Discrete Prices and Competition in a Dealer Market

Abstract

The goal of this paper is to investigate the relation between price discreteness and competition in a dealer market, and to study their impact on the welfare of different market participants (dealers and investors). We present a model featuring a finite number of dealers competing in prices for supplying liquidity to a forthcoming market order. Our main result is that there exists an interaction between price discreteness and competition. When competition is lax, dealers prefer fine price grids (small tick size), while when competition is intense they prefer coarse price grids (large tick size). When competition is lax, investors' attitude towards the tick size is ambiguous with some preference towards larger ticks. When competition among dealers is intense, investors prefer fine price grids. The rate of convergence of welfare measures towards perfect competition becomes slower, as the grid of prices becomes finer. This means that the smaller is the tick size, the larger is the number of dealers required to assure a "close to competitive" outcome. Our results regarding low levels of competition among dealers stand in contrast to the standard view and conventional wisdom, that refining the grid of prices is always beneficial for investors. Our analysis shows that when deciding on the "correct" tick size for a specific stock, market designers should take into account the level of competition among dealers for this stock.