Work on game playing in AI has typically ignored games of imperfect information such as poker. In this paper, we present a framework for dealing with such games. We point out several important issues that arise only in the context of imperfect information games, particularly the insufficiency of a simple game tree model to represent the players’ information state and the need for randomization in the players ’ optimal strategies. We describe Gala, an implemented system that provides the user with a very natural and expressive language for describing games. From a game description, Gala creates an augmented game tree with information sets which can be used by various algorithms in order to find optimal strategies for that game. In particular, Gala implements the first practical algorithm for finding optimal randomized strategies in two-player imperfect information competitive games [Koller et al., 1994]. The running time of this algorithm is polynomial in the size of the game tree, whereas previous algorithms were exponential. We present experimental results showing that this algorithm is also efficient in practice and can therefore form the basis for a game playing system. 1

The complexity of algorithms that compute strategies or operate on them typically depends on the representation length of the strategies involved. One measure for the size of a mixed strategy is the number of strategies in its support---the set of pure strategies to which it gives positive probability. This paper investigates the existence of "small" mixed strategies in extensive form games, and how such strategies can be used to create more efficient algorithms. The basic idea is that, in an extensive form game, a mixed strategy induces a small set of realization weights that completely describe its observable behavior. This fact can be used to show that for any mixed strategy ¯, there exists a realization-equivalent mixed strategy ¯ 0 whose size is at most the size of the game tree. For a player with imperfect recall, the problem of finding such a strategy ¯ 0 (given the realization weights) is NP-hard. On the other hand, if ¯ is a behavior strategy, ¯ 0 can be constructed from...

Higher levels of the data fusion process call for prediction and awareness of the development of a situation. Since the situations handled by command and control systems develop by actions performed by opposing agents, pure probabilistic or evidential techniques are not fully sufficient tools for prediction. Game-theoretic tools can give an improved appreciation of the real uncertainty in this prediction task, and also be a tool in the planning process. Based on a combination of graphical inference models and game theory, we propose a decision support tool architecture for command and control situation awareness enhancements. This paper outlines a framework for command and control decision-making in multi-agent settings. Decision-makers represent beliefs over models incorporating other decision-makers and the state of the environment. When combined, the decision-makers’ equilibrium strategies of the game can be inserted into a representation of the state of the environment to achieve a joint probability distribution for the whole situation in the form of a Bayesian network representation.