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

Dynamic club formation with coordination

We present a dynamic model of jurisdiction formation in a society of identical people. The process is described by a Markov chain that is defined by myopic optimization on the part of the players. We show that the process will converge to a Nash equilibrium club structure. Next, we allow for coordination between members of the same club,i.e. club members can form coalitions for one period and deviate jointly. We define a Nash club equilibrium (NCE) as a strategy configuration that is immune to such coalitional deviations. We show that, if one exists, this modified process will converge to a NCE configuration with probability one. Finally, we deal with the case where a NCE fails to exist due to indivisibility problems. When the population size is not an integer multiple of the optimal club size, there will be left over players who prevent the process from settling down. We define the concept of an approximate Nash club equilibrium (ANCE), which means that all but k players are playing a Nash club equilibrium, where k is defined by the minimal number of left over players. We show that the modified process converges to an ergodic set of states each of which is ANCE

Hotelling tax competition

This paper shows how competition among governments for mobile firms can bring about excessive differentiation in levels of taxation and public good provision. Hotelling’s Principle of Minimum Differentiation is applied in the context of tax competition and shown to be invalid. Instead, when an equilibrium exists, differentiation of public good provision is maximized. Non-existence of equilibrium, which can occur, is a metaphor for intense tax competition. The paper also shows that, to some extent, perfect tax discrimination presents a solution to the existence problem created by Hotelling tax competition, but that the efficiency problem of Hotelling tax competition is exacerbated

Social conformity and bounded rationality in arbitrary games with incomplete information: some first results

Intepret a set of players all playing the same pure strategy and all with similar attributes as a society. Is it consistent with self interested behaviour for a population to organise itself into a relatively small number of societies? By introducing the concept of approximate substitute players in non-cooperative games we are able to put a bound on the rationality of such social conformity for an arbitrary game and arbitrary number of societies

The efficiency, equity and politics of emissions permit trading

This paper illustrates that an international permit trading system may hurt relatively poor countries by making associated economic activities unaffordable. A model is constructed in which the free market solution is Pareto inefficient as a result of pollution. The introduction of tradable permits allows pollution to be internalised, and brings about an increase in the total social surplus. But when incomes vary, this may not lead to a Pareto improvement; those in poor countries stop the polluting activity because they cannot afford to do otherwise. Only those in relatively rich countries are made better off. This may explain why poor countries are reluctant to ratify the Kyoto Protocol, itself advocating a permit trading scheme. The politico-economic implications of permit trading are also examined. We show that the democratic requirements for ratification impose a lower bound on pollution reduction that can be achieved through a system of pollution permits with trade

The Epsilon Core of a Large Game

Sufficient conditions are given for large replica games without side payments to have non-empty approximate cores for all sufficiently large replications. No “balancedness” assumptions are required. The conditions are superadditivity, a very weak boundedness condition, and convexity of the payoff sets. An example is provided to show that under these conditions, the (exact) core well may be empty

"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

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.

Epsilon cores of games and economies with limited side payments

We introduce the concept of a parameterized collection of games with limited side payments, ruling out large transfers of utility. Under the assumption that the payoff set of the grand coalition is convex, we show that a game with limited side payments has a nonempty E-core. Our main result is that, when some degree of side-paymentness within nearly-effective small groups is assumed, then all payoffs in the E-core treat similar players similarly. A bound on the distance between E-core payoffs of any two similar players is given in terms of the parameters describing the game. These results add to the literature showing that games with many players and small effective groups have the properties of competitive markets.cooperative games ; equal treatment ; core convergence ; games without side payments (NTU games) ; large games ; approximate cores ; effective small groups ; parameterized collections of games

A law of scarcity for games

The “law of scarcity” is that scarceness is rewarded ; recall, for example, the diamonds and water paradox. In this paper, furthering research initiated in Kelso and Crawford (1982, Econometrica 50, 1483-1504) for matching models, we demonstrate a law of scarcity for cores and approximate cores of games.cooperative games ; games with side payments (TU games) ; cyclic monotonicity ; law of demand ; approximate cores ; effective small groups ; parameterized collections of games