This habilitation thesis presents advancements in computing exact and approximate solution concepts
in dynamic games. Dynamic games model scenarios that evolve over time, players are able to
perform actions that modify the environment, however, the players do not have perfect information
about the environment and receive only partial information as observations. We consider strictly
competitive (or zero-sum) games where a gain of one player is a loss of the opponent as well as
general-sum games. Similarly, we consider both games with a finite, pre-defined number of moves
(horizon) after which the game terminates, as well as games where the number of moves is not fixed.
There are several key contributions. For zero-sum games, we provide algorithmic contributions
for games with both finite and with infinite horizon. For finite games, we adopted the incremental
strategy-generation technique in order to scale-up to larger domains and also provided the first
algorithm for approximately solving games where players have imperfect memory (imperfect recall).
For games with infinite horizon, we provide the first algorithms for approximately solving games
where at least one player has partial information about the environment.
For general-sum games, we provide several theoretical results determining the complexity of
computing a Stackelberg Equilibrium and novel algorithms for its computation in finite dynamic
games. Moreover, we formally define a novel solution concept, a variant of Stackelberg Equilibrium
termed Stackelberg Extensive-Form Correlated Equilibrium, and we show that this solution concept
is important both from the theoretical perspective, since the computational complexity is often lower
compared to Stackelberg Equilibrium, as well as from the practical perspective. To this end, we
propose an algorithm that uses this new solution concept in order to quickly compute a Stackelberg
Equilibrium.
