  Modern applications require robots to comply with multiple, often conflicting
rules and to interact with the other agents. We present Posetal Games as a
class of games in which each player expresses a preference over the outcomes
via a partially ordered set of metrics. This allows one to combine hierarchical
priorities of each player with the interactive nature of the environment. By
contextualizing standard game theoretical notions, we provide two sufficient
conditions on the preference of the players to prove existence of pure Nash
Equilibria in finite action sets. Moreover, we define formal operations on the
preference structures and link them to a refinement of the game solutions,
showing how the set of equilibria can be systematically shrunk. The presented
results are showcased in a driving game where autonomous vehicles select from a
finite set of trajectories. The results demonstrate the interpretability of
results in terms of minimum-rank-violation for each player.
