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

Conditions for Cooperation and Trading in Value-Cost Dynamic Games

In value-cost dynamic games multiple agents adjust the flow and allocation of investments to action pathways that affect the value of other agents. This article determines conditions for cooperation among agents who invest to gain value from each other. These conditions are specified in a game-theoretic setting for agents that invest to realize cooperative benefits and value targets. The dynamic interaction of allocation priorities and the stability of equilibrium concepts is analyzed. One focus is to determine solutions concepts based on cost-exchange ratios and benefit-exchange ratios that represent trade-offs between the agents, as a function of the action and interaction effects of the respective action pathways. The general approach is applied to the trading between buyers and sellers of goods to determine conditions for mutually beneficial market exchange, the price of goods, and the specialization between consumers and producers