Competitive Equilibrium Research Articles

Cities and biodiversity: Spatial efficiency of land use

While there is an increased focus on promoting eco-friendly cities, biologically important but dangerous wildlife creatures encroach into cities, which can cause human-wildlife conflicts. We examine how the encroachment of wildlife affects humans’ decisions to exterminate wildlife, the spatial patterns of conflicts, and the size of cities. We develop a theoretical model where animals optimize their food intake by spreading out in response to heterogeneous feeding grounds in cities, and humans choose their housing location and exterminate wildlife in response to the presence of wildlife. We characterize a Nash equilibrium of land competition in every location and then prove the existence and uniqueness of the spatial equilibrium. We solve the optimal and the equilibrium and obtain properties with respect to human population density, the densities of wildlife species, the level of countermeasures against wildlife, and human-wildlife conflicts at each location; the numbers of species; and the size of cities.

Social Optimum in the Basic Bathtub Model

The basic bathtub model extends Vickrey’s bottleneck model to admit hypercongestion (traffic jam situations). A fixed number of identical commuters travel a fixed distance over a dense network of identical city streets between home and work in the early morning rush hour under dynamic macroscopic fundamental diagram congestion. This paper investigates social optima in the basic bathtub model and contrasts them with the corresponding competitive equilibria. The model gives rise to delay-differential equations, which considerably complicate analysis of the solution properties and design of computational solution algorithms. This paper considers the cases of smooth and strictly concave travel utility functions and of α–β–γ tastes. For each it develops a customized solution algorithm, which it applies to several examples, and for α–β–γ tastes, it derives analytical properties as well. Departures may occur continuously, in departure masses, or a mix of the two. Additionally, hypercongestion may occur in the social optimum. This paper explores how these qualitative solution properties are related to tastes.

Invisible Hand, invisible morals: An experiment

Evidence continues to suggest that humans behave consistent with selfishness when interacting in competitive markets: “this general result remains one of the most robust findings in experimental economics” (John List, 2017). However, in competitive markets, behaviour consistent with selfishness need not imply selfish preferences. Further, the competitive equilibrium may not be welfare-maximising in the presence of non-selfish preferences. I develop an experiment to scrutinize buyers’ preferences in a competitive market setting through the revelation of sellers’ profit to buyers. I find that while prices in the market may converge to standard (selfish) equilibrium predictions, buyers’ choices reveal non-selfish preferences. Controlling for prices, buyers are more likely to choose sellers who earn a smaller profit from the trade. Consequently, standard notions of efficiency may be insufficient for characterising the welfare properties of the competitive equilibrium.

Exploiting complete linear descriptions for decentralized power market problems with integralities

It is well known that linear prices supporting a competitive equilibrium exist in the case of convex markets, however, in the presence of integralities this is open and hard to decide in general. We present necessary and sufficient conditions for the existence of such prices for decentralized market problems where market participants have integral decision variables and their feasible sets are given in complete linear description. We utilize total unimodularity and the aforementioned conditions to show that such linear prices exist and present some applications. Furthermore, we compute competitive equilibria for two classes of decentralized market problems arising in energy markets and show that competitive equilibria may exist regardless of integralities.

Divine Proportion of The Invisible Hand: a New Look at Adam Smith’s Natural Theology

Recent research on labor-search-leisure model has described local multiple equilibria of Invisible hand under wage and price dispersion. This paper analyzes the general competitive equilibrium, where the Invisible hand creates harmonic proportions of mutually beneficial exchange. The analysis results in the rigorous mathematical proof that at the general competitive equilibrium both the marginal rate of substitution of leisure for consumption and marginal rate of transformation of production into services are equal to the golden ratio conjugate, whereas both the intensity of consumption and the sales-costs of production ratio are equal to the golden ratio itself, also called the divine proportion. On commodity market the golden ratio conjugate equalizes the gravitation or attractiveness of both seller and buyer. Local monopoly and monopsony disappear, and the competitive equilibrium really becomes perfect. In marriage markets the golden ratio conjugate equalizes the attractiveness of both man and woman and creates the ideal family. These results bring us back to the theological grounds of Adam Smith’s works; it gives a new view on his idea of natural rates of both wages and profit. It really can be argued that there was a good reason to apply the natural theology approach to the analysis of exchange at times of the ‘Wealth of Nations’.

Out-of-equilibrium dynamics and excess volatility in firm networks

We study the conditions under which input-output networks can dynamically attain a competitive equilibrium, where markets clear and profits are zero. We endow a classical firm network model with minimal dynamical rules that reduce supply/demand imbalances and excess profits. We show that the time needed to reach equilibrium diverges to infinity as the system approaches an instability point beyond which the Hawkins-Simons condition is violated and competitive equilibrium is no longer admissible. We argue that such slow dynamics is a source of excess volatility, through accumulation and amplification of exogenous shocks. Factoring in essential physical constraints absent in our minimal model, such as causality or inventory management, we then propose a dynamically consistent model that displays a rich variety of phenomena. Competitive equilibrium can only be reached after some time and within some restricted region of parameter space, outside of which one observes spontaneous periodic and chaotic dynamics, reminiscent of real business cycles. This suggests an alternative explanation of excess volatility in terms of purely endogenous fluctuations. Diminishing return to scale and increased perishability of goods are found to ease convergence towards equilibrium.

Commodity tax competition and cross-border shopping in a tripoint model

This paper extends commodity tax competition to cross-border shopping in a two-country model of three countries with a tripoint border and investigates whether a pure-strategy Nash equilibrium of tax competition exists. First, we find that unlike existing studies on the two-country model, there is no pure-strategy Nash equilibrium for tax competition in the three-country tripoint model. Second, we consider partial tax coordination between two countries and investigate how the population size of the countries affects the Nash equilibrium tax rates and tax revenues under tax coordination. Our results suggest that the existence of a pure-strategy Nash equilibrium is limited to a specific case of only two countries. When three countries with a tripoint engage in tax competition, we cannot predict what happens in the fiscal game between governments by the Nash equilibrium. Furthermore, the Appendix focuses on the marginally deviation-proof sets of tax rates instead of the Nash equilibrium and compares tax rates and tax revenues among the two sets of tax rates.

Engineered nanoparticles enable deep proteomics studies at scale by leveraging tunable nano–bio interactions

SignificanceDeep profiling of the plasma proteome at scale has been a challenge for traditional approaches. We achieve superior performance across the dimensions of precision, depth, and throughput using a panel of surface-functionalized superparamagnetic nanoparticles in comparison to conventional workflows for deep proteomics interrogation. Our automated workflow leverages competitive nanoparticle-protein binding equilibria that quantitatively compress the large dynamic range of proteomes to an accessible scale. Using machine learning, we dissect the contribution of individual physicochemical properties of nanoparticles to the composition of protein coronas. Our results suggest that nanoparticle functionalization can be tailored to protein sets. This work demonstrates the feasibility of deep, precise, unbiased plasma proteomics at a scale compatible with large-scale genomics enabling multiomic studies.

Scheduling Flexible Nonpreemptive Loads in Smart-Grid Networks

A market consisting of a generator with thermal and renewable generation capability, a set of <i>nonpreemptive</i> loads (i.e., loads which cannot be interrupted once started), and an independent system operator (ISO) is considered. Loads are characterized by durations, power demand rates, and utility for receiving service, as well as disutility functions giving preferences for time slots in which service is preferred. Given this information, along with the generator&#x2019;s thermal generation cost function and forecast renewable generation, the social planner solves a mixed-integer program to determine a load activation schedule which maximizes social welfare. Assuming price-taking behavior, we develop a competitive equilibrium concept based on a relaxed version of the social planner&#x2019;s problem, which includes prices for consumption and incentives for flexibility, and allows for probabilistic allocation of power to loads. Considering each load as representative of a population of identical loads with scaled characteristics, we demonstrate that the relaxed social planner&#x2019;s problem gives an exact solution to the original mixed integer problem in the large population limit, and give a market mechanism for implementing the competitive equilibrium. Finally, we evaluate via case study the benefit of incorporating load flexibility information into power consumption and generation scheduling in terms of proportion of loads served and overall social welfare.

On the Gains from Tradable Benefits‐in‐kind: Evidence for Workfare in India

Widely‐used in‐kind benefits are often rationed across potential participants in social programmes. This poses an operational challenge in implementation with limited public information. One possible solution is to randomize assignment given the available information. However, as this paper shows, neither the purposive targeting of in‐kind benefits nor randomized assignment is likely to yield a competitive equilibrium given private information on diverse personal gains. The paper characterizes equilibrium assignments and the implications for policy and evaluation. The theory is applied to an antipoverty programme providing rationed jobs on rural public works in a poor state of India. Special‐purpose survey data reveal large unexploited gains from allowing tradable assignments. The paper shows that the potential gains exceed those from poverty targeting and stylized cash transfer options. Realizing the scope for poverty reduction by such means will undoubtedly require complementary efforts in reducing the influence of other market and institutional factors creating poverty in the first place, including inequalities in access to credit and knowledge.

Illegal Immigration, Labour Supply, and Fiscal Policies

ABSTRACT This paper explores the economic impact of illegal immigration in a dynamic general equilibrium model when the domestic labour supply is elastic and the fiscal policies include various taxes and income transfers. We first find that despite the mixed effects of illegal immigration on endogenous leisure-labour and saving-investment decisions, illegal immigration improves the welfare of domestic households in a dynamic competitive economy. The countervailing effects, however, show the wage differential improves individual welfare but hurts aggregate production. We then examine how the fiscal policies of illegal immigration influence a decentralised competitive equilibrium. Whereas the equivalence of economic incidence requires taxation on illegal immigrants, partial compliance causes the nonequivalence between labour income taxes and payroll taxes. Again, due to the countervailing effects, fiscal burden causes an adversary effect on the welfare of domestic households but stimulates aggregate economic performance. The opposite effects also arise in the fiscal contribution of illegal immigrants.

Learning to Collude in a Pricing Duopoly

Problem definition: This paper addresses the question whether or not self-learning algorithms can learn to collude instead of compete against each other, without violating existing competition law. Academic/practical relevance: This question is practically relevant (and hotly debated) for competition regulators, and academically relevant in the area of analysis of multi-agent data-driven algorithms. Methodology: We construct a price algorithm based on simultaneous-perturbation Kiefer–Wolfowitz recursions. We derive theoretical bounds on its limiting behavior of prices and revenues, in the case that both sellers in a duopoly independently use the algorithm, and in the case that one seller uses the algorithm and the other seller sets prices competitively. Results: We mathematically prove that, if implemented independently by two price-setting firms in a duopoly, prices will converge to those that maximize the firms’ joint revenue in case this is profitable for both firms, and to a competitive equilibrium otherwise. We prove this latter convergence result under the assumption that the firms use a misspecified monopolist demand model, thereby providing evidence for the so-called market-response hypothesis that both firms’ pricing as a monopolist may result in convergence to a competitive equilibrium. If the competitor is not willing to collaborate but prices according to a strategy from a certain class of strategies, we prove that the prices generated by our algorithm converge to a best-response to the competitor’s limit price. Managerial implications: Our algorithm can learn to collude under self-play while simultaneously learn to price competitively against a ‘regular’ competitor, in a setting where the price-demand relation is unknown and within the boundaries of competition law. This demonstrates that algorithmic collusion is a genuine threat in realistic market scenarios. Moreover, our work exemplifies how algorithms can be explicitly designed to learn to collude, and demonstrates that algorithmic collusion is facilitated (a) by the empirically observed practice of (explicitly or implicitly) sharing demand information, and (b) by allowing different firms in a market to use the same price algorithm. These are important and concrete insights for lawmakers and competition policy professionals struggling with how to respond to algorithmic collusion.

Expectations-based loss aversion in contests

This paper studies a multi-player lottery contest in which heterogeneous contestants exhibit reference-dependent loss aversion à la Kőszegi and Rabin (2006, 2007). We verify the existence and uniqueness of pure-strategy choice-acclimating personal Nash equilibrium (CPNE) under moderate loss aversion and fully characterize the equilibrium. The equilibrium sharply contrasts with that in the two-player risk-neutral symmetric case. Loss aversion can lead contestants' individual efforts to change nonmonotonically, while the total effort strictly decreases. Further, it always leads to a more elitist distributional outcome, in the sense that a smaller set of contestants remain active in the competition and stronger contestants' equilibrium winning probabilities increase. We demonstrate that loss aversion generates a fundamentally different decision problem than risk aversion and develop a rationale that explains the contrasting predictions from the two frameworks. Finally, our results are robust under the alternative equilibrium concept of preferred personal Nash equilibrium (PPNE).

Auction mechanism and time-varying Walrasian equilibrium: an application to stock market

Cet article d&#233;veloppe une th&#233;orie analytique du prix des actions dans un environnement boursier. L&#8217;approche propos&#233;e correspond &#224; un m&#233;canisme r&#233;el d&#8217;ench&#232;res o&#249; l&#8217;information en temps r&#233;el est trait&#233;e sur un terminal &#233;lectronique de n&#233;gociation boursi&#232;re. Les ressources en actions, les ressources en capital &#171;&#160;libre&#160;&#187; (qui peut &#234;tre &#233;chang&#233; contre des actions) d&#233;tenues par les participants &#224; la n&#233;gociation sont consid&#233;r&#233;es comme des variables originales du mod&#232;le ainsi que la notion de structure de portefeuille cible des investisseurs. Les relations d&#233;riv&#233;es pour la demande nette agr&#233;g&#233;e sur le march&#233; boursier permettent de d&#233;crire le prix des actions en tant que r&#233;sultat de l&#8217;&#233;change sur le march&#233; dans l&#8217;approximation de l&#8217;&#233;quilibre walrasien. Les auteurs proposent une technique &#233;conom&#233;trique appropri&#233;e pour estimer les param&#232;tres de la demande nette agr&#233;g&#233;e instantan&#233;e. La validit&#233; de la th&#233;orie est confirm&#233;e par une comparaison directe des prix mod&#233;lis&#233;s et observ&#233;s des actions ainsi que par l&#8217;&#233;valuation des strat&#233;gies d&#8217;investissement bas&#233;es sur la th&#233;orie.

Utility-refined and budget-refined [formula omitted]-competitive equilibria

In finitely additive exchange economies the usual definition of competitive equilibrium can result in an empty equilibrium set, and therefore one has to consider notions of ɛ-competitive equilibria. In this paper we investigate the relationship between two notions of ɛ-competitive equilibria.

Integrated epi-econ assessment of vaccination

Using an integrated epi-econ model, we compute the value of vaccines for Covid-19, both under a planner’s solution and in competitive equilibrium. The specific model, developed in Boppart, Harmenberg, Hassler, Krusell, and Olsson (2020), factors in not just value-of-life aspects along with standard economic variables but also the value of leisure activities that rely on a social component. We find that the societal value of vaccination is large; we estimate that, translated into monetary terms, the value of vaccinating one young individual in the competitive equilibrium is $17,800. Externalities are large: less than half the societal value is internalized by individuals (assuming that they act purely in their self-interest). Finally, behavioral responses are important, with a substantial share of the value of vaccines being attributed to people enjoying more socially-oriented leisure when more people are vaccinated.

Accounting for structural transformation in the U.S.

I account for the sources of labor reallocation from the manufacturing sector towards services in the United States for the 1950 to 2010 period. I use a multi-sector model with sector-specific productivity growth and non-homothetic preferences to decompose the sources of labor reallocation into supply-side, demand-side, and wedge distortions. The decomposition is performed in the context of a competitive economy where the competitive equilibrium with wedges reproduces prices and quantities of the economy exactly. During the 1950–2010 period, the demand-side mechanism accounts for 57% of the reallocation of labor and the supply-side for 28%. Focusing only in the sub-period from 1950 to 1980, 70% of the reallocation is demand-driven. In the sub-period between 1980 and 2010, the three sources of labor reallocation are quantitatively important. Demand-side accounts for 47%, supply-side for 42% and wedge distortions for 10%.

Transfer paradox in a general equilibrium economy: An experimental investigation

The transfer paradox, whereby a transfer of resources that influences the equilibrium price benefits the donor while harming the recipient, is a classic paradox in general equilibrium theory. This paper pursues an experimental investigation of the transfer paradox using a three-agent pure exchange economy that is predicted to have such a paradox. The results indicate that an endowment adjustment among agents influences the market price, and consequently the donors benefit from the transfer, consistent with the competitive equilibrium theory. When given an option to make a transfer, half of donor agents voluntarily decide to adjust the endowment distribution.

An Adverse Effect of an Anticipated Tax Change: Investment Runs in Competitive Equilibrium

An Adverse Effect of an Anticipated Tax Change: Investment Runs in Competitive Equilibrium

Resource, Competition, and General Equilibrium Effects of Innovation Subsidies

Resource, Competition, and General Equilibrium Effects of Innovation Subsidies