On robustness and dynamics in (un)balanced coalitional games

In this paper we investigate robustness and dynamics for coalitional games with transferable utilities (TU games). In particular we study sequences of TU games. These sequences model dynamic situations in which the values of coalitions of players are not known beforehand, and are subject to changes over time. An allocation rule assigns a payoff to each player in each time period. This payoff is bounded by external restrictions, for example due to contractual agreements. Our main questions are: (i) under which conditions do the allocations converge to a core-element of the game, and (ii) when do the allocations converge to some specific allocation, the so-called nominal allocation? The main contribution of this paper is a design method for allocation rules that return solutions in the core or $\varepsilon$-core of the game under delayed information on the coalitions’ values, and therefore the resulting allocation rule is called robust.