Decentralised Random Competitive Dynamic Market Processes
We study a decentralised and uncoordinated market where heterogeneous self-interested firms and workers meet directly and randomly in pursuit of higher payoffs over time. Each firm hires several workers and each worker has preferences over firms and salaries, taking at most one job. When employees work for a firm, they generate a joint revenue which will be split among the firm and its employees. Neither firms nor workers possess complete knowledge of the market. Firms and workers make their own decisions independently and freely. We prove that a natural random decentralised dynamic market process widely observed in real life labour markets converges globally and almost surely to a competitive equilibrium, provided that an equilibrium exists. The proof relies on a mathematical theorem which establishes the existence of a finite sequence of successive coalition improvements with the status quo maintaining rule from an arbitrary market state to an equilibrium. Our findings also have meaningful policy implications.