An explicit bound on " for nonemptiness of "-cores of games

We consider parameterized collections of games without side payments and determine a bound on E so that all suffciently large games in the collection have non-empty E-cores. Our result makes explicit the relationship between the required size of E for non-emptiness of the E-core, the parameters describing the collection of games, and the size of the total player set. Given the parameters describing the collection, the larger the game, the smaller the E that can bechosen

Laws of Scarcity for a Finite Game : Exact Bounds on Estimations

A "law of scarcity" is that scarceness is rewarded. We demonstrate laws of scarcity for cores and approximate cores of games. Furthermore, we show that equal treatment core payout vectors satisfy a condition of cyclic monotonicity. Our results are developed for parameterized collections of games and exact bounds on the maximum possible deviation of approximate core payo® vectors from satisfying a law of scarcity are stated in terms of the parameters describing the games. We note that the parameters can, in principle, be estimated.monotonicity ; cooperative games ; clubs ; games with side payments (TU games) ; cyclic monotonicity ; law of scarcity ; law of demand ; approximate cores ; effective small groups ; parameterized collections of games

ADVANCES IN THE THEORY OF LARGE COOPERATIVE GAMES AND APPLICATIONS TO CLUB THEORY : THE SIDE PAYMENTS CASE

In a series of papers (Kovalenkov and Wooders 2001a, Games and Economic Behavior, 2001b,Mathematics of Operations Research, and 1997, Journal of Economic Theory to appear), the authors have developed the framework of parameterized collections of games and also that of parameterized collections of economies with clubs. These papers apply to collections of games with nontransferable utility and similarly to economies with clubs and general preferences. The game theoretic framework encompasses the earlier `pregame' framework (cf., Wooders 1994b Econometrica) and also earlier models of economies with clubs and with possibly multiple memberships in clubs (cf. Shubik and Wooders 1982). In this paper, we consider the special case of games with side payments and illustrate the application of our more general results in this special, and much simpler but still important, framework. The motivation for this line of research is developed and application to environmental problems is discussed.cooperative games ; clubs ; core ; approximate cores ; widespread externalities ; multiple memberships ; local public goods

"An Explicit Bound on E For Nonemptimess of E-Cores of Games"

We consider parameterized collections of games without side payments and determine a bound on E so that all sufficiently large games in the collection have non-empty E-cores. Our result makes explicit the relationship between the required size of E for non-emptiness of the E-core, the parameters describing the collection of games, and the size of the total player set. Given the parameters describing the collection, the larger the game, the smaller the E that can be chosen

Competitive Rational Expectations Equilibria without Apology

In a standard financial market model with asymmetric information with a finite number N of risk-averse informed traders, competitive rational expectations equilibria provide a good approximation to strategic equilibria as long as N is not too small: equilibrium prices in eachsituation converge to each other at a rate of 1/N as the market becomes large. Theapproximation is particularly good when the informationally adjusted risk bearing capacity of traders is not very large. This is not the case if informed traders are close to risk neutral. Both equilibria converge to the competitive equilibrium of an idealized limit continuum economy as the market becomes large at a slower rate of 1/ãN and, therefore, the limit equilibrium need not be a good approximation of the strategic equilibrium in moderately large markets.gschizophreniah problem, strategic equilibrium, large markets, information acquisition, free entry, rate of convergence

Approximate Cores of Games and Economies with Clubs

This presentation focuses on new approachs to large games introduced in five papers by the authors (one with the same title as this abstract). In a new framework of parameterised collections of games with and without side payments, we provide nonemptiness of approximate core, a law of scarcity, and convergence results. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. Our nonemptiness theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. Our convergence results provide a new sort of application of standard theorems from linear programming. The results are applied to a model of an economy with clubs. In contrast to the extant literature, our approach allows widespread externalities -- that is, the payoffs to members of a club may depend on the economy in which the club is situated.

COMPARATIVE STATICS AND LAWS OF SCARCITY FOR GAMES

A 2law of scarcity2 is that scarceness is rewarded. We demonstrate laws of scarcity for cores and approximate cores of games. Furthermore, we demonstrate conditions under which all payoffs in the core of any game in a parametized collection have an equal treatment property and show that equal treatment core payoff vectors satisfy a condition of cyclic monotonicity. Our results are developed for parameterized collections of games and exact bounds on the maximum possible deviation of approximate core payoff vectors from satisfying a law of scarcity are stated in terms of the parameters describing the games. We note that the parameters can, in principle, be estimated. Results are compared to the developments in the literature on matching markets, pregames and general equilibrium. This paper expands on results published in Kovalenkov and Wooders, Economic Theory )to appear).Monotonicity ; cooperative games ; clubs ; games with side payments (TU games) ; cyclic monotonicity ; laws of scarecity ; law of demand ; approximate cores ; effective small groups ; parameterized collection of games

Approximate cores of games and economies with clubs

We introduce the framework of parameterized collections of games and provide three nonemptiness of approximate core theorems for arbitrary games with and without sidepayments. The parameters bound (a) the number of approx-imate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. The theorems are based on a new notion of partition-balanced pro les and approximately partition-balanced profiles. The results are then applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results.cooperative games, clubs, local public goods, games without side payments (NTU games), large games, approximate cores, effective small groups, parameterized collections of games.

An explicit bound on epsilon for nonemptiness of Epsilon-cores of games

We consider parameterized collections of games without side payments and determine a bound on epsilon so that all suffciently large games in the collection have non-empty epsilon-cores. Our result makes explicit the relationship between the required size of epsilon for non-emptiness of the epsilon-core, the parameters describing the collection of games, and the size of the total player set. Given the parameters describing the collection, the larger the game, the smaller the epsilon that can be chosen.cooperative games, games without side payments (NTU games), large games, approximate cores, effective small groups, parameterized collections of games.

APPROXIMATE CORES OF GAMES AND ECONOMIES WITH CLUBS

We introduce the framework of parameterized collections of games with and without side payments and provide three no emptiness of approximate core theorems for games in parameterized collections. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact electiveness. The theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. The results are applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results.cooperative games ; clubs ; local public goods ; approximate cores ; effective small groups ; parameterized collections of games