Coalitions, agreements and efficiency

If agents negotiate openly and form coalitions, can they reach efficient agreements? We address this issue within a class of coalition formation games with externalities where agents’ preferences depend solely on the coalition structure they are associated with. We derive Ray and Vohra's [Equilibrium binding agreements, J. Econ. Theory 73 (1997) 30-78] notion of equilibrium binding agreements using von Neumann and Morgenstern [Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944] abstract stable set and then extend it to allow for arbitrary coalitional deviations (as opposed to nested deviations assumed originally). We show that, while the extended notion facilitates the attainment of efficient agreements, inefficient agreements can nevertheless arise, even if utility transfers are possible.     

Ordinal efficiency and dominated sets of assignments

Using lotteries is a common tool for allocating indivisible goods. Since obtaining preferences over lotteries is often difficult, real-life mechanisms usually rely on ordinal preferences over deterministic outcomes. Bogomolnaia and Moulin (J. Econom. Theory 19 (2002) 623) show that the outcome of an ex post efficient mechanism may be stochastically dominated. They define a random assignment to be ordinally efficient if and only if it is not stochastically dominated. In this paper we investigate the relation between ex post efficiency and ordinal efficiency. We introduce a new notion of domination defined over sets of assignments and show that a lottery induces an ordinally efficient random assignment if and only if each subset of the full support of the lottery is undominated.     

Stable schedule matching under revealed preference

Baiou and Balinski (Math. Oper. Res., 27 (2002) 485) studied schedule matching where one determines the partnerships that form and how much time they spend together, under the assumption that each agent has a ranking on all potential partners. Here we study schedule matching under more general preferences that extend the substitutable preferences in Roth (Econometrica 52 (1984) 47) by an extension of the revealed preference approach in Alkan (Econom. Theory 19 (2002) 737). We give a generalization of the Gale-Shapley algorithm and show that some familiar properties of ordinary stable matchings continue to hold. Our main result is that, when preferences satisfy an additional property called size monotonicity, stable matchings are a lattice under the joint preferences of all agents on each side and have other interesting structural properties.     

On the duality between prior beliefs and trading demands

In an abstract model with asymmetric information, we show that there is a duality relationship between the prior beliefs and trading demands of bets for any given individual. Then we aggregate all the agents to obtain a second duality relationship between common prior beliefs and trading possibilities. We easily derive from these relationships the no trade theorem and its converse. General efficiency results can be obtained. Moreover, our framework is sufficiently general to cover special cases proved previously (for example, Econometrica 62 (1994) 1327; Discussion Paper 83, Center for Rationality and Interactive Decision Theory, The Hebrew University of Jerusalem, 1995; J. Econom. Theory 91 (2000) 127; Games Econom. Behav. 24 (1998) 172. Yet, our arguments are both simple and intuitive.     

Inflation and growth: new evidence from a dynamic panel threshold analysis

We introduce a dynamic panel threshold model to estimate inflation thresholds for long-term economic growth. Advancing on Hansen (J Econom 93:345–368, 1999) and Caner and Hansen (Econom Theory 20:813–843, 2004), our model allows the estimation of threshold effects with panel data even in case of endogenous regressors. The empirical analysis is based on a large panel-dataset including 124 countries. For industrialized countries, our results confirm the inflation targets of about 2% set by many central banks. For non-industrialized countries, we estimate that inflation rates exceeding 17% are associated with lower economic growth. Below this threshold, however, the correlation remains insignificant.     

Iterated potential and robustness of equilibria

For any given set-valued solution concept, it is possible to consider iterative elimination of actions outside the solution set. This paper applies such a procedure to define the concept of iterated monotone potential maximizer (iterated MP-maximizer). It is shown that under some monotonicity conditions, an iterated MP-maximizer is robust to incomplete information [A. Kajii, S. Morris, The robustness of equilibria to incomplete information, Econometrica 65 (1997) 1283-1309] and absorbing and globally accessible under perfect foresight dynamics for a small friction [A. Matsui, K. Matsuyama, An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415-434]. Several simple sufficient conditions under which a game has an iterated MP-maximizer are also provided.     

Rank based cointegration testing for dynamic panels with fixed <Emphasis Type="Italic">T</Emphasis>

In this paper, we show that the cointegration testing procedure of Binder et al. (Econom Theory 21:795–837, 2005) for Panel Vector Autoregressive model of order 1, PVAR(1) is not valid due to the singularity of the hessian matrix. As an alternative we propose a method of moments based procedure using the rank test of Kleibergen and Paap (J Econom 133:97–126, 2006) for a fixed number of time series observations. The test is shown to be applicable in situations with time-series heteroscedasticity and unbalanced data. The novelty of our approach is that in the construction of the test we exploit the “weakness” of the Anderson and Hsiao (J Econom 18:47–82, 1982) moment conditions. The finite-sample performance of the proposed test statistic is investigated using simulated data. The results indicate that for most scenarios the method has good statistical properties. The proposed test provides little statistical evidence of cointegration in the employment data of Alonso-Borrego and Arellano (J Bus Econ Stat 17:36–49, 1999).     

The core-walras equivalence

The equivalence of cores and competitive equilibrium sets in the very general framework of Boolean rings and algebras is proved. The results include most previous results as special cases. In particular, it is shown that Theorems 1 and 2 of M. K. Richter (J. Econom. Theory3 (1971), 323–334) remain true without the usual assumptions of δ-algebras for coalitions and δ-additive measures for allocations. This permits economies with countably many agents, rather than requiring continuumly many.     

Partnerships, lemons, and efficient trade

We analyze the possibility of efficient trade with informationally interdependent valuations and with a dispersed ownership. A main role is played by the effects of adverse selection on incentive payments and budget constraints. Variations in the degree of interdependence directly influence the incentive payments and ultimately lead to a tightening or relaxation of the budget constraint, thus affecting the ability to achieve efficient trade. We derive precise possibility conditions for efficient trade, and we offer a framework in which the interplay of insights previously obtained by Akerlof (Quart. J. Econom. 89 (1970) 488), Myerson and Satterthwaite (J. Econom. Theory 28 (1983) 265), and Cramton et al. (Econometrica 55 (1987) 615) can be analyzed. In addition, we discuss to what extent possibility results previously obtained for private values environments can be generalized.     

Privatization and Price Liberalization: Comparative Analysis

Two transition paths from a mixed to market economy are investigated: a gradual increase in state retail prices and a gradual decrease of the state sector's share of the economy. The analysis is carried out in the framework of a general equilibrium model of a mixed economy with production. It is shown that, for a representative agent, privatization is better than price liberalization during the entire transition period regardless of individual preferences. For an economy with heterogeneous agents the conclusion remains valid for rich agents, but it is indeterminate for poor agents.J. Comp. Econom.,June 1997,24(3), pp. 313–334. Central Institute of Economics and Mathematics, Moscow 117418, Russia.     

An extension of Fishburn's theorem on extending orders

P. C. Fishburn [J. Econom. Theory31 (1983), 000-000] has shown that one can extend any well ordering of a set to a linear ordering of the set of all non-empty subsets of that set, while satisfying two axioms denoted (GP¹) and (M¹). By applying the compactness theorem of logic, this note shows that the well ordering assumption can be waived. Definability and well ordering properties of the extension are also discussed and shown to depend on the class of basic orderings considered.     

Persuasion games with higher-order uncertainty

Shin (J. Econom. Theory 64 (1994) 253–264) showed that a perfectly revealing equilibrium fails to exist in persuasion games when the decision maker is uncertain about the interested party's payoff-relevant information. By explicitly integrating higher-order uncertainty into the information structure, this note shows that a perfectly revealing equilibrium does exist when disclosures are not restrained to intervals of the payoff-relevant state space.     

Minimizing Regret: The General Case

In repeated games with differential information on one side, the labelling “general case” refers to games in which the action of the informed player is not known to the uninformed, who can only observe a signal which is the random outcome of his and his opponent's action. Here we consider the problem of minimizing regret (in the sense first formulated by J. Hannan (1956, in Contributions to the Theory of Games, Vol. III, Annals of Mathematics Studies, Vol. 39, Princeton, NJ: Princeton Univ. Press.) when the information available is of this type. We give a simple condition describing the approachable set. Journal of Economic Literature Classification Number: D81, D82, D83.     

Match choice and Ghettoization in evolutionary games

I study how having a choice about who to play affects the conventions that arise in a population playing a 2×2 common interest game. Match choice allows agents playing “fragile but efficient” strategies to isolate themselves, raising their returns but making it harder for outsiders to duplicate their success. When agents are myopic, the second effect dominates: long run play can shift toward either the risk-dominant equilibrium (with common interests in matching) or toward the inefficient equilibrium (with opposing interests in matching). In contrast, when agents are patient, supra-Nash payoffs can be sustained.     

Supportability and anonymous equity

W. W. Sharkey and L. G. Telser (J. Econom. Theory18 (1978), 23–37) feel that invulnerability of a natural monopoly to the threat of competitive entry is well reflected in the concept of supportability. G. R. Faulhaber and S. B. Levinson (Amer. Econom. Rev.71 (1981), 1083–1091) point out that supportability is necessary for the achievability of anonymous equity, i.e., absence of consumer subsidies in public enterprise pricing. This paper reconciles supportability with market clearance and shows that supportability is sufficient for the achievability of anonymous equity.     

Preparation

A product set of pure strategies is a prep set (‘prep’ is short for ‘preparation’) if it contains at least one best reply to any consistent belief that a player may have about the strategic behavior of his opponents. Minimal prep sets are shown to exist in a class of strategic games satisfying minor topological conditions. The concept of minimal prep sets is compared with (pure and mixed) Nash equilibria, rationalizability, minimal curb sets, and persistent retracts.     

Moments of truncated <Emphasis Type="Italic">t</Emphasis> and <Emphasis Type="Italic">F</Emphasis> distributions

Truncated distributions commonly arise in economics and related areas, see, for example, Lee (Econ Lett 3:165–169, 1979), Lien (Econ Lett 19:243–247, 1985; Econ Lett 20:45–47, 1986), Burdett (Econ Lett 52:263–267, 1996), Sercu (Insur: Math and Econ 20:79–95, 1997), Abadir and Magdalinos (Econom Theory 18:1276–1287, 2002), and Horrace (J Econom 126:335–354, 2005). In this note, we consider the most commonly encountered truncated distributions with heavy tails: the truncated t distribution and the truncated F distribution. For each of these distributions, we derive explicit expressions for the moments and estimation procedures by the method of moments and the method of maximum likelihood. An application is illustrated to a popular data set in the econometric literature.      

Are there cycles in realistic overlapping cohorts models?

Following Gale, 1973 (J. Econ. Theory 4, 110–137), Benhabib and Day, 1982 (J. Econ. Dyn. Control 4, 37–55) and Grandmont, 1985 (Econmetrica 45, 995–1045) proved the existence of P-cycles in Overlapping Generations (OLG) models. Aiyagari, 1989 (Q. J. Econ 104, 163–185) considered Overlapping Cohorts (OLC) models, with very long-lived agents of positively discounted utility functions and proved nonexistence of 2-cycles. We study OLC models with agents of normal life spans and utilities and show that: (1) for constant relative risk aversion (CRRA) utility (except for Leontief case), no 2-cycle exists; and (2) for Cobb-Douglas utility, no P-cycle exists.     

Hope springs eternal: learning and the stability of cooperation in short horizon repeated games

This paper considers learning rates in finitely repeated prisoners’ dilemmas. If players think their opponents might be relatively cooperative (e.g., tit-for-tat or grim types), they will cooperate in finitely repeated prisoners’ dilemmas (see Kreps et al., J. Econom. Theory 27 (1982) 245). However, if there are actually no cooperative types, players will eventually learn this and cooperation will break down. This paper shows that this learning is extremely slow, so it will take an extremely long time for cooperation to break down.Thus, suppose the world is either “good” or “bad.” The probability of a grim type is δ>0 if the world is good, and zero if the world is bad. Successive generations pair up to play finitely repeated prisoners’ dilemmas. Players observe play in previous generations and use Bayes’ rule to update their prior, π, that the world is good. We show that, if the world is really bad, then π falls per generation on average. Thus, if δ is small, there is less cooperation if the world is good, but cooperation may become more stable. For a representative 19 period repeated prisoners’ dilemma, beliefs fall one percentage point on average after a thousand generations.To derive these learning rates, we must refine existing results on the sensitivity of repeated games to Kreps et al. (1982) type perturbations. Specifically, we show cooperation is possible in perturbed prisoners’ dilemmas repeated O(log(1/δ)) times. This improves significantly on the O(1/δ) results in previous work. The paper thus provides two new reasons why cooperation tends to be stable, even in short horizon repeated games.     

A weak bargaining set for contract choice problems

In this paper, we consider the problem of choosing a set of multi-party contracts, where each coalition of agents has a non-empty finite set of feasible contracts to choose from. We call such problems, contract choice problems. The main result in this paper states that every contract choice problem has a non-empty weak bargaining set. The need for such a solution concept which is considerably weaker than the core arises, since it is well-known that even for very simple contract choice problems, the core may be empty. We also show by means of an example that an analog of the bargaining set due to Mas-Colell [Mas-Colell, A., 1989. An equivalence theorem for a bargaining set. Journal of Mathematical Economics 18, 129–139], as well as the natural analog of the bargaining set due to Aumann and Mashler [Aumann, R., Maschler, M., 1964. The bargaining set for cooperative games. In: Dresher, M., Shapley, L., Tucker, A. (Eds.), Advances in Game Theory. Princeton University Press, Princeton, NJ] may be empty for contract choice problems.