Showing papers in "Economic Theory in 2015"

The all-pay auction with complete information and identity-dependent externalities

Abstract: We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the all-pay auction with complete information and identity-dependent externalities. This condition shows that the generic equilibrium of the standard all-pay auction is robust to the introduction of “small” identity-dependent externalities. In general, however, the presence of identity-dependent externalities invalidates well-established qualitative results concerning the set of equilibria of the first-price all-pay auction with complete information. With identity-dependent externalities, equilibria are generally not payoff equivalent, and identical players may earn different payoffs in equilibrium. These observations show that Siegel’s (Econometrica 77(1), 71–92, 2009) results characterizing the set of equilibrium payoffs in all-pay contests, including the all-pay auction as a special case, do not extend to environments with identity-dependent externalities. We further compare the all-pay auction with identity-dependent externalities to the first-price winner-pay auction with identity-dependent externalities. We demonstrate that the equilibrium payoffs of the all-pay auction and the “undominated strategy equilibrium” payoffs of the winner-pay auction (Funk in Int J Game Theory 25(1), 51–64, 1996) cannot be ranked unambiguously in the presence of identity-dependent externalities by providing examples of environments where equilibrium payoffs in the all-pay auction dominate those of the undominated strategy equilibria in the winner-pay auction and vice versa.

The effects of credit subsidies on development

Abstract: Under credit market imperfections, the marginal product of capital may not be equalized, resulting in misallocation and lower output. Preferential interest rate policies are often used to remedy the problem. This paper constructs a general equilibrium model with heterogeneous agents, imperfect enforcement and costly intermediation. Occupational choice and firm size are determined endogenously by an agent’s type (ability and net wealth) and credit market frictions. The credit program subsidizes the interest rate on loans and requires a fixed application cost, which might be null. We find that the credit subsidy policy has no significant effect on output, but it may have negative effects on wages. The program is largely a transfer from households to a small group of entrepreneurs with minor aggregate effects. We also provide estimates of the effects of reducing the frictions directly. When comparing differences in US output per capita in a baseline case to simulations with counterfactually high frictions, intermediation costs and enforcement explain about 20–25 % of the output gap. We include a transition analysis.

Mixed equilibria in Tullock contests

Abstract: Any symmetric mixed-strategy equilibrium in a Tullock contest with intermediate values of the decisiveness parameter (“\(2

Dynamic network formation with incomplete information

Abstract: How do networks form and what is their ultimate topology? Most of the literature that addresses these questions assumes complete information: agents know in advance the value of linking even with agents they have never met and with whom they have had no previous interaction (direct or indirect). This paper addresses the same questions under the much more natural assumption of incomplete information: agents do not know in advance—but must learn—the value of linking. We show that incomplete information has profound implications for the formation process and the ultimate topology. Under complete information, the network topologies that form and are stable typically consist of agents of relatively high value only. Under incomplete information, a much wider collection of network topologies can emerge and be stable. Moreover, even with the same topology, the locations of agents can be very different: An agent can achieve a central position purely as the result of chance rather than as the result of merit. All of this can occur even in settings where agents eventually learn everything so that information, although initially incomplete, eventually becomes complete. The ultimate network topology depends significantly on the formation history, which is natural and true in practice, and incomplete information makes this phenomenon more prevalent.

Two Simple Variations of Top Trading Cycles

Abstract: Top Trading Cycles is widely regarded as the preferred method of assigning students to schools when the designer values efficiency over fairness. However, Top Trading Cycles has an undesirable feature when objects may be assigned to more than one agent as is the case in the school choice problem. If agent $$i$$ ’s most preferred object $$a$$ has a capacity of $$q_a$$ , and $$i$$ has one of the $$q_a$$ highest priorities at $$a$$ , then Top Trading Cycles will always assign $$i$$ to $$a$$ . However, until $$i$$ has the highest priority at $$a$$ , Top Trading Cycles allows $$i$$ to trade her priority at other objects in order to receive $$a$$ . Such a trade is not necessary for $$i$$ ’s assignment and may cause a distortion in the fairness of the assignment. We introduce two simple variations of Top Trading Cycles in order to mitigate this problem. The first, Clinch and Trade, reduces the number of unnecessary trades but is bossy and depends on the order in which cycles are processed. The second, First Clinch and Trade, is nonbossy and independent of the order in which cycles are processed but allows more unnecessary trades than is required to be strategyproof and efficient. Both rules are strategyproof.

Waging simple wars: a complete characterization of two-battlefield Blotto equilibria

Abstract: We analyze the strategic allocation of resources across two contests as in the canonical Colonel Blotto game. In the games we study, two players simultaneously allocate their forces across two fields of battle. The larger force on each battlefield wins that battle, and the payoff to a player is the sum of the values of battlefields won. We completely characterize the set of Nash equilibria of all two-battlefield Blotto games and provide the unique equilibrium payoffs. We also show how to extend our characterization to cover previously unstudied games with nonlinear resource constraints.

On the properties of an emission-generating technology and its parametric representation

Abstract: We propose a set of comprehensive axioms that seek to capture our intuitive understanding of the properties of an emission-generating technology (EGT). We show that an EGT that satisfies these axioms can be parametrically represented by more than one implicit production function that are derived from it. Here, these production functions take the form of distance functions first introduced by Shephard (Cost and production functions, Princeton University Press, Princeton, 1953) and Malmquist (Trabajos de estadistica 4:209–242, 1953). One of these production relations has properties of a neo-classical production function that shows how standard inputs are transformed into standard (intended) outputs. The remaining reflect trade-offs, observed in nature, between emissions, emission-causing goods, and cleaning-up activities of the producing unit. We illustrate this by considering two cases: (1) where each type of cleaning-up activity jointly mitigates all types of emissions and (2) where cleaning-up activities are emission-specific allowing also for the possibility that a cleaning-up activity, while helping to reduce certain emissions, can also contribute to more of some other types of emissions.

On the representation of incomplete preferences under uncertainty with indecisiveness in tastes and beliefs

Abstract: Recently, there has been some interest on models of incomplete preferences under uncertainty that allow for incompleteness due the multiplicity of tastes and beliefs. In particular, Galaabaatar and Karni (Econometrica 81(1):255–284, 2013) work with a strict partial order and present axiomatizations of the Multi-prior Expected Multi-utility and the Single-prior Expected Multi-utility representations. In this paper, we characterize both models using a preorder as the primitive. In the case of the Multi-prior Expected Multi-utility representation, like all the previous axiomatizations of this model in the literature, our characterization works under the restriction of a finite prize space. In our axiomatization of the Single-prior Expected Multi-utility representation, the space of prizes is a compact metric space. Later in the paper, we present two applications of our characterization of the Single-prior Expected Multi-utility representation and discuss the necessity of an axiomatization of the Multi-prior Expected Multi-utility model when the prize space is not finite. In particular, we explain how the two applications we develop in this paper could be generalized to that model if we had such an axiomatization.

Value allocation under ambiguity

Abstract: We consider a pure exchange economy with asymmetric information where individual behavior exhibits ambiguity aversion along the line of maximin expected utility decision making. For such economies, we introduce different notions of maximin value allocations. We also introduce a strong notion of incentive compatibility. We prove the existence and incentive compatibility of the maximin value allocation. We conclude that unlike the Bayesian value allocation approach in Krasa Yannelis (Econometrica 62(4):881–900, 1994), incentive compatibility is related to efficiency rather than to direct exchange of information.

International environmental agreements: coordinated action under foresight

Abstract: We examine the formation of international environmental agreements (IEAs). We extend the existing literature by endogenizing the reaction of the IEA’s members to a deviation by a group of members. We assume that when a group of countries contemplates exiting or joining an agreement, it takes into account the reactions of other countries ignited by its own actions. We identify conditions under which the solution always exists and fully characterize the coalitionally farsighted stable IEAs. The new farsighted IEAs can be much larger than those some of the previous models supported and are always Pareto efficient.

Credit search and credit cycles

Abstract: The supply and demand of credit are not always well aligned and matched, as is re‡ected in the countercyclical excess reserve-to-deposit ratio and interest spread between the lending rate and the deposit rate. We develop a search-based theory of credit allocation to explain the cyclical ‡uctuations in bank reserves, the interest spread, as well as credit rationing. We show that search frictions in the credit market can not only naturally explain the countercyclical bank reserves, interest spread and credit rationing, but also generate endogenous business cycles driven primarily by the cyclical utilization rate of credit resources, as long conjectured by the Austrian school of the business cycle. In particular, we show that credit search can lead to endogenous increasing returns to scale and variable capital utilization in a model with constant returns to scale production technology and matching functions, thus providing a micro-foundation for the indeterminacy literature of Benhabib and Farmer (1994) and Wen (1998).

Incentive contracts under product market competition and R&D spillovers

Abstract: This paper studies cost-reducing R&D incentives in a principal-agent model with product market competition. It argues that moral hazard does not necessarily decrease firms’ profits in this setting. In highly competitive industries, firms are driven by business-stealing incentives and exert such high levels of R&D that they burn up their profits. In the presence of moral hazard, underprovision of R&D incentives due to risk sharing can generate considerable cost savings, implying higher profits for both rivals. This result indicates firms’ incentives to adopt collusive-like behavior in the R&D market. We also examine the agents’ contracts and the profits-risk relationship when cross-firm R&D spillovers occur.

On existence and bubbles of Ramsey equilibrium with borrowing constraints

Abstract: We study the existence of equilibrium and rational bubbles in a Ramsey model with heterogeneous agents, borrowing constraints and endogenous labor. Applying Kakutani’s fixed-point theorem, we prove the existence of equilibrium in a time-truncated bounded economy. A common argument shows this solution to be an equilibrium for any unbounded economy with the same fundamentals. Taking the limit of a sequence of truncated economies, we eventually obtain the existence of equilibrium in the Ramsey model. In the second part of the paper, we address the issue of rational bubbles and we prove that they never occur in a productive economy a la Ramsey.

Rational housing bubble

Abstract: This paper studies an economy inhabited by overlapping generations of households and investors, with the only difference between the two being that households derive utility from housing services, whereas investors do not. Tight collateral constraint limits the borrowing capacity of households and drives the equilibrium interest rate level down to the housing price growth rate, which makes housing attractive as a store of value for investors. A housing bubble arises in an equilibrium in which investors hold houses for resale purposes only and without the expectation of receiving a dividend either in terms of utility or in terms of rent. Pension reform that reduces the contribution rate may increase the supply of credit and create the housing bubble. Empirical findings from China are consistent with theoretical predictions.

Robust stochastic stability

Abstract: A strategy profile of a game is called robustly stochastically stable if it is stochastically stable for a given behavioral model independently of the specification of revision opportunities and tie-breaking assumptions in the dynamics. We provide a simple radius–coradius result for robust stochastic stability and examine several applications. For the logit-response dynamics, the selection of potential maximizers is robust for the subclass of supermodular symmetric binary action games. For the mistakes model, the weaker property of strategic complementarity suffices for robustness in this class of games. We also investigate the robustness of the selection of risk-dominant strategies in coordination games under best-reply and the selection of Walrasian strategies in aggregative games under imitation.

Leapfrogging Cycles in International Competition

Abstract: Technological leadership has shifted at various times from one country to another. We propose a mechanism that explains this perpetual cycle of technological leapfrogging in a two-country model including the dynamic optimization of an infinitely lived consumer. In the model, each country accumulates knowledge stock over time because of domestic innovation and spillovers from foreign innovation. We show that if the international knowledge spillovers are reasonably efficient, technological leadership may shift first from one country to another, and then alternate between countries along an equilibrium path.

Collusive communication schemes in a first-price auction

Abstract: We study optimal bidder collusion in an independent private value first-price auction with two bidders and two possible valuations. There is a benevolent center that knows the bidders’ valuations and sends private signals to the bidders in order to maximize their expected payoffs. After receiving their signals, bidders compete in a standard first-price auction, that is, without side payments or bid restrictions. We find that to improve on the bidders’ payoffs, the signals must depend upon the valuations. If the bidders’ signals are restricted to be non-correlated (depend only on the opponent’s valuation), then the bidders’ payoffs are strictly higher than the larger possible set of signals. If the signals are restricted to be perfectly correlated (public), only two possible signals are needed to achieve the highest bidder payoffs. However, these payoffs can be improved upon if the two signals are allowed to be imperfectly correlated.

Revealed reputations in the finitely repeated prisoners’ dilemma

Abstract: In a sequential-move, finitely repeated prisoners’ dilemma game (FRPD), cooperation can be sustained if the first-mover believes her opponent might be a behavioral type who plays a tit-for-tat strategy in every period. We test this theory by revealing second-mover histories from an earlier FRPD experiment to their current opponent. Despite eliminating the possibility of reputation-building, aggregate cooperation actually increases when histories are revealed. Cooperative histories lead to increased trust, but negative histories do not cause decreased trust. We develop a behavioral model to explain these findings.

Moral Hazard and Sorting in a Market for Partnerships

Abstract: We examine how equilibrium sorting patterns in a matching market for partnerships are impacted by the presence of bilateral moral hazard in a repeated production setting. We find that this impact depends on how the cost of moral hazard manifests itself—whether efficient effort is not feasible or desirable from the beginning, or whether inefficient effort is resorted to only as a punishment equilibrium. Which of these is the case depends on both the details of the technology and the contractual environment. In the former case, the presence of moral hazard moves the market away from positive sorting. In the latter case, whether moral hazard favors positive or negative sorting depends on how the power of incentives needed to implement effort varies with the observable types of the agents.

Pure-Strategy Nash Equilibria in nonatomic games with infinite-dimensional action spaces

Abstract: This paper studies the existence of pure-strategy Nash equilibria for nonatomic games where players take actions in infinite-dimensional Banach spaces. For any infinite-dimensional Banach space, if the player space is modeled by the Lebesgue unit interval, we construct a nonatomic game which has no pure-strategy Nash equilibrium. But if the player space is modeled by a saturated probability space, there is a pure-strategy Nash equilibrium in every nonatomic game. Finally, if every game with a fixed nonatomic player space and a fixed infinite-dimensional action space has a pure-strategy Nash equilibrium, the underlying player space must be saturated.

Revealed preference theory for finite choice sets

Abstract: The theory of revealed preferences offers an elegant way to test the neoclassical model of utility maximization subject to a linear budget constraint. In many settings, however, the set of available consumption bundles does not take the form of a linear budget set. In this paper, we adjust the theory of revealed preferences to handle situations where the set of feasible bundles is finite. Such situations occur frequently in many real life and experimental settings. We derive the revealed preference conditions for consistency with utility maximization in this finite choice set setting. Interestingly, we find that it is necessary to make a distinction between the cases where the underlying utility function is weakly monotone, strongly monotone and/or concave. Next, we provide conditions on the structure of the finite choice sets for which the usual revealed preference condition (i.e. GARP) is still valid. We illustrate the relevance of our results by means of an illustration based on two experimental data sets that contain choice behaviour from children and young adults.

For claims problems, compromising between the proportional and constrained equal awards rules

Abstract: For the problem of adjudicating conflicting claims, we define a family of two-claimant rules that offer a compromise between the proportional and constrained equal awards rules. We identify the members of the family that satisfy particular properties. We generalize the rules to general populations by requiring “consistency”: The recommendation made for each problem should be “in agreement” with the recommendation made for each reduced problem that results when some claimants receive their awards and leave. We identify which members of the two-claimant family have consistent extensions, and we characterize these extensions. Here too, we identify which extensions satisfy particular properties. Finally, we propose and study a “dual” family.

Differential information in large games with strategic complementarities

Abstract: We study equilibrium in large games of strategic complementarities (GSC) with differential information. We define an appropriate notion of distributional Bayesian Nash equilibrium and prove its existence. Furthermore, we characterize order-theoretic properties of the equilibrium set, provide monotone comparative statics for ordered perturbations of the space of games, and provide explicit algorithms for computing extremal equilibria. We complement the paper with new results on the existence of Bayesian Nash equilibrium in the sense of Balder and Rustichini (J Econ Theory 62(2):385–393, 1994) or Kim and Yannelis (J Econ Theory 77(2):330–353, 1997) for large GSC and provide an analogous characterization of the equilibrium set as in the case of distributional Bayesian Nash equilibrium. Finally, we apply our results to riot games, beauty contests, and common value auctions. In all cases, standard existence and comparative statics tools in the theory of supermodular games for finite numbers of agents do not apply in general, and new constructions are required.

Rational exaggeration and counter-exaggeration in information aggregation games

Abstract: We study an information aggregation game in which each of a finite collection of “senders” receives a private signal and submits a report to the center, who then makes a decision based on the average of these reports. The integration of three features distinguishes our framework from the related literature: players’ reports are aggregated by a mechanistic averaging rule, their strategy sets are intervals rather than binary choices, and they are ex ante heterogeneous. In this setting, players engage in a “tug-of-war,” as they exaggerate and counter-exaggerate in order to manipulate the center’s decision. While incentives to exaggerate have been studied extensively, the phenomenon of counter-exaggeration is less well understood. Our main results are as follows. First, the cycle of counter-exaggeration can be broken only by the imposition of exogenous bounds on the space of admissible sender reports. Second, in the unique pure-strategy equilibrium, all but at most one player is constrained with positive probability by one of the report bounds. Our third and fourth results hold for a class of “anchored” games. We show that if the report space is strictly contained in the signal space, then welfare is increasing in the size of the report space, but if the containment relation is reversed, welfare is independent of the size of the space. Finally, the equilibrium performance of our heterogeneous players can be unambiguously ranked: a player’s equilibrium payoff is inversely related to the probability that her exaggeration will be thwarted by the report bounds.

Further results on essential Nash equilibria in normal-form games

Abstract: A Nash equilibrium $$x$$ of a normal-form game $$G$$ is essential if any perturbation of $$G$$ has an equilibrium close to $$x$$ . Using payoff perturbations, we identify a new collection of games containing a dense, residual subset of games whose Nash equilibria are all essential. This collection covers economic examples that cannot be handled by extant results and subsumes the sets of games considered in the literature.

Learning and Collusion in New Markets with Uncertain Entry Costs

Abstract: This paper analyzes an entry timing game with uncertain entry costs. Two firms receive costless signals about the cost of a new project and decide when to invest. We characterize the equilibrium of the investment timing game with private and public signals. We show that competition leads the two firms to invest too early and analyze two collusion schemes, one in which one firm pays the other to stay out of the market and one in which this buyout is mediated by a third party. We characterize conditions under which the efficient outcome can be implemented in both collusion schemes.

Sharing the surplus in games with externalities within and across issues

Abstract: We consider issue-externality games in which agents can cooperate on multiple issues and externalities are present both within and across issues, that is, the amount a coalition receives in one issue depends on how the players are organized on all the issues Examples of such games are several firms competing in multiple markets, and countries negotiating both a trade agreement (through, eg, WTO) and an environmental agreement (eg, Kyoto Protocol) We propose a way to extend (Shapley) values for partition function games to issue-externality games We characterize our proposal through axioms that extend the Shapley axioms to our more general environment The solution concept that we propose can be applied to many interesting games, including inter-temporal situations where players meet sequentially

Nash bargaining for log-convex problems

Abstract: We introduce log-convexity for bargaining problems. With the requirement of some basic regularity conditions, log-convexity is shown to be necessary and sufficient for Nash’s axioms to determine a unique single-valued bargaining solution up to choices of bargaining powers. Specifically, we show that the single-valued (asymmetric) Nash solution is the unique solution under Nash’s axioms without that of symmetry on the class of regular and log-convex bargaining problems, but this is not true on any larger class. We apply our results to bargaining problems arising from duopoly and the theory of the firm. These problems turn out to be log-convex but not convex under familiar conditions. We compare the Nash solution for log-convex bargaining problems with some of its extensions in the literature.

Information Transmission in Nested Sender-Receiver Games

Abstract: We introduce a “nestedness” relation for a general class of sender–receiver games and compare equilibrium properties, in particular the amount of information transmitted, across games that are nested. Roughly, game $$B$$ is nested in game $$A$$ if the players’ optimal actions are closer in game $$B$$ . We show that under some conditions, more information is transmitted in the nested game in the sense that the receiver’s expected equilibrium payoff is higher. The results generalize the comparative statics and welfare comparisons with respect to preferences in the seminal paper of Crawford and Sobel (Econometrica 50(6):1431–1452, 1982). We also derive new results with respect to changes in priors in addition to changes in preferences. We illustrate the usefulness of the results in three applications: (i) delegation to an intermediary with a different prior, (ii) the choice between centralization and delegation, and (iii) two-way communication with an informed principal.

Learning and market clearing: theory and experiments

Abstract: This paper investigates theoretically and experimentally whether traders learn to use market-clearing trading institutions or whether other (inefficient) market institutions can survive in the long run. Using a framework with boundedly rational traders, we find that market-clearing institutions are always stable under a general class of learning dynamics. However, we show that there exist other, non-market-clearing institutions that are also stable. Therefore, in the long run, traders may fail to coordinate exclusively on market-clearing institutions. Using a replica-economies approach, we find the results to be robust to large market size. The theoretical predictions were confirmed in a series of platform choice experiments. Traders coordinated on platforms predicted to be stable, including market-clearing as well as non-market-clearing ones, while platforms predicted to be unstable were avoided in the long run.