Strategic Complements, Substitutes, and Ambiguity: The Implications for Public Goods

We examine the effect of ambiguity in symmetric games with aggregate externalities. We find that ambiguity will increase/decrease the equilibrium strategy in games with strategic complements/substitutes and positive externalities. These effects are reversed in games with negative externalities. We consider some economic applications of these results to Cournot oligopoly, bargaining, macroeconomic coordination, and voluntary donations to a public good. In particular we show that ambiguity may reduce free-riding. Comparative statics analysis shows that increases in uncertainty will increase donations, to a public good. Journal of Economic Literature C72, D81, H41.     

The Paradox of Power: Principal-agent problems and administrative capacity in Imperial China (and other absolutist regimes)

Tax extraction is often low in absolutist regimes. Why are absolutists unable to convert power into revenue? Supported by evidence from Imperial China, we explain this puzzle with a principal-agent model which reveals that absolutists, unconstrained by rule of law and unable to commit to not predating on their tax-collecting agents (and the masses), may find it optimal to settle for a low wage-low tax equilibrium, while permitting agents to keep extra, unmonitored taxes. Our analysis suggests that low investment in administrative capacity is a conscious choice for an absolutist since it substitutes for credible commitment to refrain from confiscation from its agents.     

Implementation of individually rational social choice functions with guaranteed utilities

A simple mechanism is presented that allocates an indivisible object between two agents for almost any possible compensation rule. Furthermore, the equilibrium strategy guarantees a level of utility not less than −ε, where ε can be arbitrarily small.     

Representing equilibrium aggregates in aggregate games with applications to common agency

An aggregate game is a normal-form game with the property that each playerʼs payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without requiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self-generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggregates of the original n-player game. We illustrate the value of this approach in common-agency games where the playersʼ strategy space is an infinite-dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral hazard versions of these games.     

Comparative statics in a simple class of strategic market games

This paper investigates the effects of entry in two-sided markets where buyers and sellers act strategically. Applying new tools from supermodular optimization/games, sufficient conditions for different comparative statics results are obtained. While normality of one good is sufficient for the equilibrium price to be increasing in the number of buyers, normality of both goods is required for equilibrium bids and sellers' equilibrium utilities to be increasing in the number of buyers. When the economy is replicated, normality of both goods and gross substitutes guarantee that the equilibrium of the strategic market game converges monotonically (in quantities) to the competitive equilibrium. Simple counter-examples are provided to settle other potential conjectures of interest.     

Designing incentives for online question-and-answer forums

We provide a game-theoretic model of sequential information aggregation motivated by online question-and-answer forums. An asker posts a question and each user decides when to aggregate a unique piece of information with existing information. When the quality exceeds a certain threshold, the asker closes the question and allocates points to users. We consider the effect of different rules for allocating points on the equilibrium behavior. A best-answer rule provides a unique, efficient equilibrium in which all users respond in the first round, for substitutes valuations over information. However, the best-answer rule isolates the least efficient equilibrium for complements valuations. We demonstrate alternate scoring rules that provide an efficient equilibrium for distinct subclasses of complements valuations, and retain an efficient equilibrium for substitutes valuations. We introduce a reasonable set of axioms, and establish that no rule satisfying these axioms can achieve the efficient outcome in a unique equilibrium for all valuations.     

A clarification of the IS curve and the aggregate demand curve

This paper clarifies the current textbook interpretations of the IS curve and the aggregate demand (AD) curve. Most macroeconomic textbooks portray the IS curve as representing equilibrium in the product, goods, or commodity market. This paper illustrates that in flexible-price models the IS curve does not necessarily portray equilibrium in the goods market because the textbooks introduce two contradictory notions of equilibrium. Furthermore, it will be shown that, contrary to popular textbook usage, the AD curve, which is derived from the IS-LM framework, is not the economy's effective demand curve for goods.     

Intersectoral Externalities and Indeterminacy

We consider a two-sector economy with positive intersectoral external effects and nonincreasing social returns. We show that if the discount factor ρ is close to 1 then local indeterminacy may be obtained with mild market imperfections. Moreover, with additional conditions, when ρ is made smaller the steady state becomes totally unstable and quasi-periodic cycles, along which equilibrium paths are indeterminate, may appear through a Hopf bifurcation. This will be proved even if the investment good is capital intensive at the private level while this condition guarantees local determinacy in the sector specific case. Journal of Economic Literature Classification Numbers: C62, E32, O41.     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.     

Fault tolerance in large games

A Nash equilibrium is an optimal strategy for each player under the assumption that others play according to their respective Nash strategies, but it provides no guarantees in the presence of irrational players or coalitions of colluding players. In fact, no such guarantees exist in general. However, in this paper we show that large games are innately fault tolerant. We quantify the ways in which two subclasses of large games – λ-continuous games and anonymous games – are resilient against Byzantine faults (i.e. irrational behavior), coalitions, and asynchronous play. We also show that general large games have some non-trivial resilience against faults.     

Search,Concave Production,and Optimal Firm Size

This paper demonstrates that in a free entry search and bargaining economy with concave production firms over-employ. Bargaining allows the worker's wage to depend upon marginal productivity. As such, with strictly concave production, the wage declines as firms employ more labor. Firms react to this declining wage function by choosing an inefficiently large number of workers. However, in equilibrium, fewer firms are likely to enter causing aggregate employment and vacancies to fall.Journal of Economic LiteratureClassification Numbers: J30, J41, J50.     

Non-Laplacian beliefs in a global game with noisy signaling

In standard global games, individual behavior is optimal if it constitutes a best response to agnostic—Laplacian—beliefs about the aggregate behavior of other agents. This paper considers a standard binary action global game augmented with noisy signaling by an informed policy-maker and shows that in this game, equilibrium beliefs depart in quite stark ways from the Laplacian benchmark. In the limit as signals become arbitrarily precise, so that all fundamental uncertainty is removed (leaving only strategic uncertainty), the equilibrium beliefs of the marginal individual concerning the aggregate action collapse to a discrete Bernoulli distribution, giving probability mass only to the polar extreme outcomes. By contrast in the underlying standard global game the marginal individual believes the aggregate action has a continuous uniform distribution, giving equal likelihood to all possible outcomes.     

The capital gain lock-in effect and perfect substitutes

This paper analyses the effect of investors' accrued capital gains on optimal portfolio composition and equilibrium returns under the assumption that investors are able to re-balance with perfect substitute securities. No-dominance arguments are used to show that pricing differences because of accrued capital gains do not arise among securities which are perfect substitutes. These arguments are insufficient, however, to prevent pricing differences because of accrued capital gains among securities which are not perfect substitutes. Trading rules are developed which outline the conditions necessary for the realisation of accrued capital gains and the deferral of capital losses. These trading rules also provide guidance on which securities investors should sell, given their tax basis, when re-balancing their portfolios.     

On the (non-)lattice structure of the equilibrium set in games with strategic substitutes

This paper studies models where the optimal response functions under consideration are not increasing in endogenous variables, and weakly increasing in exogenous parameters. Such models include games with strategic substitutes, and include cases where additionally, some variables may be strategic complements. The main result here is that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. Indeed, for a given parameter value, a pair of distinct equilibria are never comparable. Therefore, with multiple equilibria, some of the established techniques for exhibiting increasing equilibria or computing equilibria that use the largest or smallest equilibrium, or that use the lattice structure of the equilibrium set do not apply to such models. Moreover, there are no ranked equilibria in such models. Additionally, the analysis here implies a new proof and a slight generalization of some existing results. It is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games of strategic substitutes with real-valued action spaces, symmetric equilibria increase with the parameter.)      

Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households

We prove an existence theorem for a stationary perfect foresight equilibrium under borrowing constraints in a two-sector model with infinitely lived heterogeneous agents. The most patient agent holds all the capital in this solution. We also show that if the capital goods sector is capital intensive and capital income is increasing in the aggregate capital stock, then the aggregate capital stock eventually is monotonic and converges to the steady state stock. If the consumption goods sector is more capital intensive and capital income is increasing in aggregate capital we prove convergence to the steady state under more restrictive conditions. Periodic equilibria are shown to exist under weaker hypotheses. Journal of Economic Literature Classification Numbers: D52, D90, E13.     

Sovereign risk,interbank freezes,and aggregate fluctuations

This paper shows how spillovers from sovereign risk to banks׳ access to wholesale funding establish a bank-sovereign nexus. In a dynamic stochastic general equilibrium set-up, heterogeneous banks give rise to an interbank market where government bonds are used as collateral. Government borrowing under limited commitment is costly ex ante as bank funding conditions tighten when the quality of collateral drops. These spillovers, by impeding interbank intermediation, lower the penalty from defaulting due to an interbank freeze during a recession and propagate aggregate shocks to the macroeconomy. The model is calibrated using Greek data and is capable of reproducing stylized facts from the European sovereign debt crisis. In an application, we show that the ECB׳s non-standard financing operations mitigate the adverse feedback mechanism.     

Optimal shill bidding in the VCG mechanism

This paper studies shill bidding in the Vickrey?CClarke?CGroves (VCG) mechanism applied to combinatorial auctions. Shill bidding is a strategy whereby a single decision-maker enters the auction under the guise of multiple identities (Yokoo et?al. Games Econ Behav, 46?pp. 174?C188, 2004). I formulate the problem of optimal shill bidding for a bidder who knows the aggregate bid of her opponents. A key to the analysis is a subproblem??the cost minimization problem (CMP)??which searches for the cheapest way to win a given package using shills. An analysis of the CMP leads to several fundamental results about shill bidding: (i) I provide an exact characterization of the aggregate bids b such that some bidder would have an incentive to shill bid against b in terms of a new property Submodularity at the Top; (ii) the problem of optimally sponsoring shills is equivalent to the winner determination problem (for single minded bidders)??the problem of finding an efficient allocation in a combinatorial auction; (iii) shill bidding can occur in equilibrium; and (iv) the problem of shill bidding has an inverse, namely the collusive problem that a coalition of bidders may have an incentive to merge (even after competition among coalition members has been suppressed). I show that only when valuations are additive can the incentives to shill and merge simultaneously disappear.     

Competitive bargaining equilibrium

In a simple exchange economy we propose a bargaining procedure that leads to a Walrasian outcome as the agents become increasingly patient. The competitive outcome therefore obtains even if agents have market power and are not price-takers. Moreover, where in other bargaining protocols the final outcome depends on bargaining power or relative impatience, the outcome here is determinate and depends only on preferences and endowments. Our bargaining procedure involves bargaining over prices and maximum quantity constraints, and it guarantees convergence to a Walrasian outcome for any standard exchange economy. In contrast, without quantity constraints we show that equilibrium is generically inefficient.     

Estimation of consistent multi-country FEERs

Most studies on equilibrium exchange rates focus on a limited number of G7 countries. But in a situation of world imbalances, emerging countries can no longer be excluded. The study of all equilibrium exchange rates is delicate. First, the trade model has to be balanced at the aggregate level. This paper suggests a method to achieve world balance both in volume and in value. Second, the N − 1 bilateral exchange rates cannot ensure that the N areas will reach their macroeconomic equilibrium simultaneously. This paper examines the existing solutions to solve the N − 1 problem and proposes an alternative which minimizes the distance to the current-account targets. Finally, in order to compare the relevance of the different methodologies, FEERs are calculated for 19 industrialized and developing countries. The results, which are taking into account the modification on output gap assessment induced by the 2008–2009 crisis, lead for the year 2010 to a USD closed to its equilibrium, a RMB undervalued by around 35% in real effective terms and to a EUR/USD parity equals to 1.47.     

Job matching and the distribution of producer surplus

We study wage determination in the Jovanovic model of matching, relaxing the standard assumption that wages continuously adjust to reflect on-the-job performance and studying aggregation of ex-ante heterogeneous career paths. We assume that workers have no bargaining power and consider an equilibrium where individual workers' age-earnings profiles are piecewise constant, reflecting their outside earning opportunities at each point in time. Turnover results from employers' firing decisions rather than from workers' quitting decisions, and the equilibrium delivers realistic cross-sectional and time-series implications. Employees receive only a portion rather than the whole of the ex-ante producer's surplus from established matches, and have individual incentives to lobby for increased job security. Inefficiently low aggregate turnover may result if such lobbying efforts are successful.