Market fragmentation and market consolidation: Multiple steady states in systems of adaptive traders choosing where to trade

Abstract

Technological progress is leading to proliferation and diversification of trading venues, thus increasing the relevance of the long-standing question of market fragmentation versus consolidation. To address this issue quantitatively, we analyse systems of adaptive traders that choose where to trade based on their previous experience. We demonstrate that only based on aggregate parameters about trading venues, such as the demand to supply ratio, we can assess whether a population of traders will prefer fragmentation or specialization towards a single venue. We investigate what conditions lead to market fragmentation for populations with a long memory and analyse the stability and other properties of both fragmented and consolidated steady states. Finally we investigate the dynamics of populations with finite memory; when this memory is long the true long-time steady states are consolidated but fragmented states are strongly metastable, dominating the behaviour out to long times.

Fragmentation in trader preferences among multiple markets: market coexistence versus single market dominance

“…We now give a brief description of the attractions distributions in each of the panels and explain the difference between (i) strong fragmentation, which persists in the large memory limit, and (ii) weak fragmentation, which disappears in the same limit; similar results for two market systems are discussed in [6,8]. In figure 1a, one sees that the distribution of attractions has three peaks, all of which have a size of order O(1) and correspond to subpopulations of traders who choose to trade mainly at a single market.…”

“…Here we summarize the basic assumptions and properties of the model introduced in [5,6,8] and extend it to include multiple markets.…”

“…To tackle this question of market coexistence versus single market dominance, we build on previous work [5][6][7][8] where we introduced and analysed a system consisting of double auction markets and a large number of traders choosing between them. What we showed in this setting is that for a range of parameters describing the markets and agents, the agents split into groups with a strong loyalty towards one of the markets, often giving an overall market coexistence with an equal share of traders at both markets.…”

“…What we showed in this setting is that for a range of parameters describing the markets and agents, the agents split into groups with a strong loyalty towards one of the markets, often giving an overall market coexistence with an equal share of traders at both markets. When the agents have a long memory to previous trading outcomes, other steady states with single market dominance also exist and are in fact stable, whereas the system state with markets splitting trades roughly equally between them is only metastable [6,8]. While these initial studies focused on settings with two markets for simplicity, traders do in general have a choice between multiple markets (e.g.…”

“…Multi-agent-based simulations have mostly been used in this context and allow additional layers of complexity such as adaptive markets and heterogeneous agents to be added. We pursue instead a modelling approach that strips out as much detail as possible [6][7][8] to allow for detailed theoretical analysis, which can often reveal features that would be missed when relying exclusively on numerical simulations. In this spirit, while the market mechanisms implemented in the JCAT library are continuous double auctions, we use in our model a mechanism more similar to a clearing house where the clearing process takes place at discrete time steps.…”