Collaboration in Multi-agent Games : Synthesis of Finite-state Strategies in Games of Imperfect Information
Sammanfattning: We study games where a team of agents needs to collaborate against an adversary to achieve a common goal. The agents make their moves simultaneously, and they have different perceptions about the system state after each move, due to different sensing capabilities. Each agent can only act based on its own experiences, since no communication is assumed during the game. However, before the game begins, the agents can agree on some strategy. A strategy is winning if it guarantees that the agents achieve their goal regardless of how the opponent acts. Identifying a winning strategy, or determining that none exists, is known as the strategy synthesis problem. In this thesis, we only consider a simple objective where the agents must force the game into a given state. Much of the literature is focused on strategies that either rely on that the agents (a) can remember everything that they have perceived or (b) can only remember the last thing that they have perceived. The strategy synthesis problem is (in the general case) undecidable in (a) and has exponential running time in (b). We are interested in the middle, where agents can have finite memory. Specifically, they should be able to keep a finite-state machine, which they update when they make new observations. In our case, the internal state of each agent represents its knowledge about the state of affairs. In other words, an agent is able to update its knowledge, and act based on it. We propose an algorithm for constructing the finite-state machine for each agent, and assigning actions to the internal states before the game begins. Not every winning strategy can be found by the algorithm, but we are convinced that the ones found are valid ones. An important building block for the algorithm is the knowledge-based subset construction (KBSC) used in the literature, which we generalise to games with multiple agents. With our construction, the game can be reduced to another game, still with uncertain state information, but with less or equal uncertainty. The construction can be applied arbitrarily many times, but it appears as if it stabilises (so that no new knowledge is gained) after only a few steps. We discuss this and other interesting properties of our algorithm in the final chapters of this thesis.
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