Equilibrium Search Research Articles

Predefined-time convergence strategies for multi-cluster games in hybrid heterogeneous systems

This paper explores the problem of (generalized) Nash equilibrium search in multi-cluster games with heterogeneous dynamics and multiple constraints. Within this research framework, each agent acquires information solely through local interactions with its neighbors and forms clusters based on similarity of interests. These clusters manifest dual relationships of cooperation and competition: agents within the same cluster enhance decision-making capabilities through cooperation, while different clusters compete to maximize their respective benefits. To delve into these complex interactions among clusters and the learning and evolution processes among agents, four distributed control algorithms suitable for various scenario requirements are designed and implemented. These algorithms ensure that each agent converges to a Nash equilibrium (NE) or generalized Nash equilibrium (GNE) of the multi-cluster system within predefined time points. Finally, we apply these algorithms to the connectivity control problem of unmanned aerial vehicle swarms with diverse dynamics, validating the theoretical results through comprehensive simulations.

Unions: Wage floors, seniority rules, and unemployment duration

This paper examines the impact of unions on unemployment and wages in a dynamic equilibrium search model. We model a union as imposing a minimum wage and rationing jobs to ensure that the union's most senior members are employed. This generates rest unemployment, where following a downturn in their labor market, unionized workers are willing to wait for jobs to reappear rather than search for a new labor market. We characterize the hazard rate of exiting unemployment, and show that it is low at long durations whenever the union-imposed minimum wage is high; we establish that a high union-imposed minimum wage generates a compressed wage distribution and a high turnover rate of jobs — properties consistent with the data. Finally, we show that seniority rules lead to lower unemployment levels, relative to an alternative rule allocating jobs to workers randomly.

Partially directed search in the labor market

I study the labor market implications of an equilibrium search model with flexible degrees of information availability, which nests the random and directed search models as special cases. Workers have limited information about the payoffs of applying to different firms. Firms use wages to attract workers and mediate externalities among applicants. Limited information interacts with the allocative role of wages, leading to new predictions. Reducing information friction has non-monotonic impacts on efficiency. When the cost of acquiring information is low (high), alleviating the information friction reduces (exacerbates) the distortion in the market equilibrium. I then apply this model to discuss the implications of improvements in information technology and the spillover effects among workers in the labor market.

Labour Market Screening and the Design of Social Insurance: An Equilibrium Analysis of the Labour Market for the Disabled

Abstract This article studies how firms’ screening incentives in the labour market affect the optimal design of social insurance programs and quantitatively assesses the U.S. disability policies accounting for firms’ screening of the disabled. We develop an equilibrium search model where workers with different productivities have heterogeneous preferences over non-wage benefits and firms cannot offer an employment contract that explicitly depends on worker types. In this environment, firms may use contracts to screen out a certain type of workers, distorting employment rates and contracts in equilibrium. Therefore, the optimal structure of social insurance policies depends on firms’ screening incentives. We extend and structurally estimate this framework to quantitatively understand the inefficiencies arising from firms’ incentives to screen out disabled workers and examine the optimal joint design of disability insurance (DI) and various forms of firm subsidies. We find that hiring subsidies mitigate screening distortions; at the same time, they interact with DI by reducing the labour supply disincentives it generates. The optimal policy structure leads to a considerable welfare gain by simultaneously making firm subsidies and DI benefits more generous.

Contracting and search with heterogeneous principals and agents

This paper incorporates a risk-neutral principal-agent problem into a random search model to study contracting and search in general equilibrium. I introduce heterogeneity in principals' and agents' production technologies in terms of the distribution of output across states of nature. Under optimal contracting, this heterogeneity can give rise to complementarity in contracting between specific principal and agent types. In contrast to complementarity in production, complementarity in contracting affects only the division of the surplus but not its size and can induce principals to engage in overly intense search before forming a match. I show that a reduction in search frictions and contractual innovations can induce principals to engage in overly intense search.

Worker mobility and UI extensions

We develop an equilibrium search model with a labor force participation decision, job-to-job transitions, and endogenous separations. The calibrated model perfectly matches the observed labor market flows in US data. We use the model to simulate the effects of an extension of unemployment insurance benefits to 99 weeks. The reform leads to a decrease in employment, an increase in the labor force participation and unemployment rate, while it leaves labor productivity roughly constant. Using a model-based decomposition, as well as comparisons with alternative simplified models, we show that modeling workers’ participation decisions, job-to-job transitions, and endogenous separations together is crucial for a complete and accurate analysis of UI reforms.

Problem razdvojenega subjekta v delih Marjana Rožanca

After a short argumentation of the content, we synthetically highlight some of the main characteristics of Rožanc’s writing. Our interest is largely focused on his essays, as they reveal the most important characteristics of the author’s absorbed and subtle relationship towards the world. Through the notion of split character, the author furnished the basis of questions dealing with God and mankind, man and woman, games and sport, art and creativity, with a constant search for equilibrium and meaning.

Distributed Nash equilibrium searching for multi-agent games under false data injection attacks

In this paper, for the multi-agent system, the Nash equilibrium (NE) search problem for non-cooperative game with state constraints under false data injection (FDI) attack is studied. The FDI attack can directly destroy the connectivity between agents, resulting in the performance degradation or even failure for most NE search algorithms. We propose a new distributed NE search method to improve the performance of NE algorithms under FDI attacks. The NE algorithm is designed to find the solution of NE under network attack and make the system recover after the attack. However, most of the existing results only studied the NE algorithm of the non-attacking system, and the existing results rarely take into account whether the system state exceeds the safety limit, which can cause the system to crash. This paper solves the state constraints problem of the multi-agent game under the FDI attack. Finally, the reliability of the algorithm is verified by a numerical result.

On Accelerated Coordinate Descent Methods for Searching Equilibria in Two-Stage Transportation Equilibrium Traffic Flow Distribution Model

The search for equilibrium in a two-stage traffic flow model reduces to the solution of a special nonsmooth convex optimization problem with two groups of different variables. For numerical solution of this problem, the paper proposes to use the accelerated block-coordinate Nesterov-Stich method with a special choice of block probabilities at each iteration. Theoretical estimates of the complexity of this approach can markedly improve the estimates of previously used approaches. However, in the general case they do not guarantee faster convergence. Numerical experiments with the proposed algorithms are carried out in the paper.

The Open Monopolistic Competition Models: Market Equilibrium and Social Optimality

We study the monopolistic competition model of Dixit–Stiglitz–Krugman with additive separable utility and transport costs of “iceberg types”. The production costs are not necessary linear. We study two concepts: market equilibrium and social optimality. There are well-known facts in the closed economy under monopolistic competition: (1) “in market equilibrium, the elasticity of revenue equals the elasticity of total costs” and (2) “in social optimality, the elasticity of utility equals the elasticity of total costs”. Moreover, earlier Prof. Sergey Kokovin (HSE University, Russia) generated the idea that (3) “the search for equilibrium is equivalent to the problem of optimization, but revenue, not utility”. For the case of several countries, it turns out that facts (1) and (2) and prediction (3) remain mostly true.

Application of the Global Equilibrium Search Method for Solving Boolean Programming Problems

Introduction. The significance of methods and algorithms for solving discrete optimization problems in mathematical supporting computer technologies of diverse levels and objectives is increasing. Consequently, the efficacy of discrete optimization methods deserves particular attention, as it drives the advancement of techniques capable of solving complex real-world problems. This paper introduces the Global Equilibrium Search (GES) method as a highly effective approach for solving Boolean programming problems, thus contributing to the field's progress and applicability. Purpose. We describe the successful application of the approximate probabilistic GES method for effectively solving various Boolean programming problems. Results. This paper explores the application of sequential GES algorithms for solving Boolean linear, Boolean quadratic programming, and other related problems with their specific characteristics. In our study, we conducted a comparative analysis to assess the effectiveness of GES algorithms by evaluating them against state-of-the-art approaches. Additionally, to parallelize the optimization process for discrete programming problems, we introduced algorithm unions, specifically portfolios, and teams. The efficiency of GES algorithm portfolios and teams is investigated by solving the maximum weighted graph cut problem, with subsequent comparisons to identify distinctions between them. Conclusions. Based on the accumulated experience of applying GES algorithms and their modifications to solve discrete optimization problems, this study establishes the GES method as the leading approximate approach for Boolean programming. The results demonstrate the GES algorithm unions experience a significant boost in the optimization process speed, whereas algorithm teams demonstrate higher efficiency. Keywords: global equilibrium search method, Boolean programming problems, experimental studies, algorithm efficiency, algorithm unions (portfolios and teams).

Supply Constraints and Search Equilibrium in Office Markets

AbstractWe present a new conceptual framework to estimate office supply elasticity, where net business survival, physical and economic mismatch are used to identify frictional and structural vacancy. Alongside regulatory and geographical constraints, we also find an unobserved feature of supply elasticity linked to natural vacancy. Our results confirm that US Metropolitan Statistical Areas are generally supply inelastic and the search and matching process plays a key role in supply dynamics. In the least inelastic markets, investors tend to be more flexible to respond to negative demand shocks. As a result, we observe a reduction in structural vacancy and a subsequent increase in cyclical vacancy given the slow short-term movement in absorption. These findings also shed light upon office market dynamics during the COVID-19 period.

Youth multidimensional political activism between singularization and mutualism: the case of Up network

In the past two decades, research in both social movement studies and critical youth studies has recorded growing criticism by youth political activism of the individualising processes characteristic of the neoliberal turn. Based on research conducted in Italy with the new network of activists Up, the article analyses the search for a new equilibrium between processes of singularization, and a community life where solidarity, cooperation and mutualism can build local forms of the common and the collective. In the first part of the article, we describe our analytical tools such as singularization, mutualism and generation, and the way in which they can highlight current political imagination of Italian youth; in the second part we present the results of our investigation and the way in which interviewees claim to belong to a wider frame of the transformation of politics in individualized societies.

Competitive search with two-sided risk aversion

Search theory is widely used in economics to study markets where trading frictions are prevalent. However, all existing theoretical models assume that either buyers or sellers (or both) are risk neutral, and the case where both parties are risk averse remains unexplored. This paper is a first step to fill this gap. I analyze a static competitive search model where risk-averse agents with different wealth seek to exchange an indivisible good. The housing market is an important application since a home typically represents a large part of a person’s wealth. I prove that a competitive search equilibrium is constrained efficient, and derive a generalized Hosios condition that relates the gains of the two parties in each transaction. Under risk aversion, wealthier buyers are more concerned with increasing their trading probability than with getting the best price. The opposite is true for sellers when the coefficient of absolute risk aversion is non-increasing. This results in positive sorting in equilibrium, that is, wealthier (poorer) buyers and sellers trading with each other at higher (lower) prices. This sorting mechanism offers a novel explanation for why the separation between rich and poor neighborhoods can be persistent.

Letter to the Editor - Update from Ukraine: Development of the Cloud-based Platform for Patient-centered Telerehabilitation of Oncology Patients with Mathematical-related Modeling.

This Letter to the Editor provides an update on the research from the Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine. The Institute's research team in collaboration with Ternopil National Medical University began a new project called "Development of the cloud-based platform for patient-centered telerehabilitation of oncology patients with mathematical-related modeling." The project is dedicated to the development of a hybrid cloud-based platform, and the creation on its basis of information technology for the telemedicine rehabilitation of cancer patients, and adapted for patients with combat stress disorder. The distinctive features of the proposed technology are a combination of artificial intelligence methods with accurate mathematical methods for optimization: developing mathematical models of problems of discrete, and non-smooth optimization, subgradient space transformation algorithms (to minimize non-smooth functions with tens of thousands of variables), and a method of global equilibrium search, etc.

Mental Health Nurses’ Self-Care at Work, Searching for Equilibrium: An Interpretative Phenomenological Analysis

The nursing workforce plays a central role in quality health care delivery. Nursing work is associated with high levels of stress due to often unmanageable workloads. The associated attrition poses a serious challenge for recruitment and retention strategies. Self-care is recognised as a tactic for addressing workplace stressors, shaping a sense of cohesion where the world is viewed as comprehensible, meaningful, and manageable, thereby mitigating the risk of burnout. Yet research suggests it is not widely utilised by nurses. The aim of this study was to understand mental health nurses’ lived experience of self-care at work. The research was undertaken using an Interpretative Phenomenological Analysis methodology. In-depth individual interviews explored nurses’ attitudes to self-care and how they did or did not adopt self-care practices in the workplace. Data were analysed thematically. The Search for Equilibrium, was identified as the superordinate theme, developed from three subordinate themes, The past self: “tormented and spent”, the intricacy of self-care, and the trusted inner circle: “safe and supported”. These findings highlight the complexity of self-care and the importance of considering it as much broader than purely an intra-personal phenomenon, emphasising the importance of relationships and interpersonal connections. Time past, present, and future influenced how participants made sense of their workplace experiences. These findings provide a deeper understanding of self-care in response to workplace stress and could assist in developing strategies to promote self-care for nurses, and ultimately positively enhance recruitment.

Immigration, skill acquisition, and fiscal redistribution in a search equilibrium model

AbstractAs recent immigration flows are reshaping the host countries workforce composition, this paper aims to assess whether age composition and skill adjustment dynamics play a relevant role in the welfare impact of immigration. To this end, we build and simulate a search and matching model that allows for endogenous natives’ skill acquisition and intergenerational transfers to analyze the welfare effects of immigration on a selected group of 19 OECD countries. The obtained results are then compared with those obtained under different assumptions on age composition and skill adjustment dynamics. Our comparative statics analysis shows that stronger job creation effects take place when natives adjust their skill in response to immigration. Moreover, taking into account age composition plays a key role in assessing the fiscal impact of immigration, which turns out to be positive when we include intergenerational transfers to retirees and immigration is high-skilled. Finally, we find that our model yields more optimistic welfare effects than standard search models that abstract from skill decision and intergenerational redistribution.

Marketmaking Middlemen

AbstractThis article develops a model in which market structure is determined endogenously by the choice of intermediation mode. There are two representative modes of intermediation that are widely used in real‐life markets: one is a middleman mode where an intermediary purchases inventory from the wholesale market and resells to buyers; the other is a market‐making mode where an intermediary offers a platform for buyers and sellers to meet and trade. We show that a marketmaking middleman, who adopts a mixture of these two intermediation modes, can emerge in a directed search equilibrium and discuss implications for the market structure.

“Infinitely fragile, short-lived, vulnerable…”: Motives of Frailty of the World and Human Resistance to it in Olga Tokarczuk’s Prose

The article is devoted to the analysis of motives of frailty of the world and human resistance to it in Olga Tokarczuk’s prose, based on the narrative of corporeality / materiality. All kinds and levels of the depicted reality are subject to disintegration. We consider reflexions and bodily practices connected with disintegration and death (depiction of a dying, dead, sick, deformed, old body) as well as reflexions and bodily practices which embody resistance to mortality (relic worship, resurrection, dissection, copying, counterfeiting, cloning, etc.). One of the mediated ways of resisting entropy and decay is also the search for harmony and equilibrium between the heavenly and the earthly and the interrelation of their orders, the desire for orderliness as an unattainable goal. In this context the motives of predicting the future, astrology, the place of cosmogonic, theogonic and other theories are analyzed. The way to resist entropy and decay is the word and the narrative, which allows to find a fragile balance in the perishable world. In this connection the ways of resistance to frailty of the world and thanatic fear at the biographic and autopsychotherapeutic level – by means of mythodrama narrative and desensitization narrative are considered.

On the foundations of competitive search equilibrium with and without market makers

The literature offers two interpretations of competitive search equilibrium, one based on a Nash approach and the other on a market-maker approach. When each buyer visits only one seller, the two approaches are equivalent. However, when each buyer visits multiple sellers, this equivalence can break down. We present a model in which every buyer visits 2 sellers. A buyer who trades with one seller receives a value of s, while a buyer who trades with 2 sellers receives value 1. Letting s vary from 0 (perfect complements) to 1 (perfect substitutes) we characterize the competitive search equilibrium under the two interpretations. We show that for low values of s, the Nash and market-maker competitive search equilibria coincide, but the common equilibrium is inefficient. For intermediate values of s, the two equilibria again coincide and are efficient. Finally, for high values of s, the Nash and market-maker equilibria differ, and only the latter is efficient.