Cournot–Nash equilibria in continuum games with non-ordered preferences

In the usual framework of continuum games with externalities, we substantially generalize Cournot–Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79–94; On the existence of Cournot–Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207–223; A unifying pair of Cournot–Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437–470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237–246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9–15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345–348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econ. 3 (1976) 313–316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233–245].     

Run equilibria in the Green–Lin model of financial intermediation

We study the Green–Lin model of financial intermediation [E.J. Green, P. Lin, Implementing efficient allocations in a model of financial intermediation, J. Econ. Theory 109 (2003) 1–23] under a more general specification of the distribution of types across agents. We derive the efficient allocation in closed form. We show that, in some cases, the intermediary cannot uniquely implement the efficient allocation using a direct revelation mechanism. In these cases, the mechanism also admits an equilibrium in which some (but not all) agents “run” on the intermediary and withdraw their funds regardless of their true liquidity needs. In other words, self-fulfilling runs can arise in a generalized Green–Lin model and these runs are necessarily partial, with only some agents participating.     

When is reputation bad?

In traditional reputation models, the ability to build a reputation is good for the long-run player. In [Ely, J., Valimaki, J., 2003. Bad reputation. NAJ Econ. 4, 2; http://www.najecon.org/v4.htm. Quart. J. Econ. 118 (2003) 785–814], Ely and Valimaki give an example in which reputation is unambiguously bad. This paper characterizes a class of games in which that insight holds. The key to bad reputation is that participation is optional for the short-run players, and that every action of the long-run player that makes the short-run players want to participate has a chance of being interpreted as a signal that the long-run player is “bad.” We allow a broad set of commitment types, allowing many types, including the “Stackelberg type” used to prove positive results on reputation. Although reputation need not be bad if the probability of the Stackelberg type is too high, the relative probability of the Stackelberg type can be high when all commitment types are unlikely.     

Fair allocation in networks with externalities

I prove existence and uniqueness of a component efficient and fair allocation rule when the value of the network is allowed to exhibit any type of externalities across its components. This is done by means of a new specification of the value function, generalizing partial results appearing in Myerson [Myerson, R.B., 1977a. Graphs and cooperation in games. Math. Operations Res. 2, 225–229], Feldman [Feldman, B.E., 1996. Bargaining, coalition formation and value. PhD dissertation. State University of New York at Stony Brook] and Jackson and Wolinsky [Jackson, M.O., Wolinsky, A., 1996. A strategic model of social and economic networks. J. Econ. Theory 71, 44–74]. This component efficient and fair allocation rule is found closely related to an extension of the Shapley value to TU-games in partition function form proposed by Myerson [Myerson, R.B., 1977b. Values of games in partition function form. Int. J. Game Theory 6 (1), 23–31].     

Evolutionary stability and lexicographic preferences

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. Econ. Theory 57, 278–305) are limit Nash equilibria. Modified evolutionary stability differs from “lexicographic evolutionarily stability” (defined by extending the common characterization of evolutionary stability to lexicographic preferences) in the order in which limits in the payoff space and the space of invasion barriers are taken.     

Truthful mechanism design for multidimensional scheduling via cycle monotonicity

We consider the makespan-minimization problem on unrelated machines in the context of algorithmic mechanism design. No truthful mechanisms with non-trivial approximation guarantees are known for this multidimensional domain. We study a well-motivated special case (also a multidimensional domain), where the processing time of a job on each machine is either “low” or “high.” We give a general technique to convert any c-approximation algorithm (in a black-box fashion) to a 3c-approximation truthful-in-expectation mechanism. Our construction uses fractional truthful mechanisms as a building block, and builds upon a technique of Lavi and Swamy [Lavi, R., Swamy, C., 2005. Truthful and near-optimal mechanism design via linear programming. In: Proc. 46th FOCS, pp. 595–604]. When all jobs have identical low and high values, we devise a deterministic 2-approximation truthful mechanism. The chief novelty of our results is that we do not utilize explicit price definitions to prove truthfulness. Instead we design algorithms that satisfy cycle monotonicity [Rochet, J., 1987. A necessary and sufficient condition for rationalizability in a quasilinear context. J. Math. Econ. 16, 191–200], a necessary and sufficient condition for truthfulness in multidimensional settings; this is the first work that leverages this characterization.     

Comment on “A note on the Hotelling principle of minimum differentiation: Imitation and crowd”

We argue that the minimum differentiation firm location equilibrium and the pure strategy pricing equilibrium in Di Cintio’s [Di Cintio, M., 2007. A note on the Hotelling principle of minimum differentiation: Imitation and crowd. Research in Economics 61 (3), 122–129] “Note” need not exist under the conditions claimed.     

Comment on “C.E.S. production functions in the light of the Cambridge critique”

The controversy revived in Bertram Schefold’s paper is based on three common assumptions: (1) the underlying techniques are linear (2) perfect competition obtains (3) the economy operates in a putty-putty context. The consequences of dropping these assumptions are discussed, and the relation between nonlinearity and the error due to the use of an “imprecise” production function is examined.     

Can Japan succeed in “Chigyo-ka” (intelprise-formation)?

There are two aspects in today's information revolution that started in the late 1970s. The first is an aspect referred to as “the third industrial revolution,” which triggers the transition to the “21st century system of Industrialization.” The information revolution in this sense brings the creation of new “breakthrough industries (new multimedia industries).” And the second aspect of the information revolution possesses the characteristics of both a technological revolution and a social revolution and brings about the arrival of the third phase of the historical evolutionary process of the modern civilization, which proceeds through three phases, namely “militarization, industrialization, and then informatization.”If the bearers of modern industrialization are a “group of enterprises” that have been engaged in the race in order to gain “wealth” (generalized means of exchange/exploitation power), and if these enterprises' activities have been exercised in the world market where their products have been sold, then it is appropriate to call the bearers of informatization a “group of intelprises.” They will be engaged in the race to gain “wisdom” (generalized means of persuasion/induction power), then stages of their activities can be called a “global intelplace” where “sharables,” that is, information and knowledge, will be disseminated. And now, toward the 21st century, the third phase of modernization, which can be called the “informatization/intelprise formation” or the “wisdom game” (intellectualism), is about to begin.Japan's “ie society (a society based on the ie principle—literally, it means “house” but here it is interpreted as cultural principle for organizing a society), which has been going through the process of evolution on the Japan Archipelago, has developed a network-based organization with little stratification within its infrastructure. In this sense, Japanese society can be characterized as a “network-oriented society” in which intelprises and an intelplace in the broad sense have functioned as the essential components of the society since Middle Ages. In general, an intelplace and intelprises that operate actively within this framework serve as the flexible bases for different types of social relations and institutions, such as states and markets and eventually integrate these into the society to a certain extent. In fact, it took place quite regularly during the modernization “in the narrow sense,” or Westernization of Japanese society after the Meiji Restoration. There exist some problems, however. Some of the characteristics found in Japanese society may become obstacles to activities aimed at the sharing and promotion of information and knowledge in the global intelplace and Japanese participation in the “wisdom game.” Badly needed are serious efforts for Japanese intelprise-formation to reduce these obstacles as much as possible.     

Corrigendum to “Stable matchings and preferences of couples” [J. Econ. Theory 121 (1) (2005) 75–106]

We correct an omission in the definition of the domain of weakly responsive preferences introduced in [B. Klaus, F. Klijn, Stable matchings and preferences of couples, J. Econ. Theory 121 (2005) 75–106] or KK05 for short. The proof of the existence of stable matchings [KK05, Theorem 3.3] and a maximal domain result [KK05, Theorem 3.5] are adjusted accordingly.     

Benefit and Distance Functions

We explore the relationship between R. W. Shephard's input distance function (“Cost and Production Functions,” Princeton Univ. Press, Princeton, 1953) and D. G. Luenberger's benefit function (J. Math. Econ.21(1992a), 461–481). We point out that the latter can be recognized in a production context as a directional input distance function which can exhaustively characterize technologies in both price and input space. D. McFadden's (Cost, revenue, and profit functions,in“Production Economics: A Dual Approach to Theory and Applications, “North-Holland/Elsevier, New York, 1978) composition rules for input sets and input distance functions are then extended to the directional input distance function.Journal of Economic LiteratureClassification Numbers : D21, D24, D29.     

Subjective states: A more robust model

We study the demand for flexibility and what it reveals about subjective uncertainty. As in Kreps [D. Kreps, 1979. A representation theorem for ‘preference for flexibility’. Econometrica 47, 565–577], Nehring [K. Nehring, 1996. Preference for flexibility and freedom of choice in a Savage framework. UC Davis Working Paper; K. Nehring, 1999. Preference for flexibility in a Savage framework. Econometrica 67, 101–119] and Dekel et al. [E. Dekel, B. Lipman, A. Rustichini, 2001. Representing preferences with a unique subjective state space. Econometrica 69, 891–934], the latter is represented by a subjective state space consisting of possible future preferences over actions to be chosen ex post. One contribution is to provide axiomatic foundations for a range of alternative hypotheses about the nature of these ex post preferences. Secondly, we establish a sense in which the subjective state space is uniquely pinned down by the ex ante ranking of (random) menus. Finally, we demonstrate the tractability of our representation by showing that it can model the two comparative notions “2 desires more flexibility than 1” and “2 is more averse to flexibility-risk than is 1.”     

At the crossroads of “futurism” and “prospective”: Towards a Canadian synthesis?

North American “future studies” and the French concept of “prospective” have been integrated to provide the basis for an attempted “Canadian Synthesis” in the approach developed by the Montreal-based think-tank, the Gamma Institute. In this paper the founding president of Gamma outlines the four stages of the approach in a conceptual framework entitled the “Chronospace” and illustrates its applicability by referring to some of Gamma's projects in the last 12 years.     

Tax revenues, fiscal corruption and “shame” costs

In this paper we explore tax revenues in a regime of widespread fiscal corruption in a static framework. We prove that the relationship between the tax rate and tax revenues depends on the relevance of the “shame effect” of being detected in a corrupt transaction. In countries with a “low shame” effect, tax revenues grow as the tax rate increases. Moreover, there is a critical tax rate where the growth rate of tax revenues begins to reduce. In countries with a high “shame effect” tax revenues increase up to a threshold value and then decrease.     

Optimal redistricting under geographical constraints: Why “pack and crack” does not work

We show that optimal partisan redistricting with geographical constraints is a computationally intractable (NP-complete) problem. In particular, even when voter's preferences are deterministic, a solution is generally not obtained by concentrating opponent's supporters in “unwinnable” districts (“packing”) and spreading one's own supporters evenly among the other districts in order to produce many slight marginal wins (“cracking”).     

State of the “life span revolution” between 1980 and 2000

Using data for 163 countries, state of the “life span revolution” over the period 1980–2000 is studied in terms of measures of cross-country inequality and through least-squares and quantile-regression estimation of simple convergence models. Four main points are noted. First, dynamics of the cross-country distribution of life expectancy during these 20 years seem markedly different from those for the preceding decades: instead of the sharp “convergence” noted until the 1980s, there is lack of convergence and an indication of “divergence”. Second, the divergence is particularly marked during the 1990s. Third, spread of HIV/AIDS has probably been a significant factor in generating divergence during the 1990s. Fourth, besides the sizable temporal heterogeneity, quantile-regression estimates of convergence models reveal a substantial heterogeneity across the top and the bottom quartiles within each period.     

A model of “coupled” technology transfer : A logistic curve approach

This article presents a mathematical model relating to the technology transfer problem. The origin of the problem stems from the existing trade-offs between the strategies of “technological progressiveness” and “static efficiency” employed by firms or countries defined as “leaders” and “followers,” respectively. The formulation of the model is based on the assumption that the technological development of a firm or a country follows a logistic growth curve when related to a specific technology. During the process of a “coupled” technology transfer, the development of the follower changes and its behavior is described by a first order nonhomogenous deferential equation. Different scenarios of the “coupled” technology transfer between the leader and the follower are being discussed.     

Using choice question formats to determine compensable values: The case of a landfill-siting process

Siting noxious facilities, such as community landfills, is a challenging problem for local planners who recognize the importance of economic efficiency and equity, political acceptance, and meeting federal regulatory standards. Meeting these criteria requires technical and socio-economic analyses in conjunction with public input. Planners may also recognize that political acceptance requires compensation for the host community, either in the form of monetary or in-kind transfers. Following Breffle and Rowe [Breffle, W.S., Rowe. R.D., 2002. Comparing choice question formats for evaluating natural resource tradeoffs. Land Econ. 78 (2), 298–314], we use a “resource-to-resource” paired-comparison survey method to estimate compensatory values associated with an in-county landfill for both the host and non-host communities. Our results indicate that while a host-community household's minimum willingness to accept payment for hosting a landfill may exceed a non-host-community household's maximum willingness to pay, a large difference in population sizes between the two communities enables the landfill to pass a Kaldor potential compensation test.     

“Constitutionalizing” the corporation

To become effective instruments in the attainment of a sustainable society, corporations should have their constitutional status settled. Thus far, mainly by Supreme Court decisions, corporations have an uncertain status. They are “persons” under the Constitution and have certain rights; but unlike natural persons, they do not have concomitant constitutional duties. Corporations should be viewed as “private” governments exercising substantial power in society. They are, however, considered to be associations of individuals rather than divisions of society. The need is to legitimate their governing power by “constitutionalizing” them. That can be done by corporations accepting, or having imposed upon them, two principal constitutional duties. First, means should be developed whereby corporate officers routinely take the general good into account. That duty could be implemented by making “social impact statements,” analogous to but broader than the familiar environmental impact statements, before making important corporate decisions. Secondly, as “sociological communities,” corporate officers wield considerable power over members of those communities. A bill of rights similar to the Constitution's Bill of Rights is recommended so as to make corporate power that is necessary for achievement of societal goals as tolerable and decent as possible. Acceptance of those duties would make corporations parts of, not separate from, the greater corporation called society. They would be private, profit-making entities with a definite public function. Preferably, the duties should be voluntarily accepted. Congress, however, has undoubted constitutional power to impose both, should it so desire.     

On optimality in collective institutional choice

Conditions are investigated under which democratic choice of the division of land between collective and “private” use and of the distribution of collective income between “needs” and “work” payments will produce a Pareto-optimal land allocation and optimal collective labor incentives. Sen's optimal rule for the degree of “needs” distribution is found to result from self-interested voting on this parameter when the distribution of labor inputs is unskewed or when votes are weighted by labor contributions. This in turn increases the optimality of land allocation, which can be further improved by a simple rental scheme. J. Comp. Econ., Dec. 1981, 5(4), pp. 392–403. Brown University, Providence, Rhode Island.