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

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

Subgame perfect equilibria in majoritarian bargaining

We study the division of a surplus under majoritarian bargaining in the three-person case. In a stationary equilibrium as derived by Baron and Ferejohn (1989), the proposer offers one third times the discount factor of the surplus to a second player and allocates no payoff to the third player, a proposal which is accepted without delay. Laboratory experiments show various deviations from this equilibrium, where different offers are typically made and delay may occur before acceptance. We address the issue to what extent these findings are compatible with subgame perfect equilibrium and characterize the set of subgame perfect equilibrium payoffs for any value of the discount factor. We show that for any proposal in the interior of the space of possible agreements there exists a discount factor such that the proposal is made and accepted. We characterize the values of the discount factor for which equilibria with one-period delay exist. We show that any amount of equilibrium delay is possible and we construct subgame perfect equilibria such that arbitrary long delay occurs with probability one