On the Core of Dynamic Cooperative Games

We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and thereby to give rise to a new environment. A coalition that considers a deviation needs to take the consequences into account because from the deviation point on, the game is no longer played with the original set of players. The deviating coalition becomes the new grand coalition which, in turn, induces a new dynamic game. The stage games of the new dynamical game depend on all previous allocation including those that have materialized from the deviating time on. We define three types of core solutions: fair core, stable core and credible core. We characterize the first two in case where the instantaneous game depends on the last allocation (rather than on the whole history of allocations) and the third in the general case. The analysis and the results resembles to a great extent the theory of non-cooperative dynamic games.Comment: 25 page

The Weak Sequential Core for Two-period Economies

We adapt the core concept to deal with economies in which trade in assets takes place at period 1, uncertainty about asset payoffs is released at period 2, and agents trade in commodities afterwards. We define the weak sequential core as the set of allocations that are stable against coalitional deviations ex ante, and moreover cannot be improved upon by any coalition once the uncertainty is being released. We restrict ourselves to credible deviations, i.e. coalitional deviations at period 1 that cannot be counterblocked by some subcoalition at period 2. We study the relationship of the resulting core concept with other sequential core concepts, give sufficient conditions under which the weak sequential core is non-empty, but show that it is possible to give reasonable examples where it is empty.Core assets

On the nonemptiness of approximate cores of large games

We provide a new proof of the nonemptiness of approximate cores of games with many players of a finite number of types. Earlier papers in the literature proceed by showing that, for games with many players, equal-treatment cores of their “balanced cover games,” which are nonempty, can be approximated by equal-treatment \varepsilon ? -cores of the games themselves. Our proof is novel in that we develop a limiting payoff possibilities set and rely on a fixed point theorem

The fuzzy core and the (Π, β)- balanced core

This note provides a new proof of the non–emptiness of the fuzzy core in a pure exchange economy with finitely many agents. The proof is based on the concept of (Π, β)–balanced core for games without side payments due to Bonnisseau and Iehlé (2003)

Best response cycles in perfect information games

We consider n-player perfect information games with payofffunctions having a finite image. We do not make any further assumptions, so in particular we refrain from making assumptions on the cardinality or the topology of the set of actions and assumptions like continuity or measurability of payofffunctions. We show that there exists a best response cycle of length four, that is, a sequence (σ0, σ1, σ2, σ3, σ0) of pure strategy profiles where every successive element is a best response to the previous one. This result implies the existence of point-rationalizable strategy profiles. When payoffs are only required to be bounded, we show the existence of an ϵ-best response cycle of length four for every ϵ > 0