Price vs. quantity in oligopoly games

Price-setting and quantity-setting oligopoly games lead to extremely dierent outcomes in the market. One natural way to address this problem is to formulate a model in which some rms use price while the remaining rms use quantity as their decision variable. We introduce a mixed oligopoly game of this type and determine its equilibria. In addition, we consider an extension of this mixed oligopoly game through which the choice of the decision variables can be endogenized. We prove the emergence of the Cournot game

An efficient and flexible approach for computing rovibrational polaritons from first principles

A theoretical framework is presented for the computation of rovibrational polaritonic states of a molecule in a lossless infrared (IR) microcavity. In the proposed approach the quantum treatment of the rotational and vibrational motion of the molecule can be formulated using arbitrary approximations. The cavity-induced changes in electronic structure are treated perturbatively, which allows using the existing polished tools of standard quantum chemistry for determining electronic molecular properties. As a case study, the rovibrational polaritons and related thermodynamic properties of H$_2$O in an IR microcavity are computed for varying cavity parameters and applying various approximations to describe the molecular degrees of freedom. The self-dipole interaction is found to be significant for nearly all light-matter coupling strengths investigated, and the molecular polarizability proved to be important for the correct qualitative behavior of the energy level shifts induced by the cavity. On the other hand, the magnitude of polarization remains small, justifying the perturbative approach for the cavity-induced changes in electronic structure. Comparing results obtained using a high-accuracy variational molecular model with those obtained utilizing the rigid rotor and harmonic oscillator approximations revealed that as long as the rovibrational model is appropriate for describing the field-free molecule, the computed rovibropolaritonic properties can be expected to be accurate as well. Strong light-matter coupling between the radiation mode of an IR cavity and the rovibrational states of H$_2$O lead to minor changes in the thermodynamic properties of the system, and these changes seem to be dominated by non-resonant interactions between the quantum light and matter

Three-player polaritons: nonadiabatic fingerprints in an entangled atom-molecule-photon system

A quantum system composed of a molecule and an atomic ensemble, confined in a microscopic cavity, is investigated theoretically. The indirect coupling between atoms and the molecule, realized by their interaction with the cavity radiation mode, leads to a coherent mixing of atomic and molecular states, and at strong enough cavity field strengths hybrid atom-molecule-photon polaritons are formed. It is shown for the Na$_2$ molecule that by changing the cavity wavelength and the atomic transition frequency, the potential energy landscape of the polaritonic states and the corresponding spectrum could be changed significantly. Moreover, an unforeseen intensity borrowing effect, which can be seen as a strong nonadiabatic fingerprint, is identified in the atomic transition peak, originating from the contamination of the atomic excited state with excited molecular rovibronic states

Pauli principle in polaritonic chemistry

Consequences of enforcing permutational symmetry, as required by the Pauli principle (spin-statistical theorem), on the state space of molecular ensembles interacting with the quantized radiation mode of a cavity are discussed. The Pauli-allowed collective states are obtained by means of group theory, i.e., by projecting the state space onto the appropriate irreducible representations of the permutation group of the indistinguishable molecules. It is shown that with increasing number of molecules the ratio of Pauli-allowed collective states decreases very rapidly. Bosonic states are more abundant than fermionic states, and the brightness of Pauli-allowed collective states (contribution from photon excited states) increases(decreases) with increasing fine structure in the energy levels of the material ground(excited) state manifold. Numerical results are shown for the realistic example of rovibrating H$_2$O molecules interacting with an infrared (IR) cavity mode

Finite Neighborhood Binary Games: a Structural Study

The purpose of this study is to present a systematic analysis of the long-term behavior of the agents of an artificial society under varying payoff functions in finite neighborhood binary games. By assuming the linearity of the payoffs of both cooperating and defecting agents, the type of the game is determined by four fundamental parameters. By fixing the values of three of them and systematically varying the fourth one we can observe a transition from Prisoner\'s Dilemma to Leader Game through Chicken and Benevolent Chicken Games. By using agent-based simulation we are able to observe the long-term behavior of the artificial society with different and gradually changing payoff structure. The difference between different games is explored and the effect of the transition from one game to the other on the society is investigated. The results depend on the personality types of the agents. In this study greedy and Pavlovian agents are considered. In the first case, we observe the most significant change in trajectory structure between Prisoner\'s Dilemma and Chicken Games showing significant difference in the behavioral patterns of the agents. Almost no changes can be observed between Benevolent Chicken and Leader Games, and only small change between Chicken and Benevolent Chicken. The trajectories change from always converging to regularly oscillating patterns with systematically altering amplitude and central values. The results are very similar whether the agents consider themselves as members of their neighborhoods or not. With Pavlovian agents no significant difference can be observed between the four games, the trajectories always converge and the limits smoothly and monotonically depend on the value of the varying parameter.Agent-Based Simulation, N-Person Games, Structure Analysis, Equilibrium

Robust field-dressed spectra of diatomics in an optical lattice

The absorption spectra of the cold Na2 molecule dressed by a linearly polarized standing laser wave is investigated. In the studied scenario the rotational motion of the molecules is frozen while the vibrational and translational degrees of freedom are accounted for as dynamical variables. In such a situation a light-induced conical intersection (LICI) can be formed. To measure the spectra a weak field is used whose propagation direction is perpendicular to the direction of the dressing field but has identical polarization direction. Although LICIs are present in our model, the simulations demonstrate a very robust absorption spectrum, which is insensitive to the intensity and the wavelength of the dressing field and which does not reflect clear signatures of light-induced nonadiabatic phenomena related to the strong mixing between the electronic, vibration and translational motions. However, by widening artificially the very narrow translational energy level gaps, the fingerprint of the LICI appears to some extent in the spectrum