Difference-form contest success functions and effort levels in contests

We examine players' equilibrium effort levels in a contest with difference-form contest success functions in which two players compete with each other to win a prize. We show the following. At the pure-strategy Nash equilibrium of a simultaneous-move game, and in the subgame-perfect equilibrium of a sequential-move game, only one of the players expends effort or neither player expends effort. If one player's composite strength is far greater than the other player's, only the player with greater composite strength expends effort whether they move simultaneously or sequentially. If the players' valuations for the prize and their marginal probabilities of winning at (0, 0) are sufficiently small, neither player expends effort whether they move simultaneously or sequentially.     

A simple endogenous growth model with endogenous fertility and environmental concern

We analyze the implications of endogenous fertility choices on both economic and environmental performances in a stylized AK‐type growth model. Differently from what traditionally assumed in the growth and environment literature, we allow pollution to be not only a by‐product of productive activities by firms but also a result of households’ behavior, as suggested by the celebrated IPAT equation. We show that along the balanced growth path equilibrium, economic growth may be non‐monotonically related to the population growth rate as agents care for the environment; moreover, demographic policies can be used both to achieve win‐win outcomes (simultaneously fostering economic growth and improving environmental quality) and to stabilize the otherwise non‐monotonic economic and population growth relationship.     

A multi-sectoral model with endogenous terminal conditions

In multi-period planning models the terminal conditions problem never has been fully resolved. Typically, prior assumptions on terminal period capital stock levels or post-terminal growth rates are required. In this paper, assumptions of smooth plan period growth rates are employed to eliminate the need for terminal period or post-terminal period assumptions. An iterative solution procedure is utilized and illustrations are given with a multi-sectoral, multi-year model for Korea.     

A model of attrition and income for dynamic longitudinal surveys

This paper develops a random effects model of attrition and income applicable to a dynamic longitudinal survey such as the Survey of Income and Program Participation. Based on the partial dynamic adjustment hypothsis, this study finds that the speed of adjustment of income is not instantaneous as suggeted in many past studies using annual panel data. Also, the short-run coefficients are much smaller than their long-run counterparts, and the coefficient estimates differ substantially among individuals with divergent socioeconomic characteristics. Caution should therefore be exercised when applying dynamic panel data to models with the assumption of an instantaneous speed of adjustment.     

A multi-agent bilateral bargaining model with endogenous protocol

People do bargain over how to bargain. We examine the role of individuals’ ability to pursue certain bargaining protocols in a multi-agent bilateral bargaining model. Bargaining protocols are not completely settled, but will emerge endogenously in equilibrium. We show that players’ ability to partially influence bargaining protocols plays a crucial role in determining equilibrium outcomes. When discounting is not too high, there are multiple subgame perfect equilibria, including inefficient ones. As the number of players increases, both the set of discount factors that support multiple equilibrium outcomes and the set of the first proposing player’s equilibrium payoffs expand. The maximum loss of efficiency increases with respect to the discount factor. We would like to thank Hongbin Cai, John Conlon, Andrew Daughety, Taiji Furusawa, Byoung Heon Jun, Akira Okada, Ping Wang, and two anonymous referees for their comments and suggestions. Both authors gratefully acknowledge financial support from the Social Sciences and Humanities Research Council of Canada.     

Repeated moral hazard with effort persistence

I study a problem of repeated moral hazard where the effect of effort is persistent over time: each period's outcome distribution is a function of a geometrically distributed lag of past efforts. I show that when the utility of the agent is linear in effort, a simple rearrangement of terms in his lifetime utility translates this problem into a related standard repeated moral hazard. The solutions for consumption in the two problems are observationally equivalent, implying that the main properties of the optimal contract remain unchanged with persistence. For illustration, I present the computed solution of an example.     

A dynamic theory of war and peace

In every period, an aggressive country seeks concessions from a non-aggressive country with private information about their cost. The aggressive country can force concessions via war, and both countries suffer from limited commitment. We characterize the efficient sequential equilibria. We show that war is necessary to sustain peace and that temporary wars can emerge because of the coarseness of public information. In the long run, temporary wars can be sustained only if countries are patient, if the cost of war is large, and if the cost of concessions is low.     

A dynamic analysis of an endogenous growth model with leisure

Summary. The main goal in this paper is to analyze an economic model of endogenous growth where human capital accumulation acts as the engine propelling economic activity. The added ingredient in our model is that agents derive utility from consumption and leisure, where leisure is defined as the amount of time devoted to those activities augmented by the level of education. Under regular conditions we show that there is a unique globally stable balanced growth path. We also provide a characterization of the behavior of our economic variables along the transition. Received: May 26, 1998; revised version: September 9, 1999     

A dynamic linear economy with characteristic-based endogenous technical coefficients

We develop a characteristic-based model for the endogenous determination of technical coefficients in a linear economy and use it to describe the dynamics of the economy as driven by changes in knowledge. The use of the characteristic approach to determine technical coefficients makes our model suitable to be interpreted as a first attempt towards the formulation of a formal knowledge-based model of technology.     

Optimal risk-sharing with effort and project choice

We consider first-best risk-sharing problems in which “the agent” can control both the drift (effort choice) and the volatility of the underlying process (project selection). In a model of delegated portfolio management, it is optimal to compensate the manager with an option-type payoff, where the functional form of the option is obtained as a solution to an ordinary differential equation. In the general case, the optimal contract is a fixed point of a functional that connects the agent's and the principal's maximization problems. We apply martingale/duality methods familiar from optimal consumption-investment problems.     

Contracts with endogenous information

I study covert information acquisition and reporting in a principal agent problem allowing for general technologies of information acquisition. When posteriors satisfy two dimensional versions of the standard First Order Stochastic Dominance and Concavity/Convexity of the Distribution Function conditions, a first-order approach is justified. Under the same conditions, informativeness and riskiness of reports are equivalent. High powered contracts, that make the agent's informational rents more risky, are used to increase incentives for information acquisition, insensitive contracts are used to reduce incentives for information gathering. The value of information to the agent is always positive. The value of information to the principal is ambiguous.     

Bargaining with endogenous information

This paper analyses information acquisition in ultimatum bargaining with common values. Because of an endogenous lemons problem the equilibrium payoffs of the agents are non-monotonic in the information cost. The mere possibility of information acquisition can cause no trade although the agents maintain symmetric information in equilibrium and the gain from trade is common knowledge. The agent responding to a take-it-or-leave-it offer may capture some or even the full trading surplus in a perfect Bayesian equilibrium. The implications for sequential bargaining are discussed.     

A note on endogenous transfers

In a competitive and Walrasian stable world with two goods transfer paradoxes are very robust to endogenization (relating the size of the transfer to either the donor's or the recipient's GNP). Donor enrichment and/or recipient impoverishment occur in very general formulations of endogenization if and only if they occur in the model in which transfers are exogenous (as is usually assumed). Endogenization in practice will probably cause a dampening effect (smaller price and welfare changes than in the case of pure exogenous transfers).An earlier version of this paper was presented at the Econometric Society European Meeting in Munich, 1989, and EADI (European Association of Development Research and Training Institutes) in Oslo, 1990. We are grateful to an anonymous referee, Willem Buiter, Peter van Bergeijk, Richard Gigengack, Jan Pen, Georg Tillmann, Edward Towrr, and Casper de Vries for helpful comments.     

A strategic analysis of the war against transnational terrorism

We study a two stage game in which a transnational terrorist organization interacts with an arbitrary number of countries that may differ in their political or economic power, their military effectiveness, the benefit from cooperating against terrorism and the value they assign to damage. Only a subset of countries that emerges endogenously takes proactive measures to fight the terrorist, while all countries incur defensive expenditures to protect their soil. We characterize analytically the pure strategy subgame perfect equilibrium of the game and show how the equilibrium strategies depend on the key model parameters. We provide an algorithm to find the endogenous set of cooperating countries based on their benefit from cooperation and their political/economic power.     

A common value auction model with endogenous entry and information acquisition

Summary Much of the auction literature assumes both a fixed number of bidders and a fixed information setting. This sidesteps the important and often costly decisions a potential bidder must make prior to an auction: Should I enter and, if I do, what level of resources should I expend evaluating the good prior to bidding? We answer these questions for a stylized information model of a common value auction. The expected selling price is shown to be the expected value of the good minus the expected aggregate entry and information costs of the bidders. Thus, the seller indirectly pays for these costs to the bidders. There are auctions where the seller seemingly restricts the bidders' information expenditures. While this restriction does influence the entry decision, we demonstrate that the overall effect can be to improve the selling price. Finally, the probability of entry and the chosen accuracy of the information are never more in the second-price auction than in the first-price auction, and the seller prefers the second-price auction.We are grateful for the comments and suggestions of seminar participants at the University of British Columbia, Dartmouth College, the University of Wisconsin, Yale University, and the International Conference on Game Theory and Economics at SUNY Stony Brook.     

A note on cartel stability and endogenous sequencing with tacit collusion

We use the concept of cartel stability defined by d’Aspremont et al. (Can J Econ 16(1):17–25, 1983) to obtain that the sequence of play between the cartel and the fringe affects cartel stability in a quantity-competition setting where firms tacitly collude. We also prove that an endogenous sequence of play between a cartel and a fringe depends on the discount factor. If the discount factor is large enough, the cartel and the fringe simultaneously choose quantities since the stable cartel may contain more firms under simultaneous play than under cartel leadership. This is due to the fact that under simultaneous play cartel firms have incentives to participate in the cartel because otherwise no collusion is possible.      

Market design with endogenous preferences

This paper explores the interdependence between market structure and an important class of cognitive biases. Starting with a familiar bilateral monopoly framework, we characterize the endogenous emergence of preference distortions during bargaining which cause negotiators to perceive their private valuations differently than they would outside the adversarial negotiation context. Using this model, we then demonstrate how a number of external interventions in the structure and/or organization of market interactions (occurring before trade, after trade, or during negotiations themselves) can profoundly alter the nature of these dispositions. Our results demonstrate that many such interventions frequently (though not always) share qualitatively similar characteristics to market interventions that are often proposed for overcoming more conventional forms of market failure. Nevertheless, our analysis underscores the importance of understanding the precise link between cognitive failures and market structure prior to the implementation of any particular proposed reform.