Competition is a common theme in many statistical physics problems and their extensions to biological, social and economical applications. Here we propose a simple competition model for the job market and other competitive systems. We consider a population of N agents possessing different productivities. At each time step, they join one of the two companies according to the average productivity of the companies, assuming that higher average productivity implies higher returns....[ Read more ]

Competition is a common theme in many statistical physics problems and their extensions to biological, social and economical applications. Here we propose a simple competition model for the job market and other competitive systems. We consider a population of N agents possessing different productivities. At each time step, they join one of the two companies according to the average productivity of the companies, assuming that higher average productivity implies higher returns.

In contrast to other agent-based thermal models, the fluctuation of the company size increases with decreasing temperature. The phenomenon of liquidation of a company is analyzed in the thesis, which refers to the scenario that the size of one of the two companies shrinks to zero. Two regimes of the decay rate are found. (i) At the low temperature regime, the decay rate decreases as a power law with the population size and its probability distribution can be solved by using the method of transfer matrices (ii) At the high temperature regime, the decay rate decreases exponentially with the population size and its probability distribution can be solved by using the quantum harmonic oscillator formulation. It is shown that the two regimes can be explained by the competition between random walk and diffusion in the phase space.

We then study the lifetime distribution of the winning epochs. It is found that the lifetime distribution is directly related to the diagonal step size in the phase space and has a power law relation with the system time. Finally, we investigate whether the general behaviour of the system will change with increasing number of companies in the market.