PPAD
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Related Articles from SNS
STON'R Converges to First-Order Nash~Equilibria of Multiplayer Games
arXiv:2606.09565v1 Announce Type: new Abstract: Nonconcave games present a unique challenge, as neither pure Nash equilibria nor local Nash equilibria (LNE) are guaranteed to exist, even in zero-sum settings. Additionally, computing approximate LNE in smooth multiplayer games over bounded regions is PPAD-hard. These challenges, coupled with the inherent complexity, have driven recent research toward broader equilibrium concepts, such as min-max critical points, and first-order Nash...
Randomized separations in black-box TFNP
arXiv:2606.04697v1 Announce Type: new Abstract: We study the relationship between deterministic and randomized black-box reducibility between problems in TFNP. Our main contribution is a general technique that establishes equivalence between these reducibility types from specific TFNP problems to any TFNP problem. In particular, we show that this equivalence holds for reductions from complete problems in PPP, PPAD, PPA, and $t$-PPP.
N-Player Binary Games with Unidirectional Dependencies: Cycle Robustness and Induced Indifference
new Abstract: The present study provides a closed-form characterisation of Nash equilibria in N-player binary games with unidirectional dependencies. While general network games are PPAD-complete, prior work has established that trees or paths admit polynomial-time solutions via dynamic programming. We provide a deterministic characterisation for the subclass of directed cycle graphical games, demonstrating that non-zero boundary incentives linearize the topology into a feed-forward propagation.
The Stability of Online Algorithms in Performative Prediction
Announce Type: replace Abstract: The use of algorithmic predictions in decision-making leads to a feedback loop where the models we deploy actively influence the data distributions we see, and later use to retrain on. This dynamic was formalized by Perdomo et al. 2020 in their work on performative prediction. Our main result is an unconditional reduction showing that any no-regret algorithm deployed in performative settings converges to a (mixed) performatively stable equilibrium: a solution...