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Navigating in a space of game views

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Abstract

Game-theoretic modeling entails selecting the particular elements of a complex strategic situation deemed most salient for strategic analysis. Recognizing that any game model is one of many possible views of the situation, we term this a game view, and propose that sophisticated game reasoning would naturally consider multiple views. We introduce a conceptual framework, game view navigation, for game-theoretic reasoning through a process of constructing and analyzing a series of game views. The approach is illustrated using a variety of existing methods, which can be cast in terms of navigation patterns within this framework. By formally defining these as well as recently introduced ideas as navigating in a space of game views, we recognize common themes and opportunities for generalization. Game view navigation thus provides a unifying perspective that sheds light on connections between disparate reasoning methods, and defines a design space for creation of new techniques. We further apply the framework by defining and exploring new techniques based on modulating player aggregation in equilibrium search.

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Notes

  1. Even when a PSNE exists, IBR is not guaranteed to find it. An exception is the class of potential games for which IBR is a complete algorithm [22].

  2. This claim assumes perfect BR computation. If guaranteed only to a degree of approximation, this would translate to a corresponding approximate equilibrium result.

  3. Results are sensitive to the choice of \(\sigma ^{*k}\) in cases where there are multiple equilibria in \(\text {NE}(\Gamma ^k)\). See discussion of support enumeration below.

  4. Fearnley et al. [27] study the question from a complexity-theoretic perspective, providing insights on the number of payoff queries required to guarantee identification of approximate solutions, in a variety of game contexts.

  5. The definitions can be straightforwardly generalized to role symmetry. We further assume for simplicity that \(p-1\) divides \(n-1\).

  6. This plot is too cluttered to tease apart all the methods, but provides a helpful overview. We zoom in on particular methods in subsequent figures.

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Funding

This work was supported in part by the US Army Research Office under MURI Grant # W911NF-18-1-0208.

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  1. University of Michigan, Ann Arbor, USA

    Michael P. Wellman & Katherine Mayo

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  1. Michael P. Wellman
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Contributions

MPW conceived and developed the framework and wrote the manuscript. MPW and KM designed the new methods for modulating player aggregation. KM implemented these methods and performed the experiments. Both authors reviewed the manuscript.

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Correspondence to Michael P. Wellman.

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Wellman, M.P., Mayo, K. Navigating in a space of game views. Auton Agent Multi-Agent Syst 38, 31 (2024). https://doi.org/10.1007/s10458-024-09660-x

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