An equivalence theorem for a differential information economy

In a pure exchange economy with differential information and a finite set of traders, physical commodities and states of nature, we characterize the Walrasian expectations or Radner equilibria by using the veto power of the grand coalition. We prove that an allocation x is a Radner equilibrium allocation if and only if it is “privately non-dominated” by the grand coalition in every economy obtained by perturbing the original initial endowments in the direction of x. The first and second welfare theorems become particular cases of our main result. Since the deterministic Arrow–Debreu–McKenzie model is a special case of the differential information economy model we also provide a new characterization of the Walrasian equilibria.     

A theory of coalition formation in committees

Let G = (N,W) be a strong weighted majority game and let A be a set of alternatives. Denote by L the set of linear orders on A. A social choice function F:L^N → A is a representation of G if the simple game G¹(F) associated with F equals G. A coalition S is determining in G if it satisfies the following condition. Let F be a representation of G and let R^N ? L^N. Then, if a simple majority of the members of S consider an alternative x to be their best choice, then S can ‘enforce’ x to be a Nash equilibrium payoff in the resulting non-cooperative voting game g(F,R^N). In this paper we generalize the above notion of a determining coalition to committees (i.e., proper and monotonic simple games), and give a complete characterization of the set of determining coalitions of a committee. Furthermore, we discuss our notion of a determining coalition in the light of some real-life data on formation of coalitions in town councils in Israel.     

Stable and efficient coalitional networks

We develop a theoretical framework that allows us to study which bilateral links and coalition structures are going to emerge at equilibrium. We define the notion of coalitional network to represent a network and a coalition structure, where the network specifies the nature of the relationship each individual has with her coalition members and with individuals outside her coalition. To predict the coalitional networks that are going to emerge at equilibrium we propose the concepts of strong stability and of contractual stability. Contractual stability imposes that any change made to the coalitional network needs the consent of both the deviating players and their original coalition partners. Requiring the consent of coalition members under the simple majority or unanimity decision rule may help to reconcile stability and efficiency. Moreover, this new framework can provide insights that one cannot obtain if coalition formation and network formation are tackled separately and independently.     

Spatial pillage game

A pillage game is a coalitional game as a model of Hobbesian anarchy. The spatial pillage game introduces a spatial feature into the pillage game. Players are located in regions and can travel from one region to another. The players can form a coalition and combine their power only within their destination regions, which limits the exertion of the power of each coalition. Under this spatial restriction, a coalition can pillage less powerful coalitions without any cost. The feasibility of pillages between coalitions determines the dominance relation that defines stable states in which powers among the players are endogenously balanced. With the spatial restriction, the set of stable states changes. However, if the players have forecasting ability, then the set of stable states does not change with the spatial restriction. Core, stable set, and farsighted core are adopted as alternative solution concepts.     

Importance of status quo when lobbying a coalition government

Lobbying a coalition government is different from lobbying a single-party government, since in the case of a coalition government, the interest group can intervene in the intragovernmental decision process. In the case where the interest group prefers the status quo to the surplus maximizing policy, the interest group influences the policy without any contribution due to its credible threat to block unfavorable proposals. Furthermore, we show that when, say, a leftist coalition government may be replaced by a rightist coalition government, the final policy reflects a rightist interest group’s preferences more heavily due to the interest group’s forward-looking considerations.     

Simple and powerful GMM over-identification tests with accurate size

Based on the series long run variance estimator, we propose a new class of over-identification tests that are robust to heteroscedasticity and autocorrelation of unknown forms. We show that when the number of terms used in the series long run variance estimator is fixed, the conventional J statistic, after a simple correction, is asymptotically F-distributed. We apply the idea of the F-approximation to the conventional kernel-based J tests. Simulations show that the J^∗ tests based on the finite sample corrected J statistic and the F-approximation have virtually no size distortion, and yet are as powerful as the standard J tests.     

Implementation of the recursive core for partition function form games

In partition function form games, the recursive core (r-core) is implemented by a modified version of Perry and Reny’s [Perry, M., Reny, P., 1994. A non-cooperative view of coalition formation and the core. Econometrica 62, 795-817] non-cooperative game. Specifically, every stationary subgame perfect Nash equilibrium (SSPNE) outcome is an r-core outcome. With the additional assumption of total r-balancedness, every r-core outcome is an SSPNE outcome.     

The airport problem with capacity constraints

The original airport problem is concerned with the cost sharing of an airstrip among airplanes assuming that one airstrip is sufficient to serve all airplanes. In this paper, we generalize the original airport problem by imposing capacity constraints to consider the situation when one airstrip cannot serve all airplanes and investigate how to share the cost among airplanes. We introduce the sequential equal contributions rule for our problem and show that it coincides with the Shapley value of the corresponding airport game when the worth of a coalition is defined to be the minimum cost of serving all members of the coalition. The sequential equal contributions rule requires each airplane to contribute equally to the cost of a given section of any airstrip as long as the length of the section is less than or equal to its desired length even though the airplane cannot use the airstrip. Each airplane’s contribution is the sum of terms, one for each section of the airstrip whose length is less than or equal to its desired length. We also present an axiomatic characterization of the rule by imposing the axioms of efficiency, the equal share lower bound, smaller-cost monotonicity, and population fairness.     

General Election: How would the parties' plans impact the outlook?

• Our modelling suggests that, based upon the three main parties’ economic and fiscal plans, the outcome of the General Election would have a modest, but not immaterial, impact on the UK's economic and fiscal outlook. The Liberal Democrat plans would deliver the strongest GDP growth, followed by Labour, but both would also involve higher debt servicing costs and a higher level of government debt than the plans of the Conservatives.
• In our view these premiums on debt and borrowing costs are so small that it is very difficult to argue that the UK should pursue a more austere fiscal policy and reject the opportunity of stronger growth. But with the latest opinion polls suggesting that it is likely that the next government will be either a minority administration, or a coalition consisting of three or more parties, it is most likely that we will ultimately see some combination of the main parties' plans enacted.
• The experience of 2010 suggests that such political uncertainty could mean that we see several bouts of market nervousness between now and May 7th, particularly in equity markets. However, such turbulence is likely to be short‐lived, providing that the resulting government is perceived to be strong and durable. Even a multi‐party coalition may not be such a bad thing, particularly if it watered down the more contentious policies of the main parties. The worst‐case scenario would be a weak minority government which is both unable to pass any meaningful legislation and unable to seek a fresh mandate. Such a scenario could seriously undermine confidence amongst investors and firms.

     

The hybrid equilibria and core selection in exchange economies with externalities

This paper introduces a hybrid equilibrium concept that combines the elements of cooperative and non-cooperative behaviors in an exchange economy with externalities. For a fixed coalition structure (or a partition of traders), the hybrid equilibrium is a price and consumption bundle such that each coalition chooses a core solution from its budget set and the consumption bundles are feasible. It becomes the competitive equilibrium when the position is the finest, and it selects a core allocation when the partition is the coarsest. The paper provides sufficient conditions for the existence of a hybrid equilibrium for any coalition structure.     

A simple test for regression specification with non-nested alternatives

In this paper, I introduce a simple test for the presence of the data-generating process among several non-nested alternatives. The test is an extension of the classical J test for non-nested regression models. I also provide a bootstrap version of the test that avoids possible size distortions inherited from the J test.     

An equity characterization of second price auctions when preferences may not be quasilinear

In a single item auction model that allows non-quasilinear preferences, we show that an auction rule satisfies weak envy-freeness for equals, strategy-proofness, and nonimposition if and only if it is a (generalized) second price auction. This characterization is established on a wide class of preference domains, including the quasilinear domain, a positive income effect domain, and a negative income effect domain.     

An equilibrium existence result for an economy with land

This research uses a different set of assumptions for land than those used in the standard general equilibrium framework. In particular, land is modelled explicitly as a subset of the plane with anything immobile, from flowers and trees to houses, embedded in it. There is a finite number of consumers with preference orderings over land parcels satisfying certain axioms along with endowments of land that partition this subset of the plane. Allowing for recombinations of parcels, the main result demonstrates the existence of prices in L¹ and a partition of land among consumers so that the land market clears.     

Every member of the core is as respectful as any other

We strategically separate different core outcomes. The natural counterparts of a core allocation in a strategic environment are the α-core, the β-core and the strong equilibrium, modified by assuming that utility is transferable in a strategic context as well. Given a core allocation ω of a convex transferable utility (TU) game \(v\), we associate a strategic coalition formation game with \( \left( {v, \omega } \right) \) in which ω survives, while most other core allocations are eliminated. If the TU game is strictly convex, the core allocations respected by the TU-α-core, the TU-β-core and the TU-strong equilibrium shrink to ω only in the canonical family of coalition formation games associated with \( \left( {v, \omega } \right) \). A mechanism, which strategically separates core outcomes from noncore outcomes for each convex TU game according to the TU-strong equilibrium notion is reported.     

Representation of transferable utility games by coalition production economies

We prove that, by the method of construction of a coalition production economy due to Sun et al. [Sun, N., Trockel, W., Yang, Z., 2008. Competitive outcomes and endogenous coalition formation in an n$n$-person game. Journal of Mathematical Economics 44, 853–860], every transferable utility (TU) game can be generated by a coalition production economy. Namely, for every TU game, we can construct a coalition production economy that generates the given game. We briefly discuss the relationship between the core of a given TU game and the set of Walrasian payoff vectors for the induced coalition production economy.     

Some results on the existence of utility functions on path connected spaces

This paper concerns the existence of utility representations for preferences defined on a path connected space X. This includes any convex set. A classical result of Eilenberg (1941) proves the existence of utility representations when the consumption set is connected and separable. In an infinite dimensional space the above result may not be useful, because we lack, in general, the separability of the space. The non-separable spaces L^∞ and ca(K) are typical examples in mathematical economics. In this paper we show that a continuous preference relation ≽, on X has a continuous utility representation if and only if it is countably bounded, i.e., there is some countable subset F of X such that for all x in X there exist y and z in F with y≽x≽z. An easy corollary states that any continuous preference which has a best and a worst point has a continuous representation. We also obtain a convex continuous preference on a Banach lattice that has not a utility representation, because it is not countably bounded.     

Cores of effectivity functions and implementation theory

In a committee where cooperative voting occurs, effectivity functions describe the blocking power of coalitions. It is a binary relation that says for each coalition T and each subset of outcomes B whether or not T can force the final outcome within B. The corresponding cooperative stability notion generalizes the familiar core of a simple game. We study those effectivity functions yielding a non-empty core for all preference profiles, of which additive effectivity functions are an example. This proves to be closely related to implementation by means of the strong equilibrium concept.     

Existence of a convex extension of a preference relation

In this paper we say that a preference (i.e. irreflexive) relationP isregular (or aweak order) if both it and its non-comparability relation are transitive; we also say that a preference relationP ^* is aconvex extension of another preference relationP ifP?P ^* holds andP ^* is regular and convex-valued. We prove that a convex extension ofP exists if and only if every non-empty and finite set of alternativesA is not included in the convex hull of ∪ _x∈A P(x).     

Cores of many-player games; nonemptiness and equal treatment

This paper provides sufficient conditions to ensure nonemptiness of approximate cores of many-player games and symmetry of approximate core payoffs (the equal treatment property). The conditions are: (a) essential superadditivity—an option open to a group of players is to partition into smaller groups and realize the worths of these groups and (b) small group effectiveness (SGE)—almost all gains to collective activities can be realized by cooperation only within members of some partition of players into relatively small groups. Another condition, small group negligibility (SGN), is introduced and shown to be equivalent to SGE. SGN dictates that small groups of players cannot have significant effects on average (i.e., per capita) payoffs of large populations; thus, SGN is a analogue, for games with a finite player set, of the condition built into models with a continuum of player that sets of measure zero can be ignored. SGE implies per capita boundedness (PCB), that the supremum of average or per capita payoffs is uniformly bounded above. Further characterization of SGE in terms of its relationship to PCB is provided. It is known that if SGE does not hold, then approximate cores of many-player games may be empty. Examples are developed to show that if SGE does not hold and if there are players of “scarce types” (in other works, players with scarce attributes) then even if there is only a finite number of types of players and approximate cores are non-empty, symmetry may be lost; moreover, even players of abundant types may be treated asymmetrically by the core.     

Exact permutation tests for non-nested non-linear regression models

This paper proposes exact distribution-free permutation tests for the specification of a non-linear regression model against one or more possibly non-nested alternatives. The new tests may be validly applied to a wide class of models, including models with endogenous regressors and lag structures. These tests build on the well-known J test developed by Davidson and MacKinnon [1981. Several tests for model specification in the presence of alternative hypotheses. Econometrica 49, 781–793] and their exactness holds under broader assumptions than those underlying the conventional J test. The J-type test statistics are used with a randomization or Monte Carlo resampling technique which yields an exact and computationally inexpensive inference procedure. A simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions. The test procedure developed is illustrated by an application to inflation dynamics.