Computing the Strategy to Commit to in Polymatrix Games

Giuseppe De Nittis, Alberto Marchesi, Nicola Gatti

Abstract: 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.