Congestable local public goods in an urban setting

In this paper, we recognize two types of unpure local public goods (LPGs): congestable and pollutable. This paper and the forthcoming one (Clubs in an urban setting, mimeo, 1980) are devoted to congestable LPGs (CLPG). In Part I we define, classify, and characterize CLPGs. CLPGs may vary in their degree of congestability between zero, in the case of a pure LPG, and one, in the case of a private good. Spatially, we recognize two types of LPGs: the dispersed LPG (DiLPG) and the concentrated LPG (CoLPG). The first is distributed throughout the residential ring and the second is provided in specific locations to which households must travel. The second part of this paper is devoted to the investigation of the properties of a CDiLPG in an urban setting. The properties of CoLPG are investigated in (Clubs in an urban setting, mimeo, 1980). A version of Samuelson's rule as to the optimal allocation of pure public goods is extended on one hand to local dispersed public goods and on the other hand to CLPGs. Two corrective Pigouvian taxes are identified: congestion tolls levied on households, and a residential land tax. These two taxes cover total government expenditure on the LPG. The fraction of the expenses on the LPG covered by congestion tolls is α, and that covered by land taxes is (1 − α), where α is the degree of congestability. Efficiency can also be achieved by zoning the residential ring and regulating the housing density in it. This procedure may replace taxation and its advantage is that we can control a large number of externalities by a single set of zoning rules and regulations. An a posteriori rule to guide the local government as to the desirability of its actions is provided.     

A game-theoretical model of the landscape theory

In this paper we examine a game-theoretical generalization of the landscape theory introduced by Axelrod and Bennett (1993). In their two-bloc setting each player ranks the blocs on the basis of the sum of her individual evaluations of members of the group. We extend the Axelrod–Bennett setting by allowing an arbitrary number of blocs and expanding the set of possible deviations to include multi-country gradual deviations. We show that a Pareto optimal landscape equilibrium which is immune to profitable gradual deviations always exists. We also indicate that while a landscape equilibrium is a stronger concept than Nash equilibrium in pure strategies, it is weaker than strong Nash equilibrium.     

Stable matchings and the small core in Nash equilibrium in the college admissions problem

Both rematching proof and strong equilibrium outcomes are stable with respect to the true preferences in the marriage problem. We show that not all rematching proof or strong equilibrium outcomes are stable in the college admissions problem. But we show that both rematching proof and strong equilibrium outcomes in truncations at the match point are all stable in the college admissions problem. Further, all true stable matchings can be achieved in both rematching proof and strong equilibrium in truncations at the match point. We show that any Nash equilibrium in truncations admits one and only one matching, stable or not. Therefore, the core at a Nash equilibrium in truncations must be small. But examples exist such that the set of stable matchings with respect to a Nash equilibrium may contain more than one matching. Nevertheless, each Nash equilibrium can only admit at most one true stable matching. If, indeed, there is a true stable matching at a Nash equilibrium, then the only possible equilibrium outcome will be the true stable matching, no matter how different are players' equilibrium strategies from the true preferences and how many other unstable matchings are there at that Nash equilibrium. Thus, we show that a necessary and sufficient condition for the stable matching rule to be implemented in a subset of Nash equilibria by the direct revelation game induced by a stable mechanism is that every Nash equilibrium profile in that subset admits one and only one true stable matching. Received: 30 December 1998 / Accepted: 12 October 2001 This paper is a revision of the paper “Manipulation and Stability in a College Admissions Problem” circulated since 1994. I thank Rich McLean, Abraham Neyman, Mark Satterthwaite, Sang-Chul Suh, and Tetsuji Yamada for helpful discussions. I thank the associate editor and the two anonymous referees for their helpful comments that have greatly improved the paper. I am grateful to the Kellogg G.S.M. at the Northwestern University for the hospitality for my visit. Any errors are mine.     

Repeated two-person zero-sum games with unequal discounting and private monitoring

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.     

Efficient land use in an equilibrium residential annulus

An efficient land use is one in which land is divided between residential activity and roads so as to minimize aggregate transportation costs. We analyze such an allocation for the case in which each consumer is in equilibrium. The problem synthesizes the approaches in the Mills-de Ferranti analysis and the Solow analysis. In Solow's analysis consumers were in equilibrium but land was allocated by rule of thumb; in that of Mills and de Ferranti land was efficiently allocated in aggregate but each consumer was allocated a fixed area for his residence. Our efficient allocation has a Nash equilibirum characterization. The efficient land allocation is characterized by declining convex functions of distance from the CBD for density on roads and for land rents. The nature of the pattern of land in road use is investigated.     

Locational efficiency in a federal system

A number of recent studies have concluded that differing local government tax and expenditure packages necessarily create incentives for households to locate in a non-optimal fashion. This paper shows, on the contrary, that the locational equilibrium may be optimal. For example, if migration produces no congestion costs, then as long as localities tax the locationally-fixed commodity, land, the equilibrium will be optimal. In fact, there are only two reasons why non-optimality may result: local taxes may be distortionary (by taxing the mobile rather than immobile factor), or there may be non-internalized externalities.     

Implementation of optimal contracts under adverse selection

This paper studies a 2-agent, 2-type principal-multiagent model of adverse selection under the assumption that the agents each have complete information. We construct a mechanism implementing the first-best contracts in Nash equilibrium that: satisfies a condition related to individual rationality, is renegotiation-proof, has a small-sized message space, achieves unique implementation and satisfies undomination of Nash equilibrium strategies. Moreover, we prove that other requirements which relate to individual rationality (different from the one satisfied by our mechanism) are not compatible with implementation of the first-best contracts. Received: 27 July 1998 / Accepted: 26 May 2000     

Large games with countable characteristics

We consider anonymous games with an atomless probability space of players in which players’ characteristics are countable. Our main result shows that the set of equilibrium distributions coincides with the set of distributions induced by equilibrium strategies together with the function assigning characteristics to players. This result implies the existence of Nash equilibria in continuous large games with countable characteristics.     

Investment in public infrastructure with spillovers and tax competition between contiguous regions

Two contiguous regions compete to attract a population of heterogeneous firms. They choose infrastructure levels in a first stage and compete in taxes in a second stage. We study the properties of Subgame Perfect Nash equilibria in this stage game depending on the extent to which the benefits of infrastructure spill over from one region to the other. First, we show that the presence of inter-regional spillovers allows jurisdictions to control for the intensity of tax competition and therefore affects the optimal levels of infrastructure selected at equilibrium. Second, by comparing the non-cooperative and cooperative outcomes, we show that the extent to which regions overinvest in infrastructures negatively depends on the intensity of the spillovers.     

Strategic behavior in non-atomic games

In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player’s belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. We also show that all regular equilibria of smooth non-atomic games are strategic. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.     

The economics of property taxes and land values: The elasticity of supply of structures

Land values are explained by diminishing returns to a variable factor, structure, added to fixed land. The total cost minimizing structural density determined by land value, occurs where the marginal cost of increased density equals the average cost of structure plus land. Structural demand prices equal marginal costs in equilibrium determining land demands. A general equilibrium land price establishes the uses, prices and densities of structures. A simple method of calculating structure supply elasticity and the incidence and deadweight loss of property taxes is developed. Differing property tax rates are found to be efficient.     

The spatial effects of a tax on housing and land

This paper analytically investigates the spatial consequences of a tax on housing and land. In general, a property tax is not spatially neutral; instead it disproportionately affects certain parts of the city. The property tax can therefore create distributional inequities and can distort the pattern of residential and industrial location. We derive conditions on locational preferences and housing production that determine which parts of a city will be disproportionately affected by a property tax. Empirical estimates suggest that central locations will be disproportionately affected by property taxes.     

Imitation and price competition in a differentiated market

We study the stable market outcome that evolves in a spatially differentiated market when price-competing firms choose actions by imitation of the most profitable firm. We compare and contrast the stable outcomes under two imitation procedures: one, where each firm immediately imitates the most profitable firm, and the other when a firm imitates another firm only if it is more profitable while being “sufficiently similar” (in context of the market segment it operates in) or “sufficiently close”. In either case, the symmetric pure strategy Nash equilibrium is always a stable outcome. However, when imitation of the most profitable firm is immediate and market differentiation is ‘moderate’, states with prices lower than the Nash equilibrium are also stable. In contrast, when imitation of the most profitable firm is more gradual and market differentiation is below a threshold, states with prices above the Nash equilibrium are also stable. Thus, while competitive evolutionary pressure in this imitation based model does result in the Nash equilibrium always being stable, other outcomes may be stable as well. Interestingly, the states that are stable under gradual imitation give the firms a higher profit than the stable states under immediate imitation.     

First price package auction with many traders

This paper studies a first price package auction in which multiple sellers participate in addition to multiple buyers. We generalize the notion of the profit-target strategy which is first introduced as a truthful strategy in a first price package auction with a single seller by Bernheim and Whinston (1986b). We then show that the set of equilibrium payoffs in profit-target strategies is equal to the bidder-optimal core, and is also equal to the set of coalition-proof Nash equilibria. Using this result, we find that any equilibrium payoff vector is weakly Pareto-dominated by the VCG payoff vector for buyers, and that the Walrasian competitive equilibrium payoff vector is weakly Pareto-dominated by some equilibrium payoff vector for buyers, even if goods are substitutes. This contrasts with the first price package auction with a single seller, in which it is shown that if goods are substitutes, then those three outcomes are payoff-equivalent.     

Adaptive learning in an asymmetric auction: genetic algorithm approach

Agent-based simulations are performed to study adaptive learning in the context of asymmetric first-price auctions. Non-linearity of the Nash equilibrium strategies is used to investigate the effect of task complexity on adaptive learning by varying the degree of approximation the agents can handle. In addition, learning in different information environments is explored. Social learning allows agents to imitate each other’s bidding strategies based on their relative success. Under individual learning agents are limited to their own experience. We observe convergence to steady states near the predicted equilibrium in all cases. The ability to learn non-linear functions helps the agents with a non-linear equilibrium strategy but hurts the agents with an almost linear one. Better information about the opponent population has a relatively modest impact. A larger number of strategies to experiment with and an ability to systematically compare strategies by holding a number of factors constant have a comparatively stronger beneficial effect.     

Multiproduct price competition with heterogeneous consumers and nonconvex costs

This paper extends the oligopolistic model of price competition to environments with multiple goods, heterogeneous consumers, and arbitrary continuous cost functions. A Nash equilibrium in mixed strategies with an endogenous sharing rule is proven to exist. It is also shown that, in environments with fixed costs and constant marginal costs, all (symmetric and asymmetric) equilibria exhibit price dispersion across stores. Furthermore, the paper identifies scenarios in which prices will necessarily be random. In these markets, stores keep each other guessing because, given the fixed costs, they would incur a loss if their price strategies were anticipated and beaten by competitors. This is interpreted as an important economic feature that is possibly behind random price promotions such as weekly specials.     

Nash equilibrium reconsidered and an option for maximin

In this paper we will discuss some peculiarities of the Nash equilibrium which are at odds with its standard applications: (a) the underlying dynamic interpretation, (b) the incentive independency if equilibria are mixed, and (c) the unprofitability if equilibrium and maximin are mixed and the game is 2-by-2. Maximin is proposed as an alternative solution concept in “relevant situations”.     

Federalism,taxation, and economic growth

We present a model of endogenous growth where government provides a productive public good financed by income and capital taxes. In equilibrium, a decentralized government chooses tax policy to maximize economic growth, while a centralized government does not do so. Furthermore, these conclusions hold regardless of whether governments are beholden to a median voter or are rent-maximizing Leviathans. However, a decentralized government will under-provide public goods which benefit citizens directly, while a central government beholden to the median voter will optimally invest in such public goods.     

LAND TAXATION AND ITS IMPACT ON LAND PRICE: The Case of Japan in the 1990s

The multifold increases in land prices in Tokyo, at first, and in other major cities of Japan, later, during the last half of the 1980s brought forth government proposals to strengthen the land holding taxes which were very low in the past. This paper analyzes the background of these developments as well as their rationales, and looks at possible consequences of planned increases in land holding taxes. It is argued that the rivalry between the Ministry of Finance and the Ministry of Local Autonomy is leading to a situation in which unexpectedly heavy land holding taxes will be imposed in the near future, lowering the price of land to much less than half of what it was in the past.     

Endogenous mechanisms and Nash equilibrium in competitive contracting games

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm’s catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism—and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.