Sequential Decomposition of Discrete-Time Mean-Field Games

Deepanshu Vasal ()
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Deepanshu Vasal: Northwestern University

Dynamic Games and Applications, 2024, vol. 14, issue 3, No 8, 697-715

Abstract: Abstract We consider both finite- and infinite-horizon discounted mean-field games where there is a large population of homogeneous players sequentially making strategic decisions, and each player is affected by other players through an aggregate population state. Each player has a private type that only she observes and all players commonly observe a mean-field population state which represents the empirical distribution of other players’ types. Mean-field equilibrium (MFE) in such games is defined as solution of coupled Bellman dynamic programming backward equation and Fokker–Planck forward equation, where a player’s strategy in an MFE depends on both, her private type and current population state. In this paper, we present a novel backward recursive algorithm to compute all MFEs of the game. Each step in this algorithm consists of solving a fixed-point equation. We provide sufficient conditions that guarantee the existence of this fixed-point equation for each time t. Using this algorithm, we study versions of security problem in cyber-physical system where infected nodes put negative externality on the system, and each node makes a decision to get vaccinated. We numerically compute MFE of the game.

Keywords: Game theory; Mean-field games; Sequential decomposition; Backward recursion (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13235-023-00507-w

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