Summary: On robustness and dynamics in (un)balanced coalitional games
We build upon control theoretic concepts like robustness and dynamics to better ac-
commodate all the situations where the coalitions' values are uncertain and subject to
changes over time. The proposed robust dynamic framework provides an alternative per-
spective on the study of sequences of coalitional games or interval valued games. For a
sequence of coalitional games, either balanced or unbalanced, we analyze the key roles
of instantaneous and average games. Instantaneous games are obtained by freezing the
coalitions' values at a given time and come into play when coalitions' values are known.
On the other hand, average games are derived from averaging the coalitions' values up
to a given time and are key part of our analysis when coalitions' values are unknown.
The main theoretical contribution of our paper is a design method of allocation rules that
return solutions in the core and/or -core of the instantaneous and average games. Theo-
retical results are then specialized to a simulated example to shed light on the impact of
the design method and on the performance of the resulting allocation rules.
Keywords cooperative games, dynamic games, unbalancedness.
In this work, we investigate robustness and dynamics in coalitional games. We build upon