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Learning and Solving Many-Player Games Through a Cluster-Based Representation
In addressing the challenge of exponential scaling with the number of agents we adopt a cluster-based representation to approximately solve asymmetric games of very many players. A cluster groups together agents with a similar “strategic view ” of the game. We learn the clustered approximation from data consisting of strategy profiles and payoffs, which may be obtained from observations of play or access to a simulator. Using our clustering we construct a reduced “twins” game in which each cluster is associated with two players of the reduced game. This allows our representation to be individuallyresponsive because we align the interests of every individual agent with the strategy of its cluster. Our approach provides agents with higher payoffs and lower regret on average than model-free methods as well as previous cluster-based methods, and requires only few observations for learning to be successful. The “twins ” approach is shown to be an important component of providing these low regret approximations.Engineering and Applied Science
Positional Games and QBF: The Corrective Encoding
Positional games are a mathematical class of two-player games comprising
Tic-tac-toe and its generalizations. We propose a novel encoding of these games
into Quantified Boolean Formulas (QBF) such that a game instance admits a
winning strategy for first player if and only if the corresponding formula is
true. Our approach improves over previous QBF encodings of games in multiple
ways. First, it is generic and lets us encode other positional games, such as
Hex. Second, structural properties of positional games together with a careful
treatment of illegal moves let us generate more compact instances that can be
solved faster by state-of-the-art QBF solvers. We establish the latter fact
through extensive experiments. Finally, the compactness of our new encoding
makes it feasible to translate realistic game problems. We identify a few such
problems of historical significance and put them forward to the QBF community
as milestones of increasing difficulty.Comment: Accepted for publication in the 23rd International Conference on
Theory and Applications of Satisfiability Testing (SAT2020
Approximating n-player behavioural strategy nash equilibria using coevolution
Coevolutionary algorithms are plagued with a set of problems related to intransitivity that make it questionable what the end product of a coevolutionary run can achieve. With the introduction of solution concepts into coevolution, part of the issue was alleviated, however efficiently representing and achieving game theoretic solution concepts is still not a trivial task. In this paper we propose a coevolutionary algorithm that approximates behavioural strategy Nash equilibria in n-player zero sum games, by exploiting the minimax solution concept. In order to support our case we provide a set of experiments in both games of known and unknown equilibria. In the case of known equilibria, we can confirm our algorithm converges to the known solution, while in the case of unknown equilibria we can see a steady progress towards Nash. Copyright 2011 ACM
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