Simple sequencing problems with interdependent costs

In this paper we analyze simple sequencing problems under incomplete information and interdependent costs. We prove the necessity of concave cost function for implementability of such problems. Implementability means that one can achieve aggregate cost minimization in ex-post equilibrium. We also show that simple sequencing problems are implementable if and only if the mechanism is a ‘generalized VCG mechanism.’ We then consider first best implementability, that is implementability with budget balancing transfer. We prove that for implementable n agent simple sequencing problems, with polynomial cost function of order (n−2) or less, one can achieve first best implementability. Finally, for the class of implementable simple sequencing problems with “sufficiently well behaved” cost function, this is the only first best class.     

Secure implementation in Shapley–Scarf housing markets

This paper considers the object allocation problem introduced by Shapley and Scarf (J Math Econ 1:23–37, 1974). We study secure implementation (Saijo et al. in Theor Econ 2:203–229, 2007), that is, double implementation in dominant strategy and Nash equilibria. We prove that (1) an individually rational solution is securely implementable if and only if it is the no-trade solution, (2) a neutral solution is securely implementable if and only if it is a serial dictatorship, and (3) an efficient solution is securely implementable if and only if it is a sequential dictatorship. Furthermore, we provide a complete characterization of securely implementable solutions in the two-agent case: a solution is securely implementable if and only if it is either a constant solution or a serial dictatorship.     

Implementation of college admission rules

Summary We consider both Nash and strong Nash implementation of various matching rules for college admissions problems. We show that all such rules are supersolutions of the stable rule. Among these rules the lower bound stable rule is implementable in both senses. The upper bound Pareto and individually rational rule is strong Nash implementable yet it is not Nash implementable. Two corollaries of interest are the stable rule is the minimal (Nash or strong Nash) implementable solution that is Pareto optimal and individually rational, and the stable rule is the minimal (Nash or strong Nash) implementable extension of any of its subsolutions.We wish to thank Professor William Thomson for his efforts in supervision as well as his useful suggestions. We are grateful to the participants in his reading class, workshops at Bilkent University, University of Rochester, and in particular Jeffrey Banks, Stephen Ching, Bhaskar Dutta, Rangarajan Sundaram and an anonymous referee for their helpful comments.     

Nash implementing non-monotonic social choice rules by awards

Summary. By a slight generalization of the definition of implementation (called implementation by awards), Maskin monotonicity is no more needed for Nash implementation. In fact, a weaker condition, to which we refer as almost monotonicity is both necessary and sufficient for social choice correspondences to be Nash implementable by awards. Hence our framework paves the way to the Nash implementation of social choice rules which otherwise fail to be Nash implementable. In particular, the Pareto social choice rule, the majority rule and the strong core are almost monotonic (hence Nash implementable by awards) while they are not Maskin monotonic (hence fail to be Nash implementable in the standard framework).Received: 12 April 2004, Revised: 18 March 2005, JEL Classification Numbers: D 79.I thank François Maniquet, Efe Ok and Ipek Ozkal-Sanver for their valuable contributions. The paper is part of a project on Electoral System Design supported by Bilgi University Research Fund.     

Norms as emergent properties of adaptive learning: The case of economic routines

Interaction among autonomous decision-makers is usually modelled in economics in game-theoretic terms or within the framework of General Equilibrium. Game-theoretic and General Equilibrium models deal almost exclusively with the existence of equilibria and do not analyse the processes which might lead to them. Even when existence proofs can be given, two questions are still open. The first concerns the possibility of multiple equilibria, which game theory has shown to be the case even in very simple models and which makes the outcome of interaction unpredictable. The second relates to the computability and complexity of the decision procedures which agents should adopt and questions the possibility of reaching an equilibrium by means of an algorithmically implementable strategy. Some theorems have recently proved that in many economically relevant problems equilibria are not computable. A different approach to the problem of strategic interaction is a “constructivist” one. Such a perspective, instead of being based upon an axiomatic view of human behaviour grounded on the principle of optimisation, focuses on algorithmically implementable “satisfycing” decision procedures. Once the axiomatic approach has been abandoned, decision procedures cannot be deduced from rationality assumptions, but must be the evolving outcome of a process of learning and adaptation to the particular environment in which the decision must be made. This paper considers one of the most recently proposed adaptive learning models: Genetic Programming and applies it to one the mostly studied and still controversial economic interaction environment, that of oligopolistic markets. Genetic Programming evolves decision procedures, represented by elements in the space of functions, balancing the exploitation of knowledge previously obtained with the search of more productive procedures. The results obtained are consistent with the evidence from the observation of the behaviour of real economic agents.     

Joining a Queue or Staying Out: Effects of Information Structure and Service Time on Arrival and Staying Out Decisions

We study a class of single-server queueing systems with a finite population size, FIFO queue discipline, and no balking or reneging. In contrast to the predominant assumptions of queueing theory of exogenously determined arrivals and steady state behavior, we investigate queueing systems with endogenously determined arrival times and focus on transient rather than steady state behavior. When arrival times are endogenous, the resulting interactive decision process is modeled as a non-cooperative n-person game with complete information. Assuming discrete strategy spaces, the mixed-strategy equilibrium solution for groups of n = 20 agents is computed using a Markov chain method. Using a 2 × 2 between-subject design (private vs. public information by short vs. long service time), arrival and staying out decisions are presented and compared to the equilibrium predictions. The results indicate that players generate replicable patterns of behavior that are accounted for remarkably well on the aggregate, but not individual, level by the mixed-strategy equilibrium solution unless congestion is unavoidable and information about group behavior is not provided.JEL Classification: C71, C92, D81     

Mechanism design with partial state verifiability

We study implementation in environments where agents have limited ability to imitate others. Agents are randomly and privately endowed with type-dependent sets of messages. So sending a message becomes a partial proof regarding type. For environments where agents can send any combination of available messages, we develop an Extended Revelation Principle and characterize the incentive constraints which implementable allocations must satisfy. When not all message combinations are feasible, static mechanisms no longer suffice. If a ‘punishment’ allocation exists for each agent, then implementable allocations can be characterized as equilibria of a “Revelation Game,” in which agents first select from the menus of allocation rules, then the mediator requests each agent to send some verifying messages. When a punishment allocation fails to exist for some agent, dynamic games in which agents gradually reveal their evidence implement a larger set of outcomes. The latter result provides a foundation for a theory of debate.     

On coalitional stability of anonymous interim mechanisms

Summary.   In a situation where agents have private information, we investigate the stability of mechanisms with respect to coalitional deviations. In the cooperative tradition, we first extend the notion of Core, taking into account the information a coalition may have when it forms and the conjectures of outsiders. This leads us to propose a family of Cores rather than a single one. Secondly, we study the stability of Core mechanisms to secession proposals in simple noncooperative games. The two different stability analyses, normative and strategic, tend to give support to the more natural extension of the Core, called Statistical Core, only in situations where some strong form of increasing returns to coalition is met. Without this property, arguments for a concept of Core that is non empty in a reasonably large class of problems are less compelling. Applications to taxation and insurance are given. Received: September 6, 1999; revised version: December 3, 1999     

Ex-post implementation and preference aggregation via potentials

We introduce several notions of potentials for mechanism design problems with interdependent values, and relate them to implementation in ex-post equilibrium. Whereas ex-post implementation is closely linked to the ordinal concept of best-alternative potentials, the celebrated Vickrey–Clarke–Groves mechanism corresponds to the stronger notion of a cardinal potential: agents agree not only on the best alternative, but also on the quantitative differences between all alternatives. We characterize all valuations that allow for cardinal potentials, and use this characterization for: (1) Identifying valuations for which ex-post implementation is possible; (2) Identifying classes of valuations for which all ex-post implementable choice rules correspond to cardinal potentials. The latter allows us to extend to interdependent valuations a result for dominant strategy implementation in private values settings, due to Roberts (The Characterization of Implementable Choice Rules, North-Holland, Amsterdam, 1979). We wish to thank an associate editor, two anonymous referees, Paul Milgrom and Burkhard Schipper for helpful comments and stimulating remarks.     

Adverse selection problems without the Spence-Mirrlees condition

This paper studies a class of one-dimensional screening problems where the agent's utility function does not satisfy the Spence-Mirrlees condition (SMC). The strength of the SMC for hidden information problems is to provide a full characterization of implementable contracts using only the local incentive compatibility (IC) constraints. These constraints are equivalent to the monotonicity of the decision variable with respect to the agent's unobservable one-dimensional parameter. When the SMC is violated the local IC constraints are no longer sufficient for implementability and additional (global) IC constraints have to be taken into account. In particular, implementable decisions may not be monotonic and discretely pooled types must have the same marginal utility of the decision (or equivalently, get the same marginal tariff). Moreover, at the optimal decision, the principal must preserve the same trade-off between rent extraction and allocative distortion measured in the agent's marginal rent unit. In a specific setting where non-monotone contracts may be optimal we fully characterize the solution.     

Intertemporal data and travel cost analysis

This paper considers the use of multi-year data in travel cost analysis. To exploit the information embedded within intertemporal data, two broad approaches are examined: multiple year cross sections and panel models. Multiple year cross sections can be used to detect trends, and to test for stability of behavior. Panel models can be used to control for unobservable factors that are individual specific. Unfortunately, the low intertemporal variability of travel cost data sets weakens the power of panel estimators. Using aggregate data from the Boundary Waters Canoe Area, the stability of demand processes over the 1980–1986 period is investigated, as well as the problems inherent in using panel estimators in travel cost analysis.     

Comparative Learning Dynamics*

We study economic environments in which agents make choices on the basis of relative performance criteria and call the associated class of dynamic adjustment rules comparative dynamics. We distinguish two classes of learning behavior: learning from the population experience (imitative dynamics) and learning only from one's own experience (introspective dynamics). Paradoxically, for a broad class of models, comparing stochastically stable states across dynamics, agent payoffs are lower for imitative than introspective dynamics—mimicking best practice in the population is counterproductive.     

Specification and estimation of nonstandard profit functions

This paper critically examines appropriateness of the nonstandard profit function (NSPF) as a tool for measuring profit efficiency. We show that there are some fundamental problems with the NSPF approach, the way it is currently specified and estimated. This is true irrespective of whether technical inefficiency is included or not. Instead of estimating profit efficiency directly from the NSPF, we suggest alternative specifications and recommend using the cost function approach and deriving profit efficiency therefrom. Data from US banks are used to estimate the cost function and the NSPF. Results from alternative specifications are then compared and analyzed.

Non-computable strategies and discounted repeated games

Summary A number of authors have used formal models of computation to capture the idea of bounded rationality in repeated games. Most of this literature has used computability by a finite automaton as the standard. A conceptual difficulty with this standard is that the decision problem is not closed. That is, for every strategy implementable by an automaton, there is some best response implementable by an automaton, but there may not exist any algorithm forfinding such a best response that can be implemented by an automaton. However, such algorithms can always be implemented by a Turing machine, the most powerful formal model of computation. In this paper, we investigate whether the decision problem can be closed by adopting Turing machines as the standard of computability. The answer we offer is negative. Indeed, for a large class of discounted repeated games (including the repeated Prisoner's Dilemma) there exist strategies implementable by a Turing machine for whichno best response is implementable by a Turing machine.The work was begun while Nachbar was a visitor at The Center for Mathematical studies in Economics and Management Science at Northwestern University; he is grateful for their hospitality. We are also grateful to Robert Anderson and Neil Gretsky and to seminar audiences at UCLA for useful comments, and to the National Science Foundation and the UCLA Academic Senate Committee on Research for financial support. This paper is an outgrowth of work reported in Learning and Computability in Discounted Supergames.     

Egalitarian equivalence and strategyproofness in the queueing problem

We investigate the implications of egalitarian equivalence (Pazner and Schmeidler in Q J Econ 92:671–687, 1978) together with queue efficiency and strategyproofness in the context of queueing problems. We completely characterize the class of mechanisms satisfying the three requirements. Though there is no mechanism in this class satisfying budget balance, feasible mechanisms exist and we characterize the set of all such mechanisms. We also show that it is impossible to find a mechanism satisfying queue efficiency, egalitarian equivalence, and a stronger notion of strategyproofness called weak group strategyproofness. In addition, we show that generically there is no mechanism satisfying both egalitarian equivalence and no-envy.     

Monotonicity and Nash implementation in matching markets with contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (in A Econ Rev, 95(4), 913–935, 2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable. Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence. In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.     

Optimal simple rules and the lower bound on the nominal interest rate in the Christiano–Eichenbaum–Evans model of the US business cycle

Schmitt-Grohé and Uribe (NBER wp 10724, 2004b) analyzes the optimal, simple and implementable monetary policy rules in a medium-scale macromodel, as the one proposed by Christiano et al. (J Polit Econ 113:1–45, 2005). In doing so, they use a sensible, but somewhat arbitrary constraint to account for the lower bound condition on the nominal interest rate. In this work, we check the robustness of their main results to such a criteria. We find that the optimal policies are actually absolutely robust to the easing of this criterion for all the different cases considered.

Hedging and flexing : Two ways of choosing under ignorance

Two strategies for making decisions under severe uncertainty—called here ignorance—are contrasted. A popular strategy under such conditions is to forego the best outcome in order to avoid the worst which might happen; this is hedging, and is shown to lead to a number of problems: once made, a hedge can rarely be revised if the worst does not occur; hedging often brings about the worst outcome which is being hedged against; the worst outcome is often undefined; and hedging can lead to a vicious circle, disregarding the benefits which an option might bring. Each problem is illustrated by a decision about technological change, which typically are decisions under ignorance. Flexing has none of these problems. Flexing aims at achieving the very best outcome. This too risks achieving the worst outcome, but the strategy insures against this. The decision maker should ensure that if the worst outcome arises, the original decision can be reserved quickly and without great cost. Ways in which this can be done are discussed through the examples.     

DYNAMIC MECHANISM DESIGN FOR A GLOBAL COMMONS

We model dynamic mechanisms for a global commons. Countries value both consumption and conservation of an open access resource. A country's relative value of consumption to conservation is privately observed and evolves stochastically. An optimal quota maximizes world welfare subject to being implementable by Perfect Bayesian equilibria. With complete information, the optimal quota is first best; it allocates more of the resource each period to countries with high consumption value. Under incomplete information, the optimal quota is fully compressed: Identical countries receive the same quota even as environmental costs and resource needs differ. This is true even when private information is negligible.     

From families to formal contracts: An approach to development

This paper develops a theory in which individuals can use one of two types of human/social capital to enforce contracts: “Local capital” relies on families and other personal networks; “market capital” relies on impersonal market institutions such as auditors and courts. Local capital is efficient when most trading is local, but only market capital can support trading between strangers that allows extensive division of labor and industrialization. We show that economies with a low cost of accumulating local capital (say, because people live close together) are richer than economies with a high cost of accumulation when long distance trade is difficult, but are slower to transition to impersonal market exchange (industrialize) when long distance trade becomes feasible. The model provides one way to understand why the wealthiest economies in 1600 AD, China, India, and the Islamic Middle East, industrialized more slowly than the West. We report an array of historical evidence documenting the pre-industrial importance of family and kinship networks in China, India, and the Islamic world compared to Europe, and the modernization problems linked to local capital.