Equilibrium Computation in Dynamic Games
Type of documenthabilitační práce
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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.
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