Computing the Strategy to Commit to in Polymatrix Games (Extended Version)
This addresses a problem in game theory for modeling real-world multi-agent interactions, but it is incremental as it extends existing work on leadership games.
The paper tackles the computational complexity of finding leader-follower equilibria in polymatrix games with multiple followers who act optimistically or pessimistically, showing that exact computation is hard in general but providing an exact algorithm for specific classes.
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world applications, this is unlikely. In this paper, we look for efficiently solvable games with multiple followers who play either optimistically or pessimistically, i.e., breaking ties in favour or against the leader. We study the computational complexity of finding or approximating an optimistic or pessimistic leader-follower equilibrium in specific classes of succinct games---polymatrix like---which are equivalent to 2-player Bayesian games with uncertainty over the follower, with interdependent or independent types. Furthermore, we provide an exact algorithm to find a pessimistic equilibrium for those game classes. Finally, we show that in general polymatrix games the computation is harder even when players are forced to play pure strategies.