Equilibrium selection and the dynamic evolution of preferences

A population of fully rational agents plays a symmetric 2-player game in biological fitnesses, but each agent?s play is determined by his payoffs, which are free to evolve according to “survival of the fittest” pressures. An equilibrium-selection mechanism is assumed to exist, and deliver a unique outcome for any given profile of payoffs; this allows the evolution of payoffs to be modeled as a well-defined replicator dynamics. The existing static stability results that “efficient strict Nash implies stability” and “stability implies efficiency” are translated to this dynamic context, although the latter gives way to indeterminacy in the absence of a specific equilibrium-selection mechanism. A strong form of stability is established for the efficient outcome of games with common interests, whilst a weaker stability result is provided for efficient mixed-strategy equilibria of doubly symmetric games. The results are illustrated using the equilibrium-selection mechanism provided by global games.     

Are incentives against economic justice?

We consider the problem of fairly allocating a social endowment of indivisible goods and money when the domain of admissible preferences contains, but is not restricted to, quasi-linear preferences. We analyze the manipulability of the Generalized Money Rawlsian Fair (GMRF) solutions. (i) We show that the Nash and strong Nash equilibrium correspondences of the “preference revelation game form” associated with each GMRF solution coincide with the no-envy solution (in equilibrium, efficiency is preserved according to agents' true preferences). (ii) A corollary is that the GMRF solutions “naturally implement” the no-envy solution in Nash and strong Nash equilibria.     

Asymmetric English auctions

This paper studies equilibria of the n-bidder single-object English, or open ascending price, auction in a setting with interdependent values and asymmetric bidders. Maskin (in: H. Siebert (Ed.), Privatization, Institut fur Weltwirtschaften der Universität Kiel, Kiel, 1992, pp. 115-136.) showed that if the values satisfy a “single crossing” condition, then the two-bidder English auction has an efficient equilibrium. In this paper, two extensions of the single crossing condition, the “average crossing” condition and the “cyclical crossing” condition, are introduced. The main result is that under either of these conditions the n-bidder English auction has an efficient equilibrium.     

Strategic analysis of petty corruption: Entrepreneurs and bureaucrats

This paper develops a game-theoretic model of “petty corruption” by government officials. Such corruption is widespread, especially (but not only) in developing and transition economies. The model goes beyond the previously published studies in the way it describes the structure of bureaucratic “tracks,” and the information among the participants. Entrepreneurs apply, in sequence, to a “track” of two or more bureaucrats in a prescribed order for approval of their projects. Our first result establishes that in a one-shot situation no project ever gets approved. This result leads us to consider a repeated interaction setting. In that context we characterize in more detail the trigger-strategy equilibria that minimize the social loss due to the system of bribes, and those that maximize the expected total bribe income of the bureaucrats. The results are used to shed some light on two much advocated anti-corruption policies: the single window policy and rotation of bureaucrats.     

Asymmetry, stability and growth in a step-by-step R&D-race

We define a notion of stability of equilibrium in an infinitely repeated step-by-step R&D race. The unique symmetric equilibrium is shown to be unstable, and stable asymmetric equilibria arise, if product market competition is intense, firms are patient, imitation is difficult and innovations are large. Some predictions based on symmetric equilibria, e.g. that less patient firms always invest less in research, or that more intensive competition leads to higher economic growth, are reversed for “realistic” values of the underlying parameters.     

Uniqueness of stationary equilibria in a one-dimensional model of bargaining

We prove uniqueness of stationary equilibria in a one-dimensional model of bargaining with quadratic utilities, for an arbitrary common discount factor. For general concave utilities, we prove existence and uniqueness of a “minimal” stationary equilibrium and of a “maximal” stationary equilibrium. We provide an example of multiple stationary equilibria with concave (nonquadratic) utilities.     

Law enforcement and transition

We present a simple model to analyze law enforcement problems in transition economies. Law enforcement implies coordination problems and multiplicity of equilibria due to a law abidance and a fiscal externality. We analyze two institutional mechanisms for solving the coordination problem. A first mechanism, which we call “dualism”, follows the scenario of Chinese transition where the government keeps direct control over economic resources and where a liberalized non-state sector follows market rules. The second mechanism we put forward is accession to the European Union. We show that accession to the European Union, even without external borrowing, provides a mechanism to eliminate the “bad” equilibrium, provided the “accessing” country is small enough relative to the European Union. Interestingly, we show that accession without conditionality is better than with conditionality because conditionality creates a coordination problem of its own that partly annihilates the positive effects of expected accession.     

Skills, agglomeration and segmentation

This paper studies the role of skill heterogeneity in “new economic geography” models of location. In our setting, products are both horizontally and vertically differentiated, and producing higher quality goods requires workers with higher skills. Selling to customers based in a different location entails iceberg-type transport costs and additional “communication costs” consisting of a fixed quality loss. We show that the presence of pecuniary externalities creates a mechanism which always promotes spatial sorting of workers according to their skill levels. In particular, in all stable equilibria, workers with higher skill choose to stay in the location where aggregate skill and income is higher, while the less skilled stay in the other.     

Coordination failure in repeated games with private monitoring

Players coordinate continuation play in repeated games with public monitoring. We investigate the robustness of such equilibrium behavior with respect to ex-ante small private-monitoring perturbations. We show that with full support of public signals, no perfect public equilibrium is robust if it induces a “regular” 2×2$2\times 2$ coordination game in the continuation play. This regularity condition is violated in all belief-free equilibria. Indeed, with an individual full rank condition, every interior belief-free equilibrium is robust. We also analyze block belief-free equilibria and point out that the notion of robustness is sensitive to whether we allow for uninterpretable signals.     

Crime and punishment in the “American Dream”

We observe that countries where belief in the “American dream”(i.e., effort pays) prevails also set harsher punishment for criminals. We know that beliefs are also correlated with several features of the economic system (taxation, social insurance, etc). Our objective is to study the joint determination of these three features (beliefs, punitiveness and economic system) in a way that replicates the observed empirical patterns. We present a model where beliefs determine the types of contracts that firms offer and whether workers exert effort. Some workers become criminals, depending on their luck in the labor market, the expected punishment, and an individual shock that we call “meanness”. It is this meanness level that a penal system based on “retribution” tries to detect when deciding the severity of the punishment. We find that when initial beliefs differ, two equilibria can emerge out of identical fundamentals. In the “American” (as opposed to the “French”) equilibrium, belief in the “American dream” is commonplace, workers exert effort, there are high powered contracts (and income is unequally distributed) and punishments are harsh. Economists who believe that deterrence (rather than retribution) shapes punishment can interpret the meanness parameter as pessimism about future economic opportunities and verify that two similar equilibria emerge.     

Credible group stability in many-to-many matching problems

It is known that in two-sided many-to-many matching problems, pairwise-stable matchings may not be immune to group deviations, unlike in many-to-one matching problems (Blair, 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise-responsive preferences. A credibly group-stable matching is immune to any “executable” group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.     

Intergenerational transmission of preferences

We propose a perfect empathy model of cultural transmission to capture the evolution of preferences in a population. Unlike existing imperfect empathy models, focusing on stable interior equilibria, we demonstrate that a corner outcome will eventuate. However, which corner outcome emerges is unknown, and depends on the interplay of “history” and “expectations”.     

Bidding for the future: signaling in auctions with an aftermarket

This paper considers auctions where bidders compete for an advantage in future strategic interactions. When bidders wish to exaggerate their private information, equilibrium bidding functions are biased upwards as bidders attempt to signal via the winning bid. Signaling is most prominent in second-price auctions where equilibrium bids are “above value.” In English and first-price auctions, signaling is less extreme since the winner incurs the cost of her signaling choice. The opportunity to signal lowers bidders’ payoffs and raises revenue. When bidders understate their private information, separating equilibria need not exist and the auction may not be efficient.     

Testing threats in repeated games

Under most game-theoretic solution concepts, equilibrium beliefs are justified by off-equilibrium events. I propose an equilibrium concept for infinitely repeated games, called “Nash Equilibrium with Tests” (NEWT), according to which players can only justify their equilibrium beliefs with events that take place on the equilibrium path itself. In NEWT, players test every threat that rationalizes a future non-myopic action that they take. The tests are an integral part of equilibrium behavior. Characterization of equilibrium outcomes departs from the classical “folk theorems”. The concept provides new insights into the impact of self-enforcement norms, such as reciprocity, on long-run cooperation.     

On the size and structure of group cooperation

When time preferences are heterogeneous and bounded away from one, how “much” cooperation can be achieved by an ongoing group? How does group cooperation vary with the group's size and structure? This paper examines characteristics of cooperative behavior in the class of symmetric, repeated games of collective action. These are games characterized by “free rider problems” in the level of cooperation achieved. The Repeated Prisoner's Dilemma games is a special case.We characterize the level of maximal average cooperation (MAC), the highest average level of cooperation, over all stationary subgame perfect equilibrium paths, that the group can achieve. The MAC is shown to be increasing in monotone shifts, and decreasing in mean preserving spreads of the distribution of discount factors. The latter suggests that more heterogeneous groups are less cooperative on average. Finally, in a class of Prisoner's Dilemma games, we show under weak conditions that the MAC exhibits increasing returns to scale in a range of heterogeneous discount factors. That is, larger groups are more cooperative, on average, than smaller ones. By contrast, when the group has a common discount factor, the MAC is invariant to group size.     

The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure

The Shapley value assigns, to each game that is adequately represented by its characteristic function, an outcome for each player. An elaboration on the Shapley value that assigns, to characteristic function games, a “partition function” outcome is broadly established and accepted, but elaborations to encompass games with externalities (represented by partition functions) are not. Here, I show that simultaneous consideration of the two elaborations (“generalization” and “extension”) obtains a unique Shapley-type value for games in partition function form. The key requirement is that the “Extended, Generalized Shapley Value” (EGSV) should be “recursive”: the EGSV of any game should be the EGSV of itself. This requirement forces us to ignore all but the payoffs to bilateral partitions. The EGSV can be conceptualized as the ex ante value of a process of successive bilateral amalgamations. Previous Shapley value extensions, if generalized, are not recursive; indeed, they iterate to the EGSV.     

Buyer investment, export variety, and intrafirm trade

This paper studies a model of buyer investment and its effect on the variety and vertical structure of international trade. A distinction is made between two types of buyer investment: “Flexible” and “specific”, which differ in the ability of a buyer to match with a seller. The interaction of buyer investment with the entry and pricing incentives of suppliers are analyzed. It is shown that (i) there can be multiple equilibria in the variety of products traded, and (ii) less product variety is associated with more intrafirm trade. The possibility of multiple equilibria is consistent with the observation that some similar economies, such as Taiwan and South Korea, differ substantially in their export varieties to the U.S. A cross-country empirical analysis confirms the negative correlation between export variety and intrafirm trade.     

Differentiating ambiguity and ambiguity attitude

The objective of this paper is to show how ambiguity, and a decision maker (DM)'s response to it, can be modelled formally in the context of a general decision model. We introduce a relation derived from the DM's preferences, called “unambiguous preference”, and show that it can be represented by a set of probabilities. We provide such set with a simple differential characterization, and argue that it is a behavioral representation of the “ambiguity” that the DM may perceive. Given such revealed ambiguity, we provide a representation of ambiguity attitudes. We also characterize axiomatically a special case of our decision model, the “α-maxmin” expected utility model.     

The treatment effect, the cross difference, and the interaction term in nonlinear “difference-in-differences” models

In any nonlinear “difference-in-differences” model with strictly monotonic transformation function, the treatment effect is the cross difference of the observed outcome minus the cross difference of the potential non-treatment outcome, which equals the incremental effect of the interaction term coefficient.