Efficient Equilibrium Research Articles

Coordination failure in experimental banks of different sizes

We run a laboratory experiment to investigate how group size affects coordination in a bank-run game, in which participants choose simultaneously whether to withdraw or not and group members change over time. We find that bank size significantly affects the individual withdrawal probability, which is on average 12% higher in large than in small banks. In the initial round(s), all groups exhibit a similar withdrawal rate of about 40%; then, large and medium banks converge to the bank-run equilibrium, while small banks exhibit no systematic convergence. In all banks, experience and beliefs significantly affect the probability to withdraw and to experiment, i.e., to take in the current round the decision opposite to what was the best response in the previous one. We show that experimentation is a strategic choice, and interpret it as an attempt at promoting group convergence towards the efficient equilibrium.

Naked exclusion with heterogeneous buyers

We investigate the effects of buyer heterogeneity in a market where an incumbent firm deters entry when it signs enough exclusionary contracts with buyers. With heterogeneous buyers, several well-known results in exclusionary contracting with homogenous buyers are overturned and novel ones emerge. First, inefficient equilibria exist in which exclusionary contracts are signed but entry still occurs, and the loss of consumer surplus falls on small buyers. Second, sequential contracting may be more pro-competitive than simultaneous contracting in the sense that entry occurs under sequential but not simultaneous contracting. When this happens, sequential contracting Pareto dominates simultaneous contracting. We extend our analysis to consider downstream competition and breach of contract.

Monetary Policy and Heterogeneity: An Analytical Framework

Abstract THANK is a tractable heterogeneous-agent New-Keynesian model that captures analytically core micro-heterogeneity channels of quantitative-HANK: cyclical inequality and risk; self-insurance, precautionary saving, and realistic intertemporal marginal propensities to consume. I use it to elucidate key transmission mechanisms and dynamic properties of HANK models. Countercyclical inequality yields aggregate-demand amplification and makes determinacy with Taylor rules more stringent; but solving the forward guidance puzzle requires procyclical inequality: a Catch-22. Solutions include combining inequality with a distinct risk channel, with compensating cyclicalities; I provide evidence that disposable income inequality was procyclical in the last two, Great and COVID recessions, while risk is countercyclical. Alternative policy rules also solve the Catch-22, e.g. price-level-targeting or, in the model version with liquidity, setting nominal public debt. Optimal policy with heterogeneity features a novel inequality-stabilization motive generating higher inflation volatility—but is unaffected by risk, insofar as the target efficient equilibrium entails no inequality.

Efficient risk sharing and separation

This paper extends the model of risk sharing with limited commitment to feature separation. Partners face idiosyncratic income and match quality shocks, share risk subject to limited commitment, and separate whenever they are better off doing so. We characterise analytically the sets of shock realisations where constrained-efficient separations occur and the dynamics of consumption while the risk-sharing partnership continues. The separation probability typically jumps as parameter values change continuously, and an additional inefficient equilibrium emerges. A key reason is complementarity between risk sharing and staying together today and in the future. Income inequality affects consumption inequality via its effect on separations, and consumption inequality can optimally exceed income inequality for any history of income realisations. Both partial risk sharing and separation are relevant for many applications, including the interaction between partners in a household and countries in an economic union.

A Digital Platform Strategy to Improve Food Waste Disposal Practices: Exploring the Case of "Too Good To Go"

This conceptual article delves into the intricate dynamics of global food security and the paradox of food waste, with a focus on Europe and Italy. Specifically, we examine the transformative potential of digital platforms, with a spotlight on the Too Good To Go platform, in tackling the challenge of redistributing food surpluses. In conventional market settings, the intricacies of food waste often go unnoticed by buyers and sellers, resulting in an inefficient equilibrium quantity determined solely by supply and demand forces. This failure to achieve an optimal outcome leads to a missed opportunity to maximize social benefit. Taking a microeconomic perspective, we highlight the platform's capacity to mitigate the adverse environmental and social impacts associated with food waste. Our findings illustrate how a market-based platform can address the inefficiencies and shortcomings of the Coase Theorem within the realm of food waste. By facilitating negotiation, reducing information asymmetries, and addressing environmental costs, the platform exemplifies how innovative market solutions can foster efficiency and sustainability.

Efficient equilibria in common interest voting games

We develop a unified derivation of asymmetric pure strategy equilibria and their optimality in the canonical common interest voting model of Austen-Smith and Banks (Am Polit Sci Rev 90(1):34–45, 1996). We also study the relationship between the most efficient equilibria, which have a remarkably simple and intuitive structure, and the symmetric mixed strategy equilibrium that has been commonly studied in the literature. In particular, while the efficiency in the symmetric mixed strategy equilibrium under unanimity rule is known to be decreasing in the number of voters, the efficiency does not depend on the number of voters above a threshold in the most efficient equilibria.

Pursuing a Grand Theory: Douglass C. North and the early making of a New Institutional Social Science (1950-1981)

PurposeThe paper provides a detailed historical account of Douglass C. North's early intellectual contributions and analytical developments in pursuing a Grand Theory for why some countries are rich and others poor.Design/methodology/approachThe author approaches the discussion using a theoretical and historical reconstruction based on published and unpublished materials.FindingsThe systematic, continuous and profound attempt to answer the Smithian social coordination problem shaped North's journey from being a young serious Marxist to becoming one of the founders of New Institutional Economics. In the process, he was converted in the early 1950s into a rigid neoclassical economist, being one of the leaders in promoting New Economic History. The success of the cliometric revolution exposed the frailties of the movement itself, namely, the limitations of neoclassical economic theory to explain economic growth and social change. Incorporating transaction costs, the institutional framework in which property rights and contracts are measured, defined and enforced assumes a prominent role in explaining economic performance.Originality/valueIn the early 1970s, North adopted a naive theory of institutions and property rights still grounded in neoclassical assumptions. Institutional and organizational analysis is modeled as a social maximizing efficient equilibrium outcome. However, the increasing tension between the neoclassical theoretical apparatus and its failure to account for contrasting political and institutional structures, diverging economic paths and social change propelled the modification of its assumptions and progressive conceptual innovation. In the later 1970s and early 1980s, North abandoned the efficiency view and gradually became more critical of the objective rationality postulate. In this intellectual movement, North's avant-garde research program contributed significantly to the creation of New Institutional Economics.

Wages as signals of worker mobility

We analyze a model in which workers direct their search on and off the job and employer–worker match productivities are private information. Employers can commit neither to post contracts such that wages are a function of tenure nor to disregard counteroffers. In this context, potential employers who do not observe workers' productivity in their current matches use wages as a signal of workers' willingness to switch jobs. In turn, this implies that the wage contracts that employers post in the market for entry jobs—the jobs unemployed workers search for—not only direct job search but also signal future worker mobility. When the costs of creating entry jobs are sufficiently small, the unique equilibrium supports the efficient allocation under full information. When the costs of creating entry jobs are sufficiently large, the efficient equilibrium may break down because match‐specific risk gives rise to a holdup problem in the market for entry jobs. Then the unique equilibrium may fail to reveal match productivities in the market for entry jobs. The nonrevealing equilibrium features wage posting—pooling wage contracts—as well as counteroffers, which eliminates the holdup problem at the cost of distorting worker mobility.

Delegated Persuasion and Pareto Efficient Equilibrium Selection in Games

Delegated Persuasion and Pareto Efficient Equilibrium Selection in Games

Relationships between economic and ecological indicators and greenhouse gas emissions: The perspective of farms in Poland at the regional level

Aligning farms with the European Green Deal necessitates precise identification and analysis of the interplay between primary economic factors and ecological dimensions. This study presents detailed research findings on the correlation between ecological indicators, CH4 and N2O emissions, and economic metrics within a regional framework. The research draws on data from farms participating in the European Agricultural Accounting Network (FADN) spanning 2010-2019. The resultant analysis underscores substantial correlations among the examined parameters. Regions characterised by heightened agricultural production intensity report elevated agricultural income. However, this is coupled with increased environmental impact and heightened greenhouse gas emissions, particularly among farms engaged in animal production. Mazowsze, Podlasie, Wielkopolska, and Slask exhibit notable progress in pro-environmental initiatives. In the Pomorze and Mazury regions, expenditures on fertilisation and plant protection remain close to the average, culminating in an efficient equilibrium of organic matter in the soil and minimal CH4 and N2O emissions per hectare.

Risk-adjusted efficiency and innovation: an examination of systematic difference and convergence among BRIC banks

We argue that technological progress and technology diffusion is improving innovation the banking industry, leading to a potential steady-state equilibrium in operational efficiency and innovation across banks with similar characteristics. Using the latest meta-frontier method, this study examined BRIC banks during the period from 2000 to 2020. We found that Indian and Brazilian banks are more innovative in reducing costs, whereas Indian and Chinese banks are more cost efficient. Chinese, Russian, Indian, and Brazilian banks rank first to fourth in profit efficiency and profit-making innovation, respectively. Risk-taking boosts group cost and profit efficiencies and profit-making innovation but reduces cost-reducing innovation in each country. BRIC banks diverged in innovation during the analysis period but slowly converged after the 2008 crisis. Reform policies, adoption of production technology, formulating regulations and investing in human capital and technologies are crucial for less efficient and innovative banks to catch-up with frontier banks.

Distributed Coordination of Charging Stations With Shared Energy Storage in a Distribution Network

Electric vehicle (EV) charging stations have experienced rapid growth, whose impacts on the power grid have become non-negligible. Though charging stations can install energy storage to reduce their impacts on the grid, the conventional “one charging station, one energy storage” method may be uneconomical due to the high upfront cost of energy storage. Shared energy storage can be a potential solution. However, effective management of charging stations with shared energy storage in a distribution network is challenging due to the complex coupling, competing interests, and information asymmetry between different agents. To address the aforementioned challenges, this paper first proposes an equilibrium model to characterize the interaction among charging stations, shared energy storage, and the distribution network. We prove that the equilibrium coincides with the centralized optimization result with trading prices equaling the value of dual variables at optimum. Then, to achieve the efficient equilibrium, a distributed coordination mechanism with a prediction and a correction step is developed to guide the behaviors of different agents with proof of convergence. Numerical experiments and comprehensive performance comparisons are conducted to validate the theoretical results and show the advantages of the proposed mechanism.

(In)efficiency in private value bargaining with naive players: Theory and experiment

The paper investigates two-player double-auction bargaining with private values in a setting with discrete two-point overlapping distributions of traders' valuations. We characterize parameter settings in which there exists a fully efficient equilibrium, and show that if there are traders that behave naively, i.e., set bid or ask equal to their valuation, then there is no equilibrium achieving full efficiency. We conduct an experiment to test the theoretical possibility that the presence of naive traders can reduce efficiency. We find, however, that efficiency is not lower in the presence of naive traders. Subjects mostly set bid/ask prices strategically but they do not coordinate on a fully efficient equilibrium and the extent of strategic behavior is not different in the presence of naive players. We show that a learning model of noisy strategy adjustment explains the observed behavior better than other (equilibrium or non-equilibrium) models.

Strategic default in financial networks

This paper investigates a model of default in financial networks where the decision by one agent on whether or not to default impacts the incentives of other agents to escape default. Agents' payoffs are determined by the clearing mechanism introduced in the seminal contribution of Eisenberg and Noe (2001). We first show the existence of a Nash equilibrium of this default game. Furthermore, we develop an algorithm to find all Nash equilibria and guide regulatory intervention that relies on the financial network structure. The algorithm provides a ranking for the set of Nash equilibria for specific financial network structures, which can serve as a measure of systemic risk. Finally, we show that introducing a central clearing counterparty achieves the efficient equilibrium at no additional cost.

Does a scaling exist in urban ecological infrastructure? A case for sustainability trade-off in China.

So far, urban scaling theory has proven that urban area, infrastructure, and economic output have a scaling relation with population. But if we consider ecological space as a part of urban infrastructure, would the same scaling characteristics exist? What is the scaling relationship between ecological spaces and economic social development in different stages of urbanization? This paper is based on this question and explores the trade-off between social economic system and ecosystem in 370 cities of China. The results show that the relationship between population and urban ecological space generally follows the scaling theory in terms of different types of ecological spaces and ecosystem services. For every 10-fold increase in population size, the total area of ecological space and ecosystem services increase by approximately 4 times. The manifestation of ecological space following the scaling laws is the aggregation behavior of better network connectivity. There is a trade-off between urban ecological space and socioeconomic development, with flow equilibrium reached at a population of 2 million and efficiency equilibrium reached at a population of 1 million. Starting from type I and type II megapolis, urban development gradually tends to stabilize, and there may even be a trend of slow decline in urban development potential. In the absence of ecological space, virtual network space can serve as a substitute for ecological space. The driving factors affect scaling behavior of ecological space, including connectivity of ecological space, spatial heterogeneity of natural conditions, and disturbance of economic and social activities. This research can help city to expand ecological space, promoting the added value of urban ecological assets and keeping the urban development potential within the optimal threshold range continuously.

Expropriation power in private dealings: Quota rule in collective sales

Complementarity is common in land-assembly problems, such as a developer buying the entirety of apartment units to complete a development project. Holdout (delay or block of projects by sellers) is common in these problems under unanimity-rule. Motivated by the recent policy practices in strata-sales, we introduce a new bargaining model with quota-rule. We show that under quota-rule, there is no holdout when there are two sellers or players are sufficiently patient. No-holdout equilibrium is unique, efficient and yields immediate sale of all goods as outcome. When quota rule is used, efficient equilibrium is still obtained under alternative bargaining protocols and with multiple sellers. We also show that the no-holdout result is not due to the specific bargaining protocol.

Mitigating fire sales with a central clearing counterparty

Theoretically, one rationale for central clearing counterparties is the mitigation of inefficiencies associated with distressed asset sales. With novel archival data, I empirically study the first event in economic history during which a CCP successfully played this role: the global wool crisis of 1900. In the leading wool futures market in France, an inefficient equilibrium with fire sales and cascading defaults could be avoided due to price support provided by surviving CCP members. Cooperation to achieve price support–which is nowadays the main element of CCP auctions–could arise due to family relationships and cultural proximity between traders.

Efficient effort equilibrium in cooperation with pairwise cost reduction

There are multiple situations in which bilateral interaction between agents results in considerable cost reductions. The cost reduction that an agent obtains depends on the effort made by other agents. We model this situation as a bi-form game with two states. In the first stage, agents decide how much effort to exert. We model this first stage as a non-cooperative game, in which these efforts will reduce the cost of their partners in the second stage. This second stage is modeled as a cooperative game in which agents reduce each other’s costs as a result of cooperation, so that the total reduction in the cost of each agent in a coalition is the sum of the reductions generated by the rest of the members of that coalition. The proposed cost allocation for the cooperative game in the second stage determines the payoff function of the non-cooperative game in the first stage. Based on this model, we explore the costs, benefits, and challenges associated with setting up a pairwise effort situation. We identify a family of cost allocations with weighted pairwise reductions which are always feasible in the cooperative game and contain the Shapley value. We also identify the cost allocation with weighted pairwise reductions that generate an efficient equilibrium effort level.

Endogenous ambiguity and rational miscommunication

This paper studies a sender-receiver game in which both players want the receiver to choose the state-optimal action. Before observing the state, the sender observes a “contextual signal,” a payoff-irrelevant signal that correlates with states and is imperfectly shared with the receiver. Once the sender observes the state, the sender sends a message to the receiver, incurring a small messaging cost. It is shown that there is no miscommunication in any efficient equilibrium if the messaging cost is uniform or contextual information is poorly shared between players. However, if the messaging costs are different between some messages, and contextual information can affect the probability ranking of states and is shared reasonably well, any efficient equilibrium that favors the sender exhibits miscommunication. Furthermore, the messages that cause miscommunication can be coarse or ambiguous, depending on how well players share contextual information.

Nontruthful Position Auctions Are More Robust to Misspecification

We consider the classical model of sponsored search due to Edelman et al. and Varian and examine how robust standard position auctions are to a misspecification of the position-dependent quality factors used by this model. We show that under both complete and incomplete information a nontruthful position auction admits an efficient equilibrium for a strictly broader range of parameter values than the Vickrey-Clarke-Groves (VCG) mechanism, which would be truthful if the parameters were specified correctly. Our result for complete information concerns the generalized second-price (GSP) mechanism and is driven by a detailed understanding of the Nash equilibrium polytopes of the VCG mechanism and the GSP mechanism. Our result for incomplete information concerns the generalized first-price (GFP) mechanism and uses a surprising connection between the unique candidate equilibrium bidding functions of the VCG mechanism and the GFP mechanism. Funding: F. Fischer was supported by the Engineering and Physical Sciences Research Council [Grant EP/T015187/1] and Einstein Stiftung Berlin.