Network games have provided a framework to study strategic decision making processes that are governed by an underlying network of interdependencies among agents. However, existing models do not account for environments in which agents simultaneously interact over multiple networks. In this paper, we propose a model of multiplex network games to capture the different modalities of interactions among strategic agents. We then explore how the properties of the constituent networks of a multiplex network can undermine or support the uniqueness of its Nash equilibria. We first show that in general, even if the constituent networks are guaranteed to have unique Nash equi- libria in isolation, the resulting multiplex need not have a unique equilibrium. We then identify certain subclasses of networks wherein guarantees on the uniqueness of Nash equilibria on the isolated networks lead to the same guarantees on the multiplex network game. We further highlight that both the largest and smallest eigenvalues of the constituent networks (reflecting their connectivity and two-sidedness, respectively) are instrumental in determining the uniqueness of the multiplex network equilibrium. Together, our findings shed light on the reasons for the fragility of the uniqueness of equilibria in multiplex networks, and potential interventions to alleviate them.
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Multi-scale games: Representing and solving games on networks with group structure
Network games provide a natural machinery to compactly represent strategic interactions among agents whose payoffs exhibit sparsity in their dependence on the actions of others. Besides encoding interaction sparsity, however, real networks often exhibit a multi-scale structure, in which agents can be grouped into communities, those communities further grouped, and so on, and where interactions among such groups may also exhibit sparsity. We present a general model of multi-scale network games that encodes such multi-level structure. We then develop several algorithmic approaches that leverage this multi-scale structure, and derive sufficient conditions for convergence of these to a Nash equilibrium. Our numerical experiments demonstrate that the proposed approaches enable orders of magnitude improvements in scalability when computing Nash equilibria in such games. For example, we can solve previously intractable instances involving up to 1 million agents in under 15 minutes.
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- Award ID(s):
- 1905558
- NSF-PAR ID:
- 10213629
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- ISSN:
- 2159-5399
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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