Learning Discrete-Time Major-Minor Mean Field Games

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and cannot model major players that strongly influence other players, severely limiting the class of problems that can be handled. We propose a novel discrete time version of major-minor MFGs (M3FGs), along with a learning algorithm based on fictitious play and partitioning the probability simplex. Importantly, M3FGs generalize MFGs with common noise and can handle not only random exogeneous environment states but also major players. A key challenge is that the mean field is stochastic and not deterministic as in standard MFGs. Our theoretical investigation verifies both the M3FG model and its algorithmic solution, showing firstly the well-posedness of the M3FG model starting from a finite game of interest, and secondly convergence and approximation guarantees of the fictitious play algorithm. Then, we empirically verify the obtained theoretical results, ablating some of the theoretical assumptions made, and show successful equilibrium learning in three example problems. Overall, we establish a learning framework for a novel and broad class of tractable games

CMS physics technical design report : Addendum on high density QCD with heavy ions

Peer reviewe

Is there an influence of body mass on digesta mean retention time in herbivores? A comparative study on ungulates

The relation between body mass (BM) and digesta mean retention time (MRT) in herbivores was the focus of several studies in recent years. It was assumed that MRT scaled with BM0.25 based on the isometric scaling of gut capacity (BM1.0) and allometric scaling of energy intake (BM0.75). Literature studies that tested this hypothesis produced conflicting results, arriving sometimes at higher or lower exponents than the postulated 0.25. This study was conducted with 8 ruminants (n=2–6 per species) and 6 hindgut fermenting species/breeds (n=2–6, warthog n=1) with a BM range of 60–4000 kg. All animals received a ration of 100% grass hay with ad libitum access. Dry matter intake was measured and the MRT was estimated by the use of a solute and a particle (1–2 mm) marker. No significant scaling of MRTparticle with BM was observed for all herbivores (32 BM0.04, p=0.518) and hindgut fermenters (32 BM0.00, p=1.00). The scaling exponent for ruminants only showed a tendency towards significance (29 BM0.12, p=0.071). Ruminants on average had an MRTparticle 1.61-fold longer than hindgut fermenters. Whereas an exponent of 0.25 is reasonable from theoretical considerations, much lower exponents were found in this and other studies. The energetic benefit of increasing MRT is by no means continuous, since the energy released from a given food unit via digestion decreases over time. The low and non-significant scaling factors for both digestion types suggest that in ungulates, MRT is less influenced by BM (maximal allometric exponent≤0.1) than often reported

Learning Discrete-Time Major-Minor Mean Field Games

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and cannot model major players that strongly influence other players, severely limiting the class of problems that can be handled. We propose a novel discrete time version of major-minor MFGs (M3FGs), along with a learning algorithm based on fictitious play and partitioning the probability simplex. Importantly, M3FGs generalize MFGs with common noise and can handle not only random exogeneous environment states but also major players. A key challenge is that the mean field is stochastic and not deterministic as in standard MFGs. Our theoretical investigation verifies both the M3FG model and its algorithmic solution, showing firstly the well-posedness of the M3FG model starting from a finite game of interest, and secondly convergence and approximation guarantees of the fictitious play algorithm. Then, we empirically verify the obtained theoretical results, ablating some of the theoretical assumptions made, and show successful equilibrium learning in three example problems. Overall, we establish a learning framework for a novel and broad class of tractable games

Aortic Regurgitation After Transcatheter Aortic Valve Implantation With Balloon- and Self-Expandable Prostheses A Pooled Analysis From a 2-Center Experience

ObjectivesThis study sought to assess aortic regurgitation (AR) after transcatheter aortic valve implantation (TAVI) with the self-expandable Medtronic CoreValve (MCV) (Medtronic Inc., Minneapolis, Minnesota) versus balloon-expandable Edwards Sapien XT valve (ESV) (Edwards Lifesciences, Irvine, California).BackgroundAR after TAVI has been associated with poor survival, but limited data exist comparing MCV with ESV.MethodsWe pooled the prospective TAVI databases of 2 German centers. The primary endpoint was more-than-mild post-TAVI AR assessed by echocardiography. We also assessed device success and survival within 1 year. Endpoints were adjudicated according to the Valve Academic Research Consortium criteria and analyzed by unadjusted and propensity-score–adjusted models.ResultsA total of 394 patients were included, 276 treated with MCV and 118 with ESV. More-than-mild AR was significantly higher with MCV than with ESV (12.7% vs. 2.6%, p = 0.002). This difference remained significant after propensity adjustment (adjusted odds ratio [OR]: 4.59, 95% confidence interval [CI]: 1.03 to 20.44). The occurrence of any degree of AR was also higher with MCV (71.6% vs. 56.9%, p = 0.004). Device success was mainly influenced by the occurrence of AR and was consequently higher with ESV (95.8% vs. 86.6%, p = 0.007), but this was not significant after propensity adjustment (adjusted OR: 0.34, 95% CI: 0.11 to 1.03, p = 0.06). At 1 year, survival was comparable between both valve types (83.8% MCV vs. 88.2% ESV, p = 0.42), but was significantly worse in patients with more-than-mild AR (69.8% vs. 87.4%, p = 0.004) and in those with device failure (65.6% vs. 87.4%, p < 0.001).ConclusionsMore-than-mild AR after TAVI was more frequent with MCV than with ESV. This finding deserves consideration, as more-than-mild AR was associated with higher mortality at 1 year