Monte Carlo sampling processes and incentive compatible allocations in large economies

Hammond, Peter J.; Qiao, Lei; Sun, Yeneng

doi:10.1007/s00199-020-01318-5

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…In other words, Lemma 5 says that, for λ ∞ -a.e. x ∞ ∈ I ∞ : The last statement also holds a.s. in (I ∞ , Ī∞ , λ∞ ), see [21,Section 6].…”

Section: A3 Proof Of Propositionmentioning

confidence: 99%

Stochastic Graphon Games: II. The Linear-Quadratic Case

Aurell¹,

Carmona²,

Laurière³

2021

Preprint

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In this paper, we analyze linear-quadratic stochastic differential games with a continuum of players interacting through graphon aggregates, each state being subject to idiosyncratic Brownian shocks. The major technical issue is the joint measurability of the player state trajectories with respect to samples and player labels, which is required to compute for example costs involving the graphon aggregate. To resolve this issue we set the game in a Fubini extension of a product probability space. We provide conditions under which the graphon aggregates are deterministic and the linear state equation is uniquely solvable for all players in the continuum. The Pontryagin maximum principle yields equilibrium conditions for the graphon game in the form of a forward-backward stochastic differential equation, for which we establish existence and uniqueness. We then study how graphon games approximate games with finitely many players over graphs with random weights. We illustrate some of the results with a numerical example.

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“…In other words, Lemma 5 says that, for λ ∞ -a.e. x ∞ ∈ I ∞ : The last statement also holds a.s. in (I ∞ , Ī∞ , λ∞ ), see [21,Section 6].…”

Section: A3 Proof Of Propositionmentioning

confidence: 99%