Resource Graph Games: A Compact Representation for Games with Structured Strategy Spaces (Extended Abstract)

There has been increasing interest in using game theory to model real-world systems, and in the computation of game-theoretic solution concepts given such a model [14]. The efficiency of game-theoretic computations depends crucially on how games are represented. For multiagent systems with large numbers of agents and actions, the standard normal form game representation is not a practical option as it would require exponential space. Fortunately, most large games of practical interest have highly-structured utility functions, and thus it is possible to represent them compactly. This helps to explain why people are able to reason about these games in the first place: we understand the payoffs in terms of simple relationships rather than in terms of enormous lookup tables. A line of research thus exists to look for compact game representations that are able to succinctly describe structured games, including work on graphical games [7], multi-agent influence diagrams [8] and action-graph games [6]. Many real-world multiagent systems have structured strategy spaces: there are an exponential number of pure strategies for each player, although the set of pure strategies for each player has a short description. This naturally arises in domains where each player needs to make a decision that has multiple components, e.g., assigning a set of resources, ranking a set of options, or finding a path in an network. To compactly represent these games, compact representations of the strategy spaces as well as compact representations of the utility functions are required. Of course, the single-player versions of these decision problems have been well-studied in the field of combinatorial optimization, with mature general modeling languages such as AMPL and solvers like CPLEX. Several classes of multi-player game models studied in recent literature have structured strategy spaces, including network congestion games [2], simultaneous auctions and other multi-item auctions [17, 13], dueling algorithms [3], integer programming games [9], and security games [10, 16]. These authors proposed compact game representations that are suitable for their specific domain and computation needs. However there is a lack of a general modeling language that captures a wide range of commonly seen strategy structure and utility struc-