Stability of mixed Nash equilibria in symmetric quantum games

In bi-matrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permit pure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of two-qubit initial quantum states when a switch-over to a quantum version of the game also changes the evolutionary stability of a mixed symmetric Nash equilibrium.Comment: 8 pages, no figure, to appear in Communications in Theoretical Physic

Quantum Cooperative Games

We study two forms of a symmetric cooperative game played by three players, one classical and other quantum. In its classical form making a coalition gives advantage to players and they are motivated to do so. However in its quantum form the advantage is lost and players are left with no motivation to make a coalition.Comment: Revised in the light of referee's comments. Submitted to Physics Letters A. LaTex, 9 pages, 1 figure. Parts of this paper are rewritte

Selecting the Optimal Unrelated Hematopoietic Stem Cell Transplant Donor for Relapse Prevention in Acute Myeloid Leukemia

Introduction/Background Hematopoietic cell transplantation (HCT) provides a cure for patients with acute myeloid leukemia. Natural killer cells (NK) play an important role in graft versus leukemia (GVL) effect after HCT, through killer immunoglobulin-like receptor (KIR) interaction with HLA ligands. This study is undertaken to validate our previously published mathematical model accounting for the KIR-KIRL interactions in a post HCT setting. Methods Retrospective data were obtained from the Center for International Blood and Marrow Transplant Registry for 2317 donor recipient pairs (DRP) who underwent 7/8 or 8/8 HLA allelic matched unrelated donor (URD) HCT for AML. KIR-HLA interaction scores were calculated by summing interaction values as previously described (Krieger et. Al BBMT 2019). Results Relapse risk was significantly reduced with donor-recipient pairs (DRP) with the higher inhibitory KIR-KIRL interaction and missing KIRL scores, Cox prop hazard, HR=0.86 (P=0.01) & HR=0.84 (P=0.02) respectively. The inhibitory KIR-KIRL interaction score components were then summed to give an IM-KIR score; IM KIR score =5 was also associated with a lower relapse risk, HR 0.8 (P=0.003). Subset analysis of 8/8 HLA matched patients showed further relapse reduction HR 0.75 (P=0.001); those patients with IM-KIR=5 donors who received ATG for in vivo T cell depletion (N=730) showed a 39% relapse reduction (HR 0.61, P=0.001) with a trend toward improved RFS, HR 0.84 (p=0.11). The use of ATG was shown to modify the effect of IM KIR score in interaction analysis (p=0.049), suggesting higher NK cell magnitude of KIR-KIRL interaction compensates for the general increase of relapse who receive in vivo T cell depletion. Conclusion This large international study confirms that unrelated DRPs with high iKIR and mKIR scores, as well as a combined IM-KIR scores confer significant relapse protection after MUD HCT, indicating that donors with a higher iKIR content may be considered optimal for URD HCT recipients with AML