximity of Markets with Integral Equilibria

We study Fisher markets that admit equilibria wherein each good is integrally assigned to some agent. While strong existence and computational guarantees are known for equilibria of Fisher markets with additive valuations (Eisenberg and Gale 1959; Orlin 2010), such equilibria, in general, assign goods fractionally to agents. Hence, Fisher markets are not directly applicable in the context of indivisible goods. In this work we show that one can always bypass this hurdle and, up to a bounded change in agents’ budgets, obtain markets that admit an integral equilibrium. We refer to such markets as pure markets and show that, for any given Fisher market (with additive valuations), one can efficiently compute a “near-by,” pure market with an accompanying integral equilibrium.Our work on pure markets leads to novel algorithmic results for fair division of indivisible goods. Prior work in discrete fair division has shown that, under additive valuations, there always exist allocations that simultaneously achieve the seemingly incompatible properties of fairness and efficiency (Caragiannis et al. 2016); here fairness refers to envyfreeness up to one good (EF1) and efficiency corresponds to Pareto efficiency. However, polynomial-time algorithms are not known for finding such allocations. Considering relaxations of proportionality and EF1, respectively, as our notions of fairness, we show that fair and Pareto efficient allocations can be computed in strongly polynomial time.

Scrip Economies Are Fair and (Approximately) Efficient

In many settings, resources are allocated among agents repeatedly over time without the use of monetary transfers: consider, for example, allocating server-time to company employees, rooms to students, or food among food banks. Here, the central challenge is to allocate resources efficiently despite the absence of payments. In this work we study a simple online variant of the standard Fisher market, where we endow all agents with a budget of artificial credits, and then repeatedly run simultaneous first-price auctions for each item in each period. Owing to their simplicity, such mechanisms have been gaining in popularity, with several recent successful implementations, most notably, by Feeding America for US food banks. Our goal in this paper is to understand the incentive and efficiency properties of these mechanisms. Our main contribution in this work is to show that such simple mechanisms enjoy strong performance guarantees under minimal rationality assumptions. Formally, we consider a dynamic allocation setting, where multiple items are available in each period, and each agent’s preference is a fractionally subadditive (XOS) valuation function, drawn independently from some underlying distributions. Agents start with some initial endowment of credits, and in each round, participate in simultaneous first-price auctions for each item. We benchmark the performance this mechanism against widely-adopted solution concepts from the literature on bargaining. In particular, we show that irrespective of the strategies of other agents, each agent can obtain a 1/2 − o(1) approximation of their ideal utility, i.e., the utility they derive from their favorite allocation subject to giving other agents their share (proportional to initial endowments) of the items. We do this by providing a lower-bound on the maximum value of each agent in the mechanism. Our results provide strong argument for a wider adoption of artificial currency mechanisms in several ways. First, our guarantees have frugal strategic and informational requirements – agents do not need to know the preferences or strategies of other participants in order to secure a half of their ideal utility. Second, the performance guarantees are independent of the cardinality of the type-space, and agnostic of the underlying type distributions. Finally, our results also yield operational insights into how the principal can choose the appropriate credit endowments in order to target a particular ideal utility profile.