Wage/tenure contracts with heterogeneous firms

This paper investigates equilibria where firms post wage/tenure contracts and risk averse workers search for new job opportunities whether employed or unemployed. We generalize previous work by assuming firms have different productivities. Equilibrium implies more productive firms always offer more desirable contracts. Thus workers never quit from more productive firms for less productive firms. Nevertheless turnover is inefficient as employees with long tenures at low productivity firms may reject outside job offers from more productive firms. A worker who quits to a more productive firm may accept a wage cut. Such wage cuts are compensated by faster “promotion” rates to higher wage levels in the future. We also generalize previous arguments by showing equilibria exist where the distribution of offers contains interior mass points and find equilibrium wage/tenure contracts need not be smooth.     

The Nash-threats folk theorem with communication and approximate common knowledge in two player games

We show that the use of communications to coordinate equilibria generates a Nash-threats folk theorem in two-player games with “almost public” information. The results generalize to the n-person case. However, the two-person case is more difficult because it is not possible to sustain equilibria by comparing the reports of different players, and using these “third parties” to effectively enforce contracts.     

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.     

Collusion and discrimination in organizations

In a principal-multi-agent setting we investigate how optimal contracts should be modified under relative performance evaluation when agents collude. Agents may write side-contracts, which are not contingent on their effort choices but indirectly control them through side-transfers. We show that the optimal collusion-proof contract is to introduce a “discriminatory policy” in the sense that the wage schemes offered to agents depend on their identities even if they are identical with respect to productive abilities. Such discriminatory wage schemes explain the organizational strategy of “divide and conquer” as an optimal response to collusion.     

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.     

Superstition and “lucky” apartments: Evidence from transaction-level data

Using a sample of apartment transactions during 2004–2006 in Chengdu, China, we investigate the impact of superstitions in the Chinese real estate market. Numerology forms an important component of Chinese superstitious lore, with the numbers 8 and 6 signifying good luck, and the number 4 bad luck. We find that secondhand apartments located on floors ending with “8” fetch, on average, a 235 RMB higher price (per square meter) than on other floors. For newly constructed apartments, this price premium disappears due to uniform pricing of new housing units, but apartments on floors ending in an “8” are sold, on average, 6.9 days faster than on other floors. Buyers who have a phone number containing more “8”’s are more likely to purchase apartments in a floor ending with “8”; this suggests that at least part of the price premium for “lucky” apartments arises from the buyers’ superstitious beliefs.     

The role of strategic uncertainty in games: An experimental study of cheap talk and contracts in the Nash demand game

We utilise results from a human-subjects experiment to examine the connection between strategic uncertainty and outcomes in games. Our basic game is a Nash demand game where one player has an outside option available. A “chat” treatment allows bargainers to send cheap-talk messages prior to playing the basic game, and in a “contracts” treatment, they can additionally propose and accept binding contracts. We propose that strategic uncertainty comprises at least two facets: “coordination-type”, which is lower in the chat game than in the basic game, and “rationality-type”, which is lower in the contracts game than in the chat game. We find that both types of strategic uncertainty impact bargaining outcomes: moving from the basic game to the chat game, and thence to contracts, improves several aspects of outcomes, such as higher efficiency, less opting out and less under-demanding. Other results include a treatment effect on the types of agreements that are reached.     

Between a rock and a soft place: Ecological and feminist economics in policy debates

The field of ecological economics includes both economic analysis on the one hand, and discussions of normative values and visions for society, on the other. Using feminist insights into cultural beliefs about the relative “hardness” and “softness” of these two sides, this essay discusses how ecological economists can use this unique “between” space in order to better inform policy. The current crisis of global climate change, it is argued, requires that economists move beyond modeling and measurement, while ecological thinkers need to re-examine beliefs about markets and profit.     

Self-confirming equilibrium and the Lucas critique

We examine the role of off-path “superstitions” in macro-economics, and show how a false belief about off-path play is the key element underlying both the Lucas Critique and the game-theoretic concept of self-confirming equilibrium. However, the impact of false beliefs in these two cases is different: In the Lucas case, a policy maker's incorrect beliefs about off-path play can lead to the adoption of mistaken policy innovation. However, the consequences of such an innovation provide evidence that the belief that motivated them was wrong. In contrast, play may never escape an undesirable self-confirming equilibrium, as the action implied by the mistaken belief does not generate data that contradicts it; escape from the self-confirming equilibrium requires that players do a sufficient amount of experimentation with off-path actions.     

Resolving Indeterminacy in Coordination Games: A New Approach Applied to a Pay-as-you-go Pension Scheme

This paper shows that when players ignore what outcome will emerge because of the presence of multiple equilibria, they can coordinate their expectations by forming an initial belief based on the principle of indifference followed by a process of reasoning that updates this belief. Since this procedure describes a natural way to form beliefs under indeterminacy, it is reasonable for every agent to conjecture that all the others form their beliefs according to the same logic. Exactly the fact that agents are aware that they form their beliefs following the same procedure allows them to successfully coordinate their expectations.      

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.     

Transfer fee regulations in European football

We analyze the impact of three different transfer fee systems on payoffs, contract lengths, training and effort incentives in European football. The different regimes, being used until 1995 (“pre-Bosman”), currently in use (“Bosman”), and recently approved (“Monti”) differ with respect to the transfer fee an initial club is entitled to depending on whether a player has a valid contract or not. We show that the different systems differ only with respect to the contract length if the contract which maximizes the expected joint surplus of the initial club and the player is feasible under each system. Otherwise, regime P is strictly dominated by regime B in terms of expected social welfare. Regime M leads to higher effort but lower incentives to invest in training compared to system B.     

Random belief equilibrium in normal form games

In defining random belief equilibrium (RBE) in finite, normal form games we assume a player's beliefs about others' strategy choices are randomly drawn from a belief distribution that is dispersed around a central strategy profile, the focus. At an RBE: (1) Each chooses a best response relative to her beliefs. (2) Each player's expected choice coincides with the focus of the other players' belief distributions. RBE provides a statistical framework for estimation which we apply to data from three experimental games. We also characterize the limit-RBE as players' beliefs converge to certainty. When atoms in the belief distributions vanish in the limit, not all limit-RBE (called robust equilibria) are trembling hand perfect Nash equilibria and not all perfect equilibria are robust.     

International migration and “educated unemployment”

This paper provides a novel explanation of “educated unemployment”, which is a salient feature of the labor markets in a number of developing countries. In a simple job-search framework we show that “educated unemployment” is caused by the prospect of international migration, that is, by the possibility of a “brain drain”. In addition, the analysis shows that a developing country may end up with more educated workers despite the brain drain and educated unemployment.     

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.     

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”.     

Agency in a market setting

This paper examines a market in which a continuum of principals and agents interact in a game. Principals offer contracts while agents decide on sets of acceptable contracts. A mechanism from a class satisfying efficiency, unbiasedness, and continuity properties then matches principals and agents. With risk neutral agents, when the contribution of principals and agents to the total gains from trade in a pairing are additively separable, the equilibria of the game coincide with the competitive equilibria for the market. In particular, all contracts used in Nash equilibrium induce first-best effort levels. Both principals and agents have exogenous opportunities outside this market. In equilibrium, agents have endogenously determined outside opportunities available from employment by another principal, and this may be the binding participation constraint in a principal-agent pairing. The results are extended to special non-separable cases and to the case of identical risk averse agents.We are grateful to seminar participants at Indiana University, the University of Kentucky, and Vanderbilt University for comments on earlier versions of this work. Referees' comments led us to generalize the model and to more clearly specify the point of the paper.     

Risk-bearing and entrepreneurship

In the “Knightian” theory of entrepreneurship, entrepreneurs provide insurance to workers by paying fixed wages and bear all the risk of production. This paper endogenizes entrepreneurial risk by allowing for optimal insurance contracts as well as occupational self-selection. Moral hazard prevents full insurance; increases in an agent's wealth then entail increases in risk borne. Thus, even under decreasing risk aversion, there are robust instances in which workers are wealthier than entrepreneurs. This empirically implausible result suggests that risk-based explanations for entrepreneurship are inadequate.