Inessentiality of large groups and the approximate core property: an equivalence theorem

Summary Inessentiality of large groups or, in other words, effectiveness of small groups, means that almost all gains to group formation can be realized by partitions of the players into groups bounded in absolute size. The approximate core property is that all sufficiently large games have nonempty approximate cores. I consider these properties in a framework of games in characteristic function form satisfying a mild boundedness condition where, when the games have many players, most players have many substitutes. I show that large (finite) games satisfy inessentially of large groupsif and only if they satisfy the approximate core property.This paper focuses on a part of another paper, Inessentiality of Large Coalitions and the Approximate Core Property; Two Equivalence Theorems, previously circulated as a University of Bonn Sonderforschungsbereich Discussion Paper.The author is indebted to Roger Myerson for a very stimulating comment and the term inessentiality of large coalitions. She is also indebted to Robert Anderson, Sergiu Hart, and Aldo Rustichini for helpful conversations. She is especially indebted to Robert Aumann for many stimulating and helpful discussions on research leading to this paper. The author gratefully acknowledges the financial support of the SSHRC and the hospitality and support of the University of Bonn through Sonderforschungsbereich 303.     

The economics of crowd out under mixed public/private health insurance

It is well known that public insurance sometimes crowds out private insurance. Yet, the economic theory of crowd out has remained unstudied. Here, I show that crowd out causes two countervailing effects: (a) the intensive margin effect-since high demanders are crowded out, the private market now has a larger proportion of low demanders on the intensive margin (The intensive margin are those who have already bought private insurance), and so will drop quality to lower the price to the low demanders liking; and (b) the extensive margin effect-before the public insurance expansion, the private sector had lowered quality to make insurance more affordable at the extensive margin (The extensive margin is the next group of people who would buy private insurance if the price decreased), but now that public insurance crowds out the extensive margin, quality can then be raised back up to the high demanders liking.If the extensive margin effect dominates, then a new phenomenon of push out occurs, in which crowd out causes the private sector to raise quality and to increase the number of uninsured low demanders not eligible for public insurance. If the intensive margin effect dominates, then crowd out will cause the private sector to lower quality, causing the phenomenon of crowd-in, in which the number of uninsured low demanders that take-up private insurance increases.These two countervailing effects have important implications for any government policy that desires to eradicate all uninsurance. First, if push out is dominant, then the private sector will respond to the public insurance by pushing out and leaving some people newly uninsured. If crowd-in is dominant, then all people can be insured and the government can do it at a lower-than-anticipated level of expansion due to the private sector crowding in.Received: April 2002, Accepted: February 2003, JEL Classification: I11, I38The views herein do not necessarily reflect the views or policies of AHRQ, nor the U.S. Department of Health and Human Services. I thank Pedro Pita Barros, Hugh Gravelle, and Lise Rochaix-Ranson, and participants at the 2nd Health Economics Workshop at the Universidade Nova de Lisboa for helpful comments.     

Research policy and endogenous growth

This paper studies the effects of different types of research policy on economic growth. We find that while subsidies to private research, public funding of private projects, and basic research performed at public institutions have unambiguously positive effects on growth, performing applied research at public institutions could have negative growth effects. This is due to the large crowding out of private research caused by public R&D when it competes with private firms in the patent race.JEL Classification: O31, O38, O40I thank the helpful comments of Jordi Caballé, David Pérez-Castrillo and two anonymous referees. I also aknowledge the financial support of Fundaci ón Séneca project PB/3/FS/02.     

Contests with a stochastic number of players

We study Tullock's (1980) n-player contest when each player has an independent probability 0 < p 1 of participating. A unique symmetric equilibrium is found for any n and p and its properties are analyzed. In particular, we show that for a fixed n > 2 individual equilibrium spending as a function of p is single-peaked and satisfies a single-crossing property for any two different numbers of potential players. However, total equilibrium spending is monotonically increasing in p and n. We also demonstrate that ex-post over-dissipation is a feature of the pure-strategy equilibrium in our model. It turns out that if the contest designer can strategically decide whether to reveal the actual number of participating players or not, then the actual number of participants is always revealed.     

Approximate efficiency in repeated games with correlated private signals

This paper presents repeated games with hidden moves, in which players receive imperfect private signals and are able to communicate. We propose a conditional probability approach to solve the learning problem in repeated games with correlated private signals and delayed communication. We then apply this approach to symmetric n-player games to obtain an approximate efficiency result.     

A law of large numbers for large economies

Summary LetX(i),i[0; 1] be a collection of identically distributed and pairwise uncorrelated random variables with common finite mean and variance ². This paper shows the law of large numbers, i.e. the fact that ₀ ¹ X(i)di=. It does so by interpreting the integral as a Pettis-integral. Studying Riemann sums, the paper first provides a simple proof involving no more than the calculation of variances, and demonstrates, that the measurability problem pointed out by Judd (1985) is avoided by requiring convergence in mean square rather than convergence almost everywhere. We raise the issue of when a random continuum economy is a good abstraction for a large finite economy and give an example in which it is not.I am indebted to Hugo Hopenhayn. Furthermore I would like to thank Dilip Abreu, Glenn Donaldson, Ed Green, Ramon Marimon, Nabil Al-Najjar, Victor Rios-Rull, Timothy van Zandt and the editor for useful comments. The first version of this paper was written in 1987.     

Should mobile capital pay for public infrastructure investment?

The paper contributes to the discussion of fiscal competition with infrastructure goods. We explicitly focus on the costs of providing public infrastructure capital that appear in the public budget as investment. Thus we analyse the problem in a dynamic framework. Public infrastructure is considered as a marginal product complement to private capital. A central result of the model is that the fact that public capital is a complement to private capital, so that an increase in the supply of public capital ceteris paribus improves the marginal productivity of private capital, cannot be used as an argument to support a source tax. The so-called indirect productivity effect on private capital induced by public inputs does not justify the taxation of mobile capital. Rather, the efficiency of a source tax on mobile capital income depends on the question of whether or not the public input generates a factor rent to private capital.

Perfect communication equilibria in repeated games with imperfect monitoring

This paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring. This concept is a refinement of Myerson's [Myerson, R.B., 1982. Optimal coordination mechanisms in generalized principal agent problems, J. Math. Econ. 10, 67–81] communication equilibrium. A communication equilibrium is perfect if it induces a communication equilibrium of the continuation game, after every history of messages of the mediator. We provide a characterization of the set of corresponding equilibrium payoffs and derive a Folk Theorem for discounted repeated games with imperfect private monitoring.     

An evolutionary theory of the convergence towards low inflation rates

This paper presents an evolutionary interpretation of Barro-Gordons monetary policy game. The model describes a multi-country setup where governments and private agents are boundedly rational players. The behavioral rule of players decisions leads to the imitation of the strategy giving the highest payoff. In this evolutionary monetary policy game, we show how a low inflation state is reached from an international context dominated by inflationary policies. The analysis explains the convergence towards low inflation rates observed during the past twenty years. Moreover, the low inflation state appears to be the long-run equilibrium of the game under some conditions featuring the observed macroeconomic context.JEL Classification: E5, C72, C73 Correspondence to: A. dArtigues     

Revenues in discrete multi-unit, common value auctions: a study of three sealed-bid mechanisms

This paper proposes a discrete bidding model for both quantities and pricing. It has a two-unit demand environment where subjects bid for contracts with an unknown redemption value, common to all bidders. Prior to bidding, the bidders receive private signals of information on the (common) value. The relevant task is to compare the equilibrium strategies and the seller’s revenue of the three most common auction formats with two players. The result is that the Vickrey auction always gives the most revenue to the seller, the discriminatory auction follows closely and the uniform auction clearly is the worst due to demand reduction.

Signaling in social network and social capital formation

This paper presents a model of social capital and social network formation. The key interaction within the model is that whom an individual chooses to become friends with affects the value (social capital) of the friendship. In the model, how a player searches for and then forms friendships reveals how willing she is to engage in cooperation with a potential friend. Individuals observe their local network structure (friends and cliques) and the actions of players within these. Willingness to cooperate is private information and is captured by the discount factor of an individual. Cooperative types have high discount factors and can signal their type by forming a clique through befriending a friend of a friend. Uncooperative types do not form these kinds of friendships because of the local observability of their actions to all members of a clique. Thus, when a player meets someone with whom she shares a friend, her belief that the individual has a high discount factor is greater than the population average. In this sense, people “trust” each other more when they share a friend in common. Finally, I relate the primitives of the model to characteristics of the implied social network by nesting the sequential equilibrium in an algorithm of network formation proposed by Jackson and Rogers (Am Econ Rev 97(3):890–915, 2007). The model highlights a trade-off between maximizing the total amount of social capital in a society and distributing it equitably across individuals.     

A Robust Folk Theorem for the Prisoner's Dilemma

We prove the folk theorem for the Prisoner's dilemma using strategies that are robust to private monitoring. From this follows a limit folk theorem: when players are patient and monitoring is sufficiently accurate, (but private and possibly independent) any feasible individually rational payoff can be obtained in sequential equilibrium. The strategies used can be implemented by finite (randomizing) automata. Journal of Economic Literature Classification Numbers: C72, C73, D82.     

Dynamic coordination games

Summary Gains from coordination provide incentives for delay. In this paper, the extent of delay is studied in a dynamic,N-person, coordination game. There is no social gain from delay, so an equilibrium with delay is always inefficient. For fixedN, there is no coordination failure when the period length is short: all equilibrium outcomes converge to the Pareto efficient outcome as the period length converges to zero. On the other hand, holding period length fixed, there exist equilibria in which delay is proportional toN, for arbitrarily large values ofN. In addition, it can be shown that the possibility of delay depends on the timing of strategic complementarities. However, under certain conditions, delay is shown to be a robust phenomenon, in the sense that well-behaved equilibria exhibit infinite delay forN sufficiently large.This paper grew out of discussions with Christophe Chamley. While writing it I benefited from discussions with Ken Binmore, Russell Cooper, Bob Rosenthal and Michael Manove. Joe Farrell, Drew Fudenberg, Martin Hellwig and Sawoong Kang made very useful comments on an earlier version that led to substantial improvements. Helpful comments were also made by seminar participants at the London School of Economics, the SUNY at Stoney Brook, the NBER Summer Institute, Northwestern University, and the University of Chicago. I would like to thank Nick Yannelis and an anonymous referee for their editorial advice. Financial support for this research was provided by the National Science Foundation under Grant No. SES 9196061.     

Market equilibrium with heterogeneous recursive-utility-maximizing agents

Summary The paper by C. Ma [1] contains several errors. First, statement and proof of Theorem 2.1 on the existence of intertemporal recursive utility function as a unique solution to the Koopmans equation must be amended. Several additional technical conditions concerning the consumption domain, measurability of certainty equivalent and utility process need to be assumed for the validity of the theorem. Second, the assumptions for Theorem 3.1 need to be amended to include the Feller's condition that, for any bounded continuous functionf C(S × ⁿ ₊), (f(S_t+1, )¦s_t =s) is bounded and continuous in (s, ). In addition, for Theorem 3.1, the pricep, the endowmente and the dividend rate as functions of the state variables S are assumed to be continuous.The Feller's condition for Theorem 3.1 is to ensure the value function to be well-defined. This condition needs to be assumed even for the expected additive utility functions (See Lucas [2]). It is noticed that, under this condition, the right hand side of equation (3.5) in [1] defines a bounded continuous function ins and. The proof of Theorem 3.1 remains valid with this remark in place.A correct version of Theorem 2.1 in [1] is stated and proved in this corrigendum. Ozaki and Streufert [3] is the first to cast doubt on the validity of this theorem. They point out correctly that additional conditions to ensure the measurability of the utility process need to be assumed. This condition is identified as conditionCE ₄ below. In addition, I notice that, the consumption space is not suitably defined in [1], especially when a unbounded consumption set is assumed. In contrast to what claimed in [3], I show that the uniformly bounded consumption setX and stationary information structure are not necessary for the validity of Theorem 2.1.I would like to thank Hiroyuki Ozaki and Peter Streufert for pointing out correctly some mistakes made in the original article. Comments and suggestions from an anonymous referee are gratefully appreciated. Financially support from SSHRC of Canada is acknowledged.     

On Political Competition: Democracy, Opinion and Responsibility

In this paper, I consider the influence of political competition on opinion. After reflecting on the notion opinion as a concept in the economic analysis of politics, I turn to Hayek's Constitution of Liberty and consider his argument for democracy on the grounds that it is the form of government which best promotes progress in opinion. Yet Hayek's claim that democratically formed opinion improves is unsubstantiated. I turn to accounts of expressive voting thereafter to show why opinions which are realised in the form of votes may be anything other than propitious to democratic culture. I then return to Hayek and consider what becomes of opinion in Law, Legislation and Liberty. His claim that opinion improves under democratic institutions is no longer of great significance to him. Indeed, his account of the rise of bargaining politics provides evidence against the claim that opinion improves. I conclude by asking how democracy can be shielded from opinion, that is, how opinion might be improved in ways which go beyond Hayek's model of political competition outlined in Constitution of Liberty. To this end, I look to accounts of deliberative democracy and expressive politics for support.     

Communication in repeated network games with imperfect monitoring

I consider repeated games with private monitoring played on a network. Each player has a set of neighbors with whom he interacts: a player's payoff depends on his own and his neighbors' actions only. Monitoring is private and imperfect: each player observes his stage payoff but not the actions of his neighbors. Players can communicate costlessly at each stage: communication can be public, private or a mixture of both. Payoffs are assumed to be sensitive to unilateral deviations. First, for any network, a folk theorem holds if some Joint Pairwise Identifiability condition regarding payoff functions is satisfied. Second, a necessary and sufficient condition on the network topology for a folk theorem to hold for all payoff functions is that no two players have the same set of neighbors not counting each other.     

Dynamic Performance Benchmarking of Indian General Insurers

In India, competition scenario in the general insurance sector changed since the year 2000–2001 with the entry of several private sector players in the respective market. While a few studies attempted to benchmark the performance of Industry players using early data available from the market regulator, the existing research studies have a number of weaknesses. Against this backdrop, the present paper seeks to evaluate the performance of 15 general insurance companies for the period 2009–2010 to 2013–2014 using a two stage approach. In the first stage, the study uses the dynamic DEA model suggested by Tone and Tsutsui (Omega, 38(3–4):145–156, 2010) to evaluate the in-sample companies in terms of slacks based measure of technical efficiency. In the second stage, the efficiency scores have been explained by solvency performance of the insurers in terms of a panel data censored regression model with robust residuals. The results indicate a very strong association between efficiency and solvency.

     

The Statistical Mechanics of Best-Response Strategy Revision

This paper compares local and global strategic interaction when players update using the (myopic) best-response rule. I show that randomizing the order in which players update their strategic choice suffices to achieve coordination on the risk-dominant strategy in symmetric 2 × 2 coordination games. The "persistant randomness" which is necessary to achieve similar coordination with global interaction is replaced under local interaction by spatial variation in the initial condition. An extension of the risk-dominance idea gives the same convergence result for K × K games with strategic complementarities. Similar results for K × K pure coordination games and potential games are also presented. Journal of Economic Literature Classification Number: C78.     

On Failing to Cooperate When Monitoring Is Private

I consider a repeated prisoners' dilemma where in each period, each player receives an imperfect private signal about his opponent's current action. I show that when players are patient enough, any equilibrium where players use trigger strategies (i.e., do not revert to cooperation once they have started defecting) yields players a value arbitrarily close to the mutual minimax. I also examine the robustness of the result to perturbations of the game. Journal of Economic Literature Classification Numbers: C72.