Tracing Equilibrium in Dynamic Markets via Distributed Adaptation

Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a significant amount of interest in algorithmic game theory, mainly for the prominent case of Fisher markets. Natural and decentralized processes like tatonnement and proportional response dynamics (PRD) converge quickly towards equilibrium in large classes of Fisher markets. Almost all of the literature assumes that the market is a static environment and that the parameters of agents and goods do not change over time. In contrast, many large real-world markets are subject to frequent and dynamic changes. In this paper, we provide the first provable performance guarantees of discrete-time tatonnement and PRD in markets that are subject to perturbation over time. We analyze the prominent class of Fisher markets with CES utilities and quantify the impact of changes in supplies of goods, budgets of agents, and utility functions of agents on the convergence of tatonnement to market equilibrium. Since the equilibrium becomes a dynamic object and will rarely be reached, our analysis provides bounds expressing the distance to equilibrium that will be maintained via tatonnement and PRD updates. Our results indicate that in many cases, tatonnement and PRD follow the equilibrium rather closely and quickly recover conditions of approximate market clearing. Our approach can be generalized to analyzing a general class of Lyapunov dynamical systems with changing system parameters, which might be of independent interest

Econometricmodel of industry, profits, and tatonnement adjustment

This study presents a quantitative analysis of one of the main forces in an economy, disaggregated short term profits, and of the process whereby the system adjusts itself to the temporary equilibrium indicated by such forces, a generalised tatonnement. Quarterly ten-equation econometric models explaining industry behaviour and profits are developed from a basic industry model for ten mutually exclusive and exhaustive industries. These models are connected with each other and with the whole by a number of linkages and by being embedded in a skeletal economy model. The system is solved at two levels. Firstly the industry models are solved individually for given values of the linking variables; the results are used to choose between alternative specifications of the models and to assess the adequacy of the formulation adopted. Secondly the whole system is solved iteratively by solving the industry models for some given trial values of the linking variables, using these solutions to derive new trial values, and repeating the process until these values converge; the results are used to assess the efficacy of the tatonnement process. The results indicate that the models proposed are good predictors of disaggregated short term profits and that the tatonnement process used produces rapid convergence to a consistent equilibrium. It is also suggested from the discrepancy between the tatonnement (quasi-competitive) and actual (imperfectly competitive) solutions that the capitalist system is inefficient in that it produces too much

Convex-Concave Min-Max Stackelberg Games

Min-max optimization problems (i.e., min-max games) have been attracting a great deal of attention because of their applicability to a wide range of machine learning problems. Although significant progress has been made recently, the literature to date has focused on games with independent strategy sets; little is known about solving games with dependent strategy sets, which can be characterized as min-max Stackelberg games. We introduce two first-order methods that solve a large class of convex-concave min-max Stackelberg games, and show that our methods converge in polynomial time. Min-max Stackelberg games were first studied by Wald, under the posthumous name of Wald's maximin model, a variant of which is the main paradigm used in robust optimization, which means that our methods can likewise solve many convex robust optimization problems. We observe that the computation of competitive equilibria in Fisher markets also comprises a min-max Stackelberg game. Further, we demonstrate the efficacy and efficiency of our algorithms in practice by computing competitive equilibria in Fisher markets with varying utility structures. Our experiments suggest potential ways to extend our theoretical results, by demonstrating how different smoothness properties can affect the convergence rate of our algorithms.Comment: 25 pages, 4 tables, 1 figure, Forthcoming in NeurIPS 202

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 t\^{a}tonnement, and run experiments that confirm our theoretical results

Statistical Inference for Fisher Market Equilibrium

Statistical inference under market equilibrium effects has attracted increasing attention recently. In this paper we focus on the specific case of linear Fisher markets. They have been widely use in fair resource allocation of food/blood donations and budget management in large-scale Internet ad auctions. In resource allocation, it is crucial to quantify the variability of the resource received by the agents (such as blood banks and food banks) in addition to fairness and efficiency properties of the systems. For ad auction markets, it is important to establish statistical properties of the platform's revenues in addition to their expected values. To this end, we propose a statistical framework based on the concept of infinite-dimensional Fisher markets. In our framework, we observe a market formed by a finite number of items sampled from an underlying distribution (the "observed market") and aim to infer several important equilibrium quantities of the underlying long-run market. These equilibrium quantities include individual utilities, social welfare, and pacing multipliers. Through the lens of sample average approximation (SSA), we derive a collection of statistical results and show that the observed market provides useful statistical information of the long-run market. In other words, the equilibrium quantities of the observed market converge to the true ones of the long-run market with strong statistical guarantees. These include consistency, finite sample bounds, asymptotics, and confidence. As an extension, we discuss revenue inference in quasilinear Fisher markets

Insurance mechanisms for the reliability of electricity supply

In the context of rapid shifts in the energy supply mix and the onset of climate change, tail risk in power systems presents an emergent threat to system reliability. Flexible resources like load control, storage and distributed energy resources are potent tools to alleviate system strains during extreme events. However, market participants need appropriate economic incentives to exploit the value of such resources. While spot prices serve as robust indicators of real-time scarcity, a complex challenge lies in translating short-term signals to long-term investment decisions. This is especially pertinent in the context of markets marked by incompleteness, and agents with pronounced aversion to risk. The financial technology of insurance is targeted at the assessment, pricing, and management of extreme and catastrophic risks. This thesis proposes the novel application of insurance contracts and risk architectures to modern electricity markets, extending existing approaches to reliability risk management. This leads to the central research question of this thesis: Can the delivery of electricity service to consumers be made more reliable through the application of insurance mechanisms? The thesis investigates this question through three main streams of research: This first stream proposes the novel application of insurance contracts and capital reserving frameworks on the procurement of strategic reserves in electricity markets. A strategic reserve is a reliability mechanism in electricity markets that seeks to contract generation capacity incremental to that incentivised by short-term spot markets, for use in times of critical supply shortage. The insurance contracts allow consumers to elect differentiated reliability preferences, and align the financial interests of the insurer with such preferences. Application to a case study suggests the potential for improved consumer and social welfare while maintaining insurer viability and solvency. The design is also robust to non-transparent market parameters such as generator risk aversion. The second stream develops a locational insurance model to value resilience in power systems exposed to high-impact low-probability common-mode events. It is demonstrated that the implementation of this scheme in a large-scale power system could reduce load losses via investment in resilient distributed energy resources. However the cost of such insurance may be expensive, and appropriate calibration of consumer expectations and preferences is important. The final stream examines the interaction between the design of contracts between central agencies and storage resources, and the operation of the resources in the market. Five principles for central agency contracting are proposed, focusing on incentive compatibility with existing spot dispatch and limiting distortions to long-term hedging markets. The principles are applied specifically to contracts with storage resources. It is demonstrated that many early designs for storage auctions may be inconsistent with the identified principles. A novel storage contract ‘yardstick’ is proposed, which is shown to align participant dispatch incentives, while maintaining revenue support

Multiattribute Call Markets.

Multiattribute auctions support automated negotiation in settings where buyers and sellers have valuations for alternate configurations of a good, as defined by configuration attributes. Bidders express offers to buy or sell alternate configurations by specifying configuration-dependent reserve prices, and the auction determines both the traded goods and transaction prices based on these offers. While multiattribute auctions have been deployed in single-buyer procurement settings, the development of double-sided multiattribute auctions-allowing the free participation of both buyers and sellers-has received little attention from academia or industry. In this work I develop a multiattribute call market, a specific type of double auction in which bids accumulate over an extended period of time, before the auction determines trades based on the aggregate collection of bids. Building on a polynomial-time clearing algorithm, I contribute an efficient algorithm for information feedback. Supporting the implementation of market-based algorithms, information feedback support extends the range of settings for which multiattribute call markets achieve efficiency. Multiattribute auctions are only one of many auction variants introduced in recent years. The rapidly growing space of alternative auctions and trading scenarios calls for both a standardized language with which to specify auctions, as well as a computational test environment in which to evaluate alternate designs. I present a novel auction description language and deployment environment that supports the specification of a broad class of auctions, improving on prior approaches through a scripting language that employs both static parameter settings and rule-based behavior invocation. The market game platform, AB3D, can execute these auction scripts to implement multi-auction and multi-agent trading scenarios. The efficiency of multiattribute call markets depends crucially on the underlying valuations of participants. I analyze the expected performance limitations of multiattribute call markets, using existing analytical results where applicable. Addressing a lack of theoretical guidance in many natural settings, I introduce a computational metric on bidder valuations, and show a correlation between this metric and the expected efficiency of multiattribute call markets. As further validation, I integrate multiattribute markets into an existing supply chain simulation, demonstrating efficiency gains over a more conventional negotiation procedure.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60822/1/klochner_1.pd