Nash equilibrium mapping vs Hamiltonian dynamics vs Darwinian evolution for some social dilemma games in the thermodynamic limit

How cooperation evolves and manifests itself in the thermodynamic or infinite player limit of social dilemma games is a matter of intense speculation. Various analytical methods have been proposed to analyse the thermodynamic limit of social dilemmas. In a previous work [Chaos Solitons and fractals 135, 109762(2020)] involving one among us, two of those methods, Hamiltonian Dynamics(HD) and Nash equilibrium(NE) mapping were compared. The inconsistency and incorrectness of HD approach vis-a-vis NE mapping was brought to light. In this work we compare a third analytical method, i.e, Darwinian evolution(DE) with NE mapping and a numerical agent based approach. For completeness, we give results for HD approach as well. In contrast to HD which involves maximisation of payoffs of all individuals, in DE, payoff of a single player is maximised with respect to its nearest neighbour. While, HD utterly fails as compared to NE mapping, DE method gives a false positive for game magnetisation -- the net difference between the fraction of cooperators and defectors -- when payoffs obey the condition a+d=b+c, wherein a, d represent the diagonal elements and b, c the off diagonal elements in symmetric social dilemma games. When either a+d =/= b+c or, when one looks at average payoff per player, DE method fails much like the HD approach. NE mapping and numerical agent based method on the other hand agree really well for both game magnetisation as well as average payoff per player for the social dilemmas in question, i.e., Hawk-Dove game and Public goods game. This paper thus bring to light the inconsistency of the DE method vis-a-vis both NE mapping as well as a numerical agent based approach.Comment: 15 pages, 4 figures, 2 table

Search for top squarks in the four-body decay mode with single lepton final states in proton-proton collisions at s= \sqrt{s}= 13 TeV

A search for the pair production of the lightest supersymmetric partner of the top quark, the top squark ($\tilde{\mathrm{t}}_{1}$), is presented. The search targets the four-body decay of the $\tilde{\mathrm{t}}_{1}$, which is preferred when the mass difference between the top squark and the lightest supersymmetric particle is smaller than the mass of the W boson. This decay mode consists of a bottom quark, two other fermions, and the lightest neutralino ($\tilde{\chi}_{1}^{0}$), which is assumed to be the lightest supersymmetric particle. The data correspond to an integrated luminosity of 138 fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS experiment at the CERN LHC. Events are selected using the presence of a high-momentum jet, an electron or muon with low transverse momentum, and a significant missing transverse momentum. The signal is selected based on a multivariate approach that is optimized for the difference between $m(\tilde{\mathrm{t}}_{1})$ and $m(\tilde{\chi}_{1}^{0})$. The contribution from leading background processes is estimated from data. No significant excess is observed above the expectation from standard model processes. The results of this search exclude top squarks at 95% confidence level for masses up to 480 and 700 GeV for $m(\tilde{\mathrm{t}}_{1}) - m(\tilde{\chi}_{1}^{0}) =$ 10 and 80 GeV, respectively.A search for the pair production of the lightest supersymmetric partner of the top quark, the top squark (${\overset{\sim }{\textrm{t}}}_1$), is presented. The search targets the four-body decay of the ${\overset{\sim }{\textrm{t}}}_1$, which is preferred when the mass difference between the top squark and the lightest supersymmetric particle is smaller than the mass of the W boson. This decay mode consists of a bottom quark, two other fermions, and the lightest neutralino (${\overset{\sim }{\chi}}_1^0$), which is assumed to be the lightest supersymmetric particle. The data correspond to an integrated luminosity of 138 fb$^{−1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS experiment at the CERN LHC. Events are selected using the presence of a high-momentum jet, an electron or muon with low transverse momentum, and a significant missing transverse momentum. The signal is selected based on a multivariate approach that is optimized for the difference between m(${\overset{\sim }{\textrm{t}}}_1$) and m(${\overset{\sim }{\chi}}_1^0$). The contribution from leading background processes is estimated from data. No significant excess is observed above the expectation from standard model processes. The results of this search exclude top squarks at 95% confidence level for masses up to 480 and 700 GeV for m(${\overset{\sim }{\textrm{t}}}_1$) − m(${\overset{\sim }{\chi}}_1^0$) = 10 and 80 GeV, respectively.[graphic not available: see fulltext]A search for the pair production of the lightest supersymmetric partner of the top quark, the top squark ($\tilde{\mathrm{t}}_1$), is presented. The search targets the four-body decay of the $\tilde{\mathrm{t}}_1$, which is preferred when the mass difference between the top squark and the lightest supersymmetric particle is smaller than the mass of the W boson. This decay mode consists of a bottom quark, two other fermions, and the lightest neutralino ($\tilde{\chi}^0_1$), which is assumed to be the lightest supersymmetric particle. The data correspond to an integrated luminosity of 138 fb$^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS experiment at the CERN LHC. Events are selected using the presence of a high-momentum jet, an electron or muon with low transverse momentum, and a significant missing transverse momentum. The signal is selected based on a multivariate approach that is optimized for the difference between $m(\tilde{\mathrm{t}}_1)$ and $m(\tilde{\chi}^0_1)$. The contribution from leading background processes is estimated from data. No significant excess is observed above the expectation from standard model processes. The results of this search exclude top squarks at 95% confidence level for masses up to 480 and 700 GeV for $m(\tilde{\mathrm{t}}_1) - m(\tilde{\chi}^0_1$) = 10 and 80 GeV, respectively

Search for top squarks in the four-body decay mode with single lepton final states in proton-proton collisions at s= \sqrt{s}= 13 TeV

Journal of high energy physics 06(6), 060 (2023). doi:10.1007/JHEP06(2023)060 A search for the pair production of the lightest supersymmetric partner of the top quark, the top squark (${\overset{\sim }{\textrm{t}}}_1$), is presented. The search targets the four-body decay of the ${\overset{\sim }{\textrm{t}}}_1$, which is preferred when the mass difference between the top squark and the lightest supersymmetric particle is smaller than the mass of the W boson. This decay mode consists of a bottom quark, two other fermions, and the lightest neutralino (${\overset{\sim }{\chi}}_1^0$), which is assumed to be the lightest supersymmetric particle. The data correspond to an integrated luminosity of 138 fb$^{−1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS experiment at the CERN LHC. Events are selected using the presence of a high-momentum jet, an electron or muon with low transverse momentum, and a significant missing transverse momentum. The signal is selected based on a multivariate approach that is optimized for the difference between m(${\overset{\sim }{\textrm{t}}}_1$) and m(${\overset{\sim }{\chi}}_1^0$). The contribution from leading background processes is estimated from data. No significant excess is observed above the expectation from standard model processes. The results of this search exclude top squarks at 95% confidence level for masses up to 480 and 700 GeV for m(${\overset{\sim }{\textrm{t}}}_1$) − m(${\overset{\sim }{\chi}}_1^0$) = 10 and 80 GeV, respectively.[graphic not available: see fulltext] Published by SISSA, [Trieste

Search for Higgs Boson and Observation of Z Boson through their Decay into a Charm Quark-Antiquark Pair in Boosted Topologies in Proton-Proton Collisions at s\sqrt{s} =13 TeV

A search for the standard model (SM) Higgs boson (H) produced with transverse momentum greater than 450 GeV and decaying to a charm quark-antiquark ($\mathrm{c\bar{c}}$) pair is presented. The search is performed using proton-proton collision data collected at $\sqrt{s}$ = 13 TeV by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. Boosted H $\to$$\mathrm{c\bar{c}}$ decay products are reconstructed as a single large-radius jet and identified using a deep neural network charm tagging technique. The method is validated by measuring the Z $\to$$\mathrm{c\bar{c}}$ decay process, which is observed in association with jets at high $p_\mathrm{T}$ for the first time with a signal strength of 1.00 $_{-0.14}^{+0.17}$ (syst) $\pm$ 0.08 (theo) $\pm$ 0.06 (stat), defined as the ratio of the observed process rate to the standard model expectation. The observed (expected) upper limit on $\sigma$(H) $\mathcal{B}$(H $\to$$\mathrm{c\bar{c}}$) is set at 47 (39) times the SM prediction at 95% confidence level