Competitive equilibria in trading

TL;DR

This paper provides a comprehensive solution for finding equilibrium trading strategies in competitive, unconstrained scenarios, revealing when trade centralization benefits firms and when it does not.

Contribution

It offers a complete analytical framework for equilibrium strategies in unconstrained trading competition, extending previous work and analyzing trade centralization effects.

Findings

Naive trade centralization often does not benefit firms.

Strategic centralization can lead to competitive advantages.

Complete solutions for equilibrium strategies in arbitrary situations.

Abstract

This is the third paper in a series concerning the game-theoretic aspects of position-building while in competition. The first paper set forth foundations and laid out the essential goal, which is to minimize implementation costs in light of how other traders are likely to trade. The majority of results in that paper center on the two traders in competition and equilibrium results are presented. The second paper, introduces computational methods based on Fourier Series which allows the introduction of a broad range of constraints into the optimal strategies derived. The current paper returns to the unconstrained case and provides a complete solution to finding equilibrium strategies in competition and handles completely arbitrary situations. As a result we present a detailed analysis of the value (or not) of trade centralization and we show that firms who naively centralize trades do not generally benefit and sometimes, in fact, lose. On the other hand, firms that strategically centralize their trades generally will be able to benefit.