Fast algorithms for finding randomized strategies in game trees
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Computing sequential equilibria for two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Robust planning in domains with stochastic outcomes, adversaries, and partial observability
Robust planning in domains with stochastic outcomes, adversaries, and partial observability
Average-reward decentralized Markov decision processes
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
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We describe a generalization of extensive-form games that greatly increases representational power while still allowing efficient computation in the zero-sum setting. A principal feature of our generalization is that it places arbitrary convex optimization problems at decision nodes, in place of the finite action sets typically considered. The possibly-infinite action sets mean we must "forget" the exact action taken (feasible solution to the optimization problem), remembering instead only some statistic sufficient for playing the rest of the game optimally. Our new model provides an exponentially smaller representation for some games; in particular, we show how to compactly represent (and solve) extensive-form games with outcome uncertainty and a generalization of Markov decision processes to multi-stage adversarial planning games.