Disappearing private reputations in long-run relationships

For games of public reputation with uncertainty over types and imperfect public monitoring, Cripps et al. [Imperfect monitoring and impermanent reputations, Econometrica 72 (2004) 407-432] showed that an informed player facing short-lived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is long-lived and has private beliefs, so that the informed player's reputation is private. The rate at which reputations disappear is uniform across equilibria and reputations also disappear in sufficiently long discounted finitely repeated games.     

An impossibility result for virtual implementation with status quo

In this paper, virtual implementation is restricted to deliver, on the equilibrium path, either a socially optimal outcome or a status quo: an outcome fixed for all preference profiles. Under such a restriction, for any unanimous and implementable social choice function there is a dictator, who obtains her most preferable outcome as long as all agents prefer this outcome to the status quo. Further restrictions on the lottery space and the range of social choice functions allow the dictator to impose her most preferred outcome even when other agents prefer the status quo to this outcome.     

Economic considerations in the optimal size and number of reserve sites

The debate among ecologists on the optimal number of reserve sites under a fixed maximum total reserve area—the single large or several small (SLOSS) problem—has so far neglected the economic aspects of the problem. This paper argues that economic considerations can affect the optimal number and size of reserve sites and should therefore be taken into consideration in the SLOSS discussion. The paper presents a tractable analytical model to determine the socially optimal number of reserve sites to be allocated in a farming area under a fixed total reserve area, taking the opportunity costs of nature conservation (in this case, agricultural profits) into consideration. Furthermore, the effect of land trade and related transaction costs on the socially optimal number of reserve sites is analyzed. The analysis suggests that in the presence of diminishing returns to farming area, the socially optimal number of reserve sites (which maximizes social welfare) is generally larger than the ecologically optimal number (which maximizes an ecological objective such as population viability). When the opportunity costs of conservation can be offset by land transactions, however, the socially optimal number of reserve sites might be closer to the ecological optimum.     

Sequential equilibrium in monotone games: A theory-based analysis of experimental data

A monotone game is an extensive-form game with complete information, simultaneous moves and an irreversibility structure on strategies. It captures a variety of situations in which players make partial commitments and allows us to characterize conditions under which equilibria result in socially desirable outcomes. However, since the game has many equilibrium outcomes, the theory lacks predictive power. To produce stronger predictions, one can restrict attention to the set of sequential equilibria, or Markov equilibria, or symmetric equilibria, or pure-strategy equilibria. This paper explores the relationship between equilibrium behavior in a class of monotone games, namely voluntary contribution games, and the behavior of human subjects in an experimental setting. Several key features of the symmetric Markov perfect equilibrium (SMPE) are consistent with the data. To judge how well the SMPE fits the data, we estimate a model of Quantal Response Equilibrium (QRE) [R. McKelvey, T. Palfrey, Quantal response equilibria for normal form games, Games Econ. Behav. 10 (1995) 6-38; R. McKelvey, T. Palfrey, Quantal response equilibria for extensive form games, Exp. Econ. 1 (1998) 9-41] and find that the decision rules of the QRE model are qualitatively very similar to the empirical choice probabilities.     

Coase theorem, complexity and transaction costs

This paper, by introducing complexity considerations, provides a dynamic foundation for the Coase theorem and highlights the role of transaction costs in generating inefficient bargaining/negotiation outcomes. We show, when the players have a preference for less complex strategies, the Coase theorem holds in negotiation models with repeated surplus and endogenous disagreement payoffs if and only if there are no transaction costs. Specifically, complexity considerations select only efficient equilibria in these models without transaction costs while every equilibrium induces perpetual disagreement and inefficiency with transaction costs. We also show the latter is true in the Rubinstein bargaining model with transaction costs.     

The supercore for normal-form games

This paper analyzes the supercore of a system derived from a normal-form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore coincides with the set of Nash equilibria of the last game in that sequence. This result is illustrated with the characterization of the supercore for the n-person prisoner's dilemma. With regard to the mixed extension of a normal-form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria.     

Harvesting to Extinction: Is It Socially Rational?

This paper presents a critique of the neoclassical view of the optimal use of renewable resources and offers an alternative view based on the method of classical thermodynamics. The presentation is forwarded via the issue of harvesting to extinction. Based on simple models, the traditional theory suggests that society would benefit from wiping out any renewable resource whose intrinsic growth rate, though positive, is smaller than the social rate of time preference. The latter is the rate society is using to discount its future benefits and costs. To bypass this ecologically implausible outcome, the simplistic assumptions have been modified in various ways. For example, either the costs or the benefits of harvesting have been made to depend on the stock of the resource as well as on the yield. The modifications offered make society less prone to wipe out resources intentionally, but they still disregard a more fundamental difficulty: The traditional theory is not consistent with the second law of thermodynamics; it describes a process that defies the second law, which no known system is able to be undergoing. No doubt, the theory should be challenged first and foremost on this ground, but none of the offered modifications is capable of annulling this inconsistency. A deeper change is needed because the social values of the resource as perceived by a society that behaves in manners consistent with the second law and as defined by the traditional theory necessarily differ. The paper identifies the socially consistent value and shows that harvesting to extinction is never optimal socially. Were society to follow the socially inconsistent value, it would always underestimate the importance of self-sustained resources. However, the unlikely refutability of the second law turns this possibility and the socially favored extinctions into arguable outcomes of an untenable theory rather than undesirable outcomes of a sound theory. Potentially growing renewable resources are wiped out in real life for various reasons, but when they are preyed to extinction, their unfortunate fate is an outcome of the dynamics of a socially unregulated system rather than a social objective coming to fruition. This revised version was published online in July 2006 with corrections to the Cover Date.     

Indeterminacy and directed search

The directed search approach assumes each seller posts a fixed price and, ex post, randomly allocates the good should more than one buyer desire the good. This paper assumes sellers can post prices which are contingent on ex post realized demand; e.g. an advertisement might state the Bertrand price should there be more than one buyer, which corresponds to an auction outcome. Competition in fixed prices and ex post rationing describes equilibrium behavior. There is also real market indeterminacy: a continuum of equilibria exists which are not payoff equivalent. Sellers prefer the equilibrium in auctions.     

Quality Competition and Social Welfare in Markets with Partial Coverage: New Results*

We use a vertical product differentiation model under partial market coverage to study the social welfare optimum and duopoly equilibrium when convex costs of quality provision are either fixed or variable in terms of production. We show the following new results. First, under fixed costs, the social planner charges a uniform price for the single variant that just covers costs of quality provision. Like the duopoly equilibrium, this socially optimal pricing entails a partially uncovered market, but a smaller share of the market is served compared with the duopoly equilibrium. Second, for the variable cost case, it is socially optimal to provide both high‐ and low‐quality variants, but market shares need not be equal. This differs from the result in fully covered markets. Third, in the duopoly equilibrium, the quality spread is too wide under variable costs relative to the social optimum. Under fixed costs, the duopoly produces two variants, but quality is too low relative to the social optimum, which has only one variant.     

A NONCOOPERATIVE SHIPPING COURNOT DUOPOLY WITH LINEAR‐QUADRATIC TRANSPORT COSTS AND CIRCULAR SPACE*

The mixed strategy equilibria in a location quantity duopoly model with circular markets are investigated. We find that a continuum of equilibria exists when the transport cost function is linear. However, if costs are strictly concave or convex, most strategies fail to qualify as equilibria. For any integer n, there are nondegenerate mixed strategy equilibria in which each firm locates at n possible locations with equal probability. This result explains possible outcomes in which firms’ on‐path locations are not minimally or maximally differentiated.     

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x — and on the principal?s costs c(y) — which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal?s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal?s optimal strategy — and similarly of the strategy maximizing the expected welfare of the agents when the principal?s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang?s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.     

Existence of perfect equilibria: a direct proof

We provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. It is done by constructing a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by a generalization of Kakutani theorem, which is proved in this paper. This work offers a new approach to perfect equilibria, which would hopefully facilitate further study on this topic. We also hope our direct proof would be the first step toward building an algorithm to find the set of all perfect equilibria of a strategic game.     

Regularity of pure strategy equilibrium points in a class of bargaining games

Summary. We develop an index theory for the Stationary Subgame Perfect (SSP) equilibrium set in a class of n-player sequential bargaining games with probabilistic recognition rules. For games with oligarchic voting rules (a class that includes unanimity rule), we establish conditions on individual utilities that ensure that for almost all discount factors, the number of SSP equilibria is odd and the equilibrium correspondence lower-hemicontinuous. For games with general, monotonic voting rules, we show generic (in discount factors) determinacy of SSP equilibria under the restriction that the agreement space is of dimension one. For non-oligarchic voting rules and agreement spaces of higher finite dimension, we establish generic determinacy for the subset of SSP equilibria in pure strategies. The analysis also extends to the case of fixed delay costs. Lastly, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games.Received: 13 May 2004, Revised: 1 March 2005, JEL Classification Numbers: C62, C72, C78.I thank John Duggan and participants of the 2003 annual meeting of the American Political Science Association, Philadelphia, PA, the Political Economy Seminar at Northwestern University, and the Economic Theory seminar at the University of Rochester for helpful comments.     

Optimal search auctions

We study the design of profit maximizing single unit auctions under the assumption that the seller needs to incur costs to contact prospective bidders and inform them about the auction. With independent bidders’ types and possibly interdependent valuations, the seller's problem can be reduced to a search problem in which the surplus is measured in terms of virtual utilities minus search costs. Compared to the socially efficient mechanism, the optimal mechanism features fewer participants, longer search conditional on the same set of participants, and inefficient sequence of entry.     

Pareto-optimal Nash equilibria are competitive in a repeated economy

Consider a finite exchange economy first as a static, 1 period, economy and then as a repeated economy over T periods when the utility of each agent is the mean utility over T. A family of strategic games is defined via a set of six general properties the most distinct of which is the ability of agents to move commodities forward in time. Now consider Pareto optimal allocations in the T period economy which are also Nash equilibria in this family of strategic games. We prove that as T becomes large this set converges to the set of competitive utility allocations in the one period economy. The key idea is that a repetition of the economy when agents can move commodities forward in the time acts as a convexification of the set of individually feasible outcomes for player i holding all other strategies fixed.     

Employment changes, the structure of adjustment costs, and plant size

In this paper, we analyze the pattern of employment adjustment using a rich panel of Norwegian plants. The data suggest that the frequency of episodes of zero net employment changes is inversely related to plant size. We develop and estimate a simple “q” model of labor demand, allowing for the presence of fixed, linear and quadratic components of adjustment costs. The econometric evidence supports the existence of purely fixed components, unrelated to plant size. As a result, the range of inaction is wider for smaller plants. The quadratic component of costs is also always important. In most specifications fixed costs are higher for employment contractions. The quadratic component is higher during employment contractions compared to expansions for small plants, while this is not true for larger plants.     

Duopoly models with a joint capacity constraint

The paper proposes a two-stage mixed duopoly model of exhaustible resource market where at the first stage the government decides on the degree of privatization of public firm and at the second stage the public and private firms decide simultaneously on the two-period extraction paths. It is demonstrated that if the two firms have symmetric technologies with increasing marginal extraction costs and the same resource stocks, then neither full nationalization of any of the two firms nor full privatization will be socially desirable. It is shown that the presence of a semi-public firm improves intertemporal allocation of the fixed resource stock. Thus, partial privatization is optimal even under exogenously fixed total outputs of each firm. For asymmetric cost case, when the public firm is less efficient than the private firm, we derive the conditions under which full nationalization or full privatization is optimal.     

Combining an improved multi-delivery policy into a single-producer multi-retailer integrated inventory system with scrap in production

Operating in highly competitive global markets, management of the contemporary corporations constantly seeks to cut down various operating costs, such as inventory holding costs in the production units and their affiliated retailers. For the purpose of reducing stock holding cost, this paper combines an improved multi-delivery policy into a single-producer multi-retailer integrated inventory system with scrap in production. We extend a study by Chiu et al. (2013a) by augmenting an alternative n + 1 product distribution policy to their integrated inventory system. An initial delivery of finished items is shipped to multiple retailers to meet demand during the production unit's uptime. After the remaining production lot is produced and screened, fixed quantity n installments of the finished products are delivered to retailers at a fixed time interval. With the help of a mathematical model along with Hessian matrix equations, the closed-form optimal operating policies for the proposed system are derived. Further, the study demonstrates, through a numerical example, significant savings in stock holding cost for both the production unit and retailers.     

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.