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Conventional game theory assumes that players are perfectly rational. In a realistic situation, however, players are rarely perfectly rational. This bounded rationality is one of the main reasons why the predictions of Nash equilibrium in normative game theory often diverge from human behavior in real experiments. Motivated by the Boltzmann weight formalism, here we present a theoretical framework to predict the non-Nash equilibrium probabilities of possible outcomes in strategic games by focusing on the differences in expected payoffs of players rather than traditional utility metrics. In this model, bounded rationality is parameterized by assigning a temperature to each player, reflecting their level of rationality by interpolating between two decision-making regimes, i.e., utility maximization and equiprobable choices. Our framework predicts all possible joint strategies and is able to determine the relative probabilities for multiple pure or mixed strategy equilibria. To validate model predictions, by analyzing experimental data we demonstrated that our model can successfully explain non-Nash equilibrium strategic behavior in experimental games. Our approach reinterprets the concept of temperature in game theory, leveraging the development of theoretical frameworks to bridge the gap between the predictions of normative game theory and the results of behavioral experiments.

Choice overload occurs when individuals feel overwhelmed by an excessive number of options. Experimental evidence suggests that a larger selection can complicate the decision-making process. Consequently, choice satisfaction may diminish when the costs of making a choice outweigh its benefits, indicating that satisfaction follows an inverted U-shaped relationship with the size of the choice set. However, the theoretical underpinnings of this phenomenon remain underexplored. Here, we present a theoretical framework based on relative entropy and effective information to elucidate the inverted U-shaped relationship between satisfaction and choice set size. We begin by positing that individuals assign a probability distribution to a choice set based on their preferences, characterized by an observed Shannon entropy. We then define a maximum entropy that corresponds to a worst-case scenario where individuals are indifferent among options, leading to equal probabilities for all alternatives. We hypothesized that satisfaction is related to the probability of identifying an ideal choice within the set. By comparing observed entropy to maximum entropy, we derive the effective information of choice probabilities, demonstrating that this metric reflects satisfaction with the options available. For smaller choice sets, individuals can more easily identify their best option, resulting in a sharper probability distribution around the preferred choice and, consequently, minimum entropy, which signifies maximum information and satisfaction. Conversely, in larger choice sets, individuals struggle to compare and evaluate all alternatives, leading to missed opportunities and increased entropy. This smooth probability distribution ultimately reduces choice satisfaction, thereby producing the observed inverted U-shaped trend.

In this paper, we present the black hole solution of the Einstein-Yang-Mills model incorporating a non-minimal coupling between the Ricci tensor and the Yang-Mills field strength tensor using a perturbative method. We then explore the thermodynamic phase transitions of the black hole within an extended phase space, examining both canonical and grand canonical ensembles. Our findings reveal that altering the sign of the perturbation coefficient $\lambda$ leads to a significant shift in the thermodynamic behavior of the black hole, transitioning between Van der Waals-like fluid phase transitions and Hawking-Page-like transitions., Comment: 27 pages, 29 figures, three references were added to the revised version

In this paper, we examine Einstein-Hilbert gravity featuring a cosmological constant and a non-abelian nonlinear electromagnetic field that is minimally coupled to gravity. We first present the black brane solution for this model and subsequently calculate the color non-abelian DC conductivity for this solution using AdS/CFT duality. Our results retrieve the Yang-Mills model in the limit as $q_1$ approaches zero., Comment: 12 Pages, no figure, accepted for publication in CJP

In this paper, we explore a modified black brane within AdS spacetime, characterized by the Lagrangian density $\frac{1}{q} \text{arcsin}(qR)-2\Lambda$. Due to the absence of an analytic solution, we approach the Einstein equations using a perturbative method, extending our analysis to the second order in $q$. Subsequently, we compute the ratio of shear viscosity to entropy density. Our results suggest that the KSS Bound is not saturated in this model., Comment: 10 Pages, no figure, accepted for publication in Int. J. Mod. Phys. A (IJMPA)

In this paper, we present an exponential modification for the action of an AdS black hole in the absence of a matter field. An approximated black hole solution is obtained up to the third order of perturbation coefficient. A thermodynamic investigation in canonical ensemble shows that the behavior of a Van der Waals fluid is not seen in this model. Nevertheless, the study of thermodynamic potentials and other related quantities suggests that the thermodynamic phase transitions of the first and second types can occur in this model. The forms of the phase transitions are more similar to the Hawking-Page phase transitions., Comment: 18 Pages, 9 figures, title changed, ref added

In this paper, AdS black brane solution of Einstein-Hilbert gravity with non-abelian exponential guage theory of Yang-Mills type is introduced. DC conductivity and the ratio of shear viscosity to entropy density as two important transport coefficients are calculated by using of Kubo formula in the context of AdS/CFT duality. Our results recover the Yang-Mills model in $q\to \infty$ limit., Comment: 17 pages, 6 figures, typo corrected, references added, improved version, to appear in EPJP

In this paper, we present an exact spherically symmetric and Yang-Mills charged AdS black hole solution in the context of $4D$ Einstein-Gauss-Bonnet (EGB) gravity in the presence of a cloud of strings. The regularity of the solution is checked. Thermodynamics of this solution is studied. The critical behavior, the types of phase transitions in canonical ensemble, the Joule-Thomson expansion, the Clapeyron equation and the critical exponents shall be investigated., Comment: 23 pages, 14 figures

In this paper, a non-abelian $arcsin$-Yang-Mills AdS black brane solution is introduced. Then, the color non-abelian direct current (DC) conductivity and shear viscosity to entropy density ratio of this model is calculated using fluid-gravity duality. Our results show that the Kovtun, Son and Starinets (KSS) bound is saturated and is exactly equal to $\frac{1}{4 \pi}$ but the color conductivity bound is violated for this model. Also, our outcomes recover the Yang-Mills AdS black brane when the coupling of Yang-Mills and gravity fields approaches zero., Comment: 9 Pages, no figure, version accepted for publication in INJP

In this paper, we shall study the phase transition of non-minimal coupling of Einstein-Hilbert gravity and electric field of Yang-Mills type in AdS space-time. We couple the Ricci scalar to the Yang-Mills invariant to obtain a modified theory of gravity. A black brane solution is introduced up to the first order of the term $RF^{(a)}_{\mu \alpha }F^{(a)\mu \alpha} $ in this model. Then, the phase transition of this solution will be investigated in canonical ensemble. Our investigation shows that only the second order phase transition behavior is seen in this model. Also, due to the coupling of the Yang-Mills field and Ricci scalar, there are differences with the phase transitions of the usual minimal models. We shall show that in the absence of non-minimal coupling there is no any phase transition., Comment: 17 Pages, 11 figures, to appear in IJMPA

In this paper, we consider Einstein-Hilbert gravity in the presence of cosmological constant with cylindrical symmetry to introduce the black hole solution of this model. Here, we solve the Einstein's vacuum field equation, and then we calculate the appropriate metric for this problem., Comment: 9 pages, 1 figure, to appear in INJP

In this paper, we consider Einstein-Hilbert gravity in the presence of cosmological constant and an electric field of Yang-Mills type, which is minimally coupled to gravity. We couple the Ricci scalar to the Yang-Mills invariant to obtain a modified theory of gravity. The black brane solution of this model is introduced up to the first order of the $RF^{(a)}_{\mu \alpha }F^{(a)\mu \alpha} $ term. Then, the color non-abelian direct current (DC) conductivity and the ratio of shear viscosity to entropy density are calculated for this solution. Our results recover the Yang-Mills Schwarzschild AdS black brane in the limit of $q_2 \to 0$., Comment: 13 pages, no figure, typo corrected, references added, minor modifications, to appear in MPLA

In this paper, we introduce the black hole solution in Rastall theory of gravity in the presence of quintessence and the cloud of strings. Our investigations show that this model meets only second-order phase transition in four dimensions. While both the first and second order phase transitions are seen in five dimensions. Therefore, according to the AdS/CFT duality, the confinement-deconfinement phase transition only occurs in five dimensions for this model., Comment: 15 pages, 11 figures, , remove typos, references added, minor modifications, to appear in IJMPA

In this paper, we study the holographic dual to an asymptotically anti-de Sitter black brane in an Einstein-Yang-Mills model with a non-minimal coupling between the Riemann and Yang-Mills fields. First, we construct a planar black hole solution of this model up to the first order of the non-minimal coupling of the Yang-Mills field with the Riemann-Christoffel tensor, denoted as $q_2$. Then, we calculate the color non-abelian direct current (DC) conductivity and the ratio of shear viscosity to entropy density for this solution. Our result for the shear viscosity $\eta$ to entropy density $s$ ratio saturates the Kovtun, Son, and Starinets (KSS) bound, which is proportional to $\frac{1}{4 \pi}$. However, our result for the conductivity is new up to the first order of $q_2$., Comment: 11 Pages, no figure, typo corrected, references added, minor modifications, accepted for publication in CQG

In this paper we introduce the black brane solutions in AdS space in 4-dimensional (4D) Einstein-Gauss-Bonnet-Yang-Mills theory in the presence of string cloud and quintessence. Shear viscosity to entropy density ratio is computed via fluid-gravity duality, as a transport coefficient for this model., Comment: 11 Pages, no figure, typo corrected, references added, minor modifications, accepted for publication in MPLA

In this paper, we consider Einstein-Hilbert gravity in the presence of cosmological constant and non-abelian nonlinear electromagnetic field of Born-Infeld type which is minimally coupled to gravity. First, black brane solution of this model is introduced and then color non-abelian DC conductivity is calculated for this solution by using AdS/CFT duality., Comment: 9 Pages, no figure, references added, minor modifications, accepted by the Indian Journal of Physics

In this paper, the Einstein AdS black brane solution in the presence of quintessence in context of massive gravity is introduced. The ratio of shear viscosity to entropy density for this solution violates the KSS bound by applying the Dirichlet boundary and regularity on the horizon conditions. Our result shows that this value is independent of quintessence in arbitrary dimensions., Comment: 11 Pages, no figure

In this paper, the Einstein AdS black brane solution in the presence of a string cloud in the context of d-dimensional massive gravity is introduced. The ratio of shear viscosity to entropy density for this solution violates the KSS bound by applying the Dirichlet boundary and regularity on the horizon conditions. Our result shows that this value is independent of string cloud in any arbitrary dimensions., Comment: v3: 13 pages, title changed, typo corrected, no figure, references added, minor modifications, to appear in MPLA

Following previous study about AdS-Schwarzschild black holes minimally coupled to a cloud of strings in the context of massive gravity {Ghanaatian:2019} and inspired by strong connection between Gauss-Bonnet Gravity and heterotic string theory, in this paper, we first take into account the Gauss-Bonnet term and we study thermodynamics and critical behavior of these black holes in the extended phase space. The effects of Gauss-Bonnet, massive, and string cloud parameters on the criticality of these black holes has been investigated. It can be seen that the Gauss-Bonnet and massive parameters have opposite effects on the criticality and phase transition of the solutions. We also observe that the increase in the value of the string cloud parameter above a critical value, eliminates the van der Waals like behavior of these solutions. Also, the Joule-Thomson effect is not observed. Then we examine thermal stability of these black holes in canonical ensemble by calculating the heat capacity. In addition, we explore critical behavior in extended phase space by employing heat capacity and consequently, we observe that the results are in agreement with the previous results from the usual method in section 3., Comment: 24 pages, 60 figures

In this paper we study AdS-Schwarzschild black holes in four and five dimensions in dRGT minimally coupled to a cloud of strings and investigate the effects of this string cloud on the thermodynamics of the black holes. It is observed that the entropy of the string cloud and massive terms does not affect the black hole entropy. The observations about four dimensions indicate that the massive term in the presence of external string cloud can not exhibit Van der Waals like behavior for AdS-Schwarzschild black holes and therefore there is only the Hawking-Page phase transition. In contrast, in five dimensions, the graviton mass modifies this behavior through the third massive term, so that a critical behavior and second order phase transition is deduced. Also, the Joule-Thomson effect is not observed. The black hole stability conditions are also studied in four and five dimensions and a critical value for the string cloud parameter is presented. In five dimensions a degeneracy between states for extremal black holes is investigated. After studying black holes as thermodynamic systems, we consider such systems as heat engines, and finally the efficiency of them is calculated., Comment: 23 pages, 32 figures

The Einstein AdS black brane with a cloud of strings background in context of massive gravity is introduced. There is a momentum dissipation on the boundary because of graviton mass on the bulk. The ratio of shear viscosity to entropy density is calculated for this solution. This value violates the KSS bound if we apply the Dirichlet boundary and regularity on the horizon conditions. Our result shows that this value is independent of the cloud of strings., Comment: 12 pages, no figure, v2: minor changes and references added

In this paper we calculate the ratio of transverse shear viscosity to entropy density for the general anisotropic black brane in Horava-Lifshitz gravity. There is a well-known conjecture that states this ratio should be larger than $\frac{1}{4\pi}$. The ratio of shear viscosity to entropy density is proportional to the inverse square coupling of quantum thermal field theory,$\frac{\eta }{s} \sim \frac{1}{\lambda^2 }$. Especially in QFT with gravity dual the stronger coupling means the shear viscosity per entropy density gets closer to the lower bound of $\frac{1}{4\pi}$. The KSS bound preserves in the anisotropic scaling model., Comment: 7 pages,to appear in INJP

We introduce the Einstein-Yang-Mills AdS black brane solution in context of massive gravity. The ratio of shear viscosity to entropy density is calculated for this solution. This value violates the KSS bound if we apply the Dirichlet boundary and regularity on the horizon conditions., Comment: 10 pages, accepted by the European Physical Journal C

In this paper, we introduced the black brane solution in Rastall theory and in the context of massive gravity. The ratio of shear viscosity to entropy density is calculated for this solution. Our result shows that the KSS bound violates for this theory., Comment: Accepted in Modern Physics Letters A

We study the holographic dual of a massive gravity with Gauss-Bonnet and cubic quasi-topological higher curvature terms. Firstly, we find the energy-momentum two-point function of the 4-dimensional boundary theory where the massive term breaks the conformal symmetry as expected. An $a$-theorem is introduced based on the null energy condition. Then we focus on a black brane solution in this background and derive the ratio of shear viscosity to entropy density for the dual theory. It is worth mentioning that the concept of viscosity as a transport coefficient is obscure in a nontranslational invariant theory as in our case. So although we use the Green-Kubo's formula to derive it, we rather call it the rate of entropy production per the Planckian time due to a strain. Results smoothly cover the massless limit., Comment: v2: 20 pages, typo corrected, references added; v3: section 2.2 revised; v4: section 2.2 modified, viscosity formula revised, 2 figs added, references added; v5: 23 pages, a sign mistake in eq. (74) fixed (results modified), eq. (34) modified, one fig added, refs added, to appear in EPJC

A black brane solution to a Gauss-Bonnet massive gravity is introduced. In the context of AdS/CFT correspondence, the viscosity to entropy ratio is found by the Green-Kubo formula. The result indicates violation of the well-known KSS bound as expected in a higher derivative theory. Setting mass zero gives back the known viscosity to entropy ratio dependent on the Gauss-Bonnet coupling, while without Gauss-Bonnet term, a nonzero mass parameter doesn't contribute to the ratio which saturates the bound of $1/4\pi$., Comment: 11 Pages, no figure; v2: refs added, minor modifications