Equilibrium Allocations Research Articles

A welfare criterion with endogenous welfare weights for belief disagreement models

Belief disagreement generates a fundamental tension between two desirable features of a resource allocation: Pareto optimality and risk sharing. While Pareto optimality generally opposes restrictions to trade, a growing literature rejects it in the presence of heterogeneous beliefs and proposes welfare criteria that instead assume risk sharing as fundamentally desirable. We propose a welfare criterion that balances out these two desirable features by endogenously determining admissible welfare weights based on competitive equilibrium allocation as a benchmark. Applying our method to several belief disagreement models, we show how the welfare-optimal degree of risk sharing is between those suggested by Pareto optimality (which implies less) and by other existing approaches (which imply more).

Coalition Formation in Legislative Bargaining

We propose a new model of legislative bargaining in which coalitions may have different values, reflecting the fact that the policies they can pursue are constrained by the identity of the coalition members. As the delay between offers goes to zero, the equilibrium allocation of the model converges to a generalized version of a Nash bargaining solution in which—in contrast to the standard solution—the winning coalition is endogenous and determined by the relative coalitional values. A form of the holdup problem specific to these bargaining games contributes to generate significant inefficiencies in the selection of the coalition. The model helps rationalize well-known empirical facts that are in conflict with the predictions of standard noncooperative models of bargaining.

On the inefficiency of perfect price discrimination

In a general equilibrium model with at least three goods, a perfectly price-discriminating monopoly (PDM) selects an inefficient production plan even if consumers are homogeneous, their preferences are representable by quasi-linear utilities, and their characteristics are known to the monopolist. In the same setting, regulation via a two-part tariff induces an efficient equilibrium allocation.

Migration and urban economic dynamics

What generates the large amount of heterogeneity and persistence in U.S. city growth rates? To answer this question we construct a dynamic general equilibrium model of urban migration that is consistent with the approximately linear relation between gross and net migration rates that we uncover in a panel of 381 metropolitan statistical areas. Consistency with this relation together with the model’s structure of moving costs delivers a parsimonious reduced form in which competitive equilibrium allocations are given by the solution to a city’s social planner problem subject to quadratic population adjustment costs. A calibrated version of the model indicates that empirically measured total factor productivity shocks account for most of the short-run and long-run population dynamics observed in U.S. data.

Deposit insurance and reinsurance

We study the consequences and optimal design of bank deposit insurance and reinsurance in a general equilibrium setting. The model involves two production sectors, financed by bonds and bank loans, respectively. Financial intermediation by banks is required in the model as we assume that one of the production sectors is risky and requires monitoring by banks. Households fund banks through deposits and equity. Deposits are explicitly insured and banks pay a premium per unit of deposits. Any remaining shortfall is implicitly guaranteed by the government. Two types of equilibria emerge: One type of equilibria supports the Pareto optimal allocation. In the other type, bank lending and the default risk are excessively large. The intuition is as follows: the combination of financial intermediation by banks, limited liability of bank shareholders, and deposit insurance makes deposits risk-free from the individual households’ perspective, although they involve risk from the societal point of view. This distorts investment choices and the resulting input allocation to production sectors. We show, however, that a judicious combination of deposit insurance and reinsurance eliminates all non-optimal equilibrium allocations. Our paper thus may provide a benchmark result for policy proposals advocating deposit insurance cum reinsurance.

Allocating positions fairly: Auctions and Shapley value

We study the problem of fairly allocating heterogenous items, priorities, positions, or property rights to participants with equal claims from three perspectives: cooperative, decision theoretic, and non-cooperative. We characterize the Shapley value of the cooperative game and then introduce a class of auctions for non-cooperatively allocating positions. We show that for any auction in this class, each bidder obtains his Shapley value when every bidder follows the auction's unique maxmin perfect bidding strategy. When information is incomplete we characterize the Bayesian equilibrium of these auctions, and show that equilibrium play converges to maxmin perfect play as bidders become infinitely risk averse. The equilibrium allocations thus converges to the Shapley value allocation as bidders become risk averse. Together these results provide both decision theoretic and non-cooperative equilibrium foundations for the Shapley value in the position allocation problem.

On the Foundations of Competitive Search Equilibrium with and without Market Maker

The literature offers two foundations for competitive search equilibrium, a Nash approach and a market-maker approach. When each buyer visits only one seller (or each worker makes only one job application), the two approaches are equivalent. However, when each buyer visits multiple sellers, this equivalence can break down. Our paper analyzes competitive search equilibrium with simultaneous search using the two approaches. We consider four cases defined by (i) the surplus structure (are the goods substitutes or complements?) and (ii) the mechanism space (do sellers post fees or prices?). With fees, the two approaches yield the same constrained efficient equilibrium. With prices, the equilibrium allocation is the same using both approaches if the goods are complements, but is not constrained efficient. In the case in which only prices are posted and the goods are substitutes, the equilibrium allocations from the two approaches are different.

A political-economy perspective on mayoral elections and urban crime

We provide a political-economy analysis of crime prevention in an arbitrary city in the United States. City residents (voters) elect mayors (politicians) and elected mayors determine the resources to be allocated to crime prevention. Between the two time periods, there is an election. Politicians are either honest or dishonest. The marginal cost of public monies ψ measures how efficiently an elected mayor converts tax receipts into crime prevention. Voters have identical per period utility functions. We ascertain the equilibrium outcome and per period voter well-being. Second, we show that an increase in ψ reduces the equilibrium allocation of resources to crime prevention and voter well-being. Third, a dishonest politician can delay the revelation of his dishonesty. A critical value of ψ,ψ∗, exists such that a dishonest incumbent separates and loses the election if and only if ψ>ψ∗ and he pools and is re-elected otherwise. Finally, we note that an increase in ψ can raise voter well-being when politicians are more likely to be dishonest.

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.

Central Bank Digital Currency and Balance Sheet Policy

This paper studies how the introduction of a central bank digital currency (CBDC) interacts with ongoing monetary policies. We distinguish two kind of policies: standard policy, where the central bank invests in treasuries, and quantitative easing, where the central bank invests in risky securities. In each scenario, we introduce an interest-bearing CBDC, and study the equilibrium allocations. Our analysis reaches three main conclusions. The first is that the equilibrium impact of a CBDC depends on the ongoing monetary policy. Second, when the central bank conducts quantitative easing, the introduction of a CBDC is neutral under two conditions: the cost of issuing a CBDC is equal to the interest on reserves, and the demand for CBDC deposits is smaller than the amount of excess reserves in the system. Third, the introduction of a CBDC might render quantitative easing a quasi-permanent policy, as commercial banks optimally use their excess reserves to accommodate retailers’ demand for switching from bank deposits to CBDC deposits.

OUTWARD HABITS AND ENVIRONMENTAL QUALITY IN AN OVERLAPPING GENERATIONS MODEL

Outward habit formation affects consumption decisions. Since consumption displays a negative environmental externality, outward habits has as well an (adverse) effect on the environment. This research paper centers around the theoretical linkage between the combination of both externalities (environmental deterioration and outward habits). The objective of this study is to examine the impacts of outward habits on the state of the environment in the context of an overlapping generations economy. In our study, environmental quality is a public good negatively affected by consumption activity and positively affected by maintenance investment. With outward habit formation, the build-up level of average past consumption in the economy at large influences the current utility of an individual consumer. Thus, individuals draw utility not only from their own level of current consumption, but also from its level relative to the average consumption in the economy. How does outward habit influence the state of the environment? We analyze this question using an overlapping generations model with outward habit and environmental quality in the utility function. In steady state equilibrium allocation, we show that whether outward habits are destructive to the environment depends on the degrees of outward habit formation and the size of the economy.

Consistent Allocation of Emission Responsibility in Fossil Fuel Supply Chains

Since 2016, Canada’s federal government has pledged to factor in upstream emissions during the environmental impact assessment of fossil fuel energy projects. The upstream emissions attributable to a proposed project could be compared against a rejection threshold—a maximum permissible level of emissions—or the firm could be mandated to offset the attributed emissions. We adopt a cooperative game-theoretic model and propose the nucleolus mechanism to apportion upstream emission responsibilities in a fossil fuel supply chain, represented by a directed tree, wherein the nodes correspond to various entities in the supply chain such as extractors, distributors, refineries, and end consumers. The nucleolus allocation avoids the distortionary effects of double counting and exhibits a certain consistency property that is especially important in a regulatory context wherein fossil fuel supply chains span multiple legal jurisdictions. We develop a polynomial-time algorithm to compute the nucleolus and further prove that it arises as the unique subgame perfect equilibrium allocation of a noncooperative game induced by two easily stated and verifiable policies, thereby providing an implementation framework. We then demonstrate the strong Nash stability of the nucleolus mechanism subject to the two policies, study its sensitivity to parameter changes, and characterize it on the basis of fairness considerations. Furthermore, under the common assumption that the emissions allocated to a firm and the resulting financial penalties do not impact the revenues from the firm’s core operations, we also provide lower-bound guarantees on the welfare gains it delivers to firms in the fossil fuel supply chain and on the incentives it offers such firms to adopt emission abatement technologies. Finally, we contextualize our discussion with a case study on a proposed expansion of the Trans Mountain pipeline in Western Canada. This paper was accepted by Chung Piaw Teo, optimization.

Nash Social Welfare Approximation for Strategic Agents

We study the problem of allocating divisible resources to agents with different preferences. We analyze a market game known as Trading Post, first considered by Shapley and Shubik, where each agent gets a budget of virtual currency to bid on goods: after bids are placed, goods are allocated to players in proportion to their bids. In this setting, the agents choose their bids strategically, aiming to maximize their utility, and this gives rise to a game. We study the equilibrium allocations of this game, measuring the quality of an allocation via the Nash social welfare, the geometric mean of utilities (a measure of aggregate welfare that respects individual needs). We show that any Nash equilibrium of Trading Post approximates the optimal Nash welfare within a factor of two for all concave valuations, and the mechanism is essentially optimal for Leontief valuations.

Revisiting the Coase theorem

We provide a version of the Coase theorem within a general equilibrium framework. We consider an economy with other-regarding preferences, and where rights, licenses, or permissions are required to use, consume or transform some specific commodities. These permissions are initially allocated among consumers and, as the commodities, can be costlessly traded. In this scenario, we define different veto mechanisms and the corresponding core solutions that, naturally, result in the same set of efficient allocations. Our final result sets sufficient conditions on preferences and the requirement of rights to ensure that any equilibrium allocation belongs to the core and, in particular, is efficient.

On the Foundations of Competitive Search Equilibrium with and Without Market Makers

The literature offers two foundations for competitive search equilibrium, a Nash approach and a market-maker approach. When each buyer visits only one seller (or each worker makes only one job application), the two approaches are equivalent. However, when each buyer visits multiple sellers, this equivalence can break down. Our paper analyzes competitive search equilibrium with simultaneous search using the two approaches. We consider four cases defined by (i) the surplus structure (are the goods substitutes or complements?) and (ii) the mechanism space (do sellers post fees or prices?). With fees, the two approaches yield the same constrained efficient equilibrium. With prices, the equilibrium allocation is the same using both approaches if the goods are complements, but is not constrained efficient. In the case in which only prices are posted and the goods are substitutes, the equilibrium allocations from the two approaches are different.

Уклонение от уплаты налогов и субсидирование R&D в смешанной отрасли

In this paper I consider a mixed duopoly where a private firm competes with a public one. The private firm maximizes its profit and the public firm maximizes social welfare. R&D investments of firms are subsidized by the government, profits of both firms are taxed and the private firm might evade taxes. It is shown that tax evasion (decision not to declare part of profit) directly affects a rate of the optimal R&D subsidy and makes it dependent on a profit tax rate. While making a choice on the rate of the R&D subsidy the government takes into account both positive and negative effects of the subsidy on social welfare. On the one hand the R&D subsidy results in a decrease in total production costs because an allocation of total output between two firms is improved; on the other hand it results in an increase in social costs of tax evasion. The optimal R&D subsidy decreases with an increase in a profit tax rate and increases with an increase in tax evasion costs. An equilibrium allocation is not efficient, but an increase in tax evasion costs leads to the reduction of difference between efficient and equilibrium welfare levels.

Price-Based Resource Allocation for Edge Computing: A Market Equilibrium Approach

The emerging edge computing paradigm promises to deliver superior user experience and enable a wide range of Internet of Things (IoT) applications. In this paper, we propose a new market-based framework for efficiently allocating resources of heterogeneous capacity-limited edge nodes (EN) to multiple competing services at the network edge. By properly pricing the geographically distributed ENs, the proposed framework generates a market equilibrium (ME) solution that not only maximizes the edge computing resource utilization but also allocates optimal resource bundles to the services given their budget constraints. When the utility of a service is defined as the maximum revenue that the service can achieve from its resource allotment, the equilibrium can be computed centrally by solving the Eisenberg-Gale (EG) convex program. We further show that the equilibrium allocation is Pareto-optimal and satisfies desired fairness properties including sharing incentive, proportionality, and envy-freeness. Also, two distributed algorithms, which efficiently converge to an ME, are introduced. When each service aims to maximize its net profit (i.e., revenue minus cost) instead of the revenue, we derive a novel convex optimization problem and rigorously prove that its solution is exactly an ME. Extensive numerical results are presented to validate the effectiveness of the proposed techniques.

Equilibrium Allocations under Alternative Waitlist Designs: Evidence from Deceased Donor Kidneys Kidneys.

Waitlists are often used to ration scarce resources, but the trade-offs in designing these mechanisms depend on agents' preferences. We study equilibrium allocations under alternative designs for the deceased donor kidney waitlist. We model the decision to accept an organ or wait for a preferable one as an optimal stopping problem and estimate preferences using administrative data from the New York City area. Our estimates show that while some kidney types are desirable for all patients, there is substantial match-specific heterogeneity in values. We then develop methods to evaluate alternative mechanisms, comparing their effects on patient welfare to an equivalent change in donor supply. Past reforms to the kidney waitlist primarily resulted in redistribution, with similar welfare and organ discard rates to the benchmark first come first served mechanism. These mechanisms and other commonly studied theoretical benchmarks remain far from optimal. We design a mechanism that increases patient welfare by the equivalent of an 18.2 percent increase in donor supply.

Efficient multi-period distribution mechanism for the innovation investment system under uncertainty

In this paper, we study the problem of a venture investor who distributes the budget between several innovation projects under conditions of uncertainty. A common method for solving this problem is through bilateral negotiations with the external evaluation of projects. However, the effectiveness almost entirely depends on the evaluation quality, but external evaluation seldom reduces the knowledge asymmetry for innovation projects. We propose an iterative revelation mechanism for this problem when the investor sequentially offers possible allocations of the limited budget in the form of threshold dividing questions. The binary choices of innovators serve as a signal of internal estimates of the project implementation costs. Under perfect information, such a mechanism, regardless of the method for determining budget allocations, always produces an effective allocation in subgame-perfect Nash equilibrium. Under uncertainty, the method of offering distribution options matters – the optimal solution is found under the English auction class of mechanisms. In an efficient iterative allocation mechanism for innovation investment, the investor proposes a new allocation of the budget each round until an efficient allocation is achieved. The proposed mechanism does not necessarily need to identify the exact minimum budgets for each innovator. Another advantage of the proposed mechanism is the ability to use different processes for organizing rounds.

Speculative Bubbles and Talent Misallocation

There is increasing evidence that the vibrant financial industry has generated a misallocation of human capital between the manufacturing sector and the service sector. In addition, growth in the financial sector has usually been accompanied by bubble booms. Thus, this paper advances a greater fool-theoretical approach to talent misallocation when an economy experiences speculation-driven extrapolative bubbles. The equilibrium allocation of talent in the decentralized economy encourages too many agents to enter the financial sector. Not only do the overcrowded markets in the financial sector per se generate a negative externality on the manufacturing sector, but speculation is also a source of financial fragility. The reason for this is that when agents make decisions based on their information sets, they ignore the negative externality of congestion and the impact of the endogenous bubble-burst probability of their entry into the financial sector. An optimal policy across sectors is then proposed to fix the talent misallocation caused by speculative bubbles.