Equilibrium Analysis

Wealth or Stealth? The Camouflage Effect in Insider Trading ArXiv ID: 2512.06309 “View on arXiv” Authors: Jin Ma, Weixuan Xia, Jianfeng Zhang Abstract We consider a Kyle-type model where insider trading takes place among a potentially large population of liquidity traders and is subject to legal penalties. Insiders exploit the liquidity provided by the trading masses to “camouflage” their actions and balance expected wealth with the necessary stealth to avoid detection. Under a diverse spectrum of prosecution schemes, we establish the existence of equilibria for arbitrary population sizes and a unique limiting equilibrium. A convergence analysis determines the scale of insider trading by a stealth index $γ$, revealing that the equilibrium can be closely approximated by a simple limit due to diminished price informativeness. Empirical aspects are derived from two calibration experiments using non-overlapping data sets spanning from 1980 to 2018, which underline the indispensable role of a large population in insider trading models with legal risk, along with important implications for the incidence of stealth trading and the deterrent effect of legal enforcement. ...

Optimal Execution among $N$ Traders with Transient Price Impact ArXiv ID: 2501.09638 “View on arXiv” Authors: Unknown Abstract We study $N$-player optimal execution games in an Obizhaeva–Wang model of transient price impact. When the game is regularized by an instantaneous cost on the trading rate, a unique equilibrium exists and we derive its closed form. Whereas without regularization, there is no equilibrium. We prove that existence is restored if (and only if) a very particular, time-dependent cost on block trades is added to the model. In that case, the equilibrium is particularly tractable. We show that this equilibrium is the limit of the regularized equilibria as the instantaneous cost parameter $\varepsilon$ tends to zero. Moreover, we explain the seemingly ad-hoc block cost as the limit of the equilibrium instantaneous costs. Notably, in contrast to the single-player problem, the optimal instantaneous costs do not vanish in the limit $\varepsilon\to0$. We use this tractable equilibrium to study the cost of liquidating in the presence of predators and the cost of anarchy. Our results also give a new interpretation to the erratic behaviors previously observed in discrete-time trading games with transient price impact. ...

Insider trading in discrete time Kyle games ArXiv ID: 2312.00904 “View on arXiv” Authors: Unknown Abstract We present a new discrete time version of Kyle’s (1985) classic model of insider trading, formulated as a generalised extensive form game. The model has three kinds of traders: an insider, random noise traders, and a market maker. The insider aims to exploit her informational advantage and maximise expected profits while the market maker observes the total order flow and sets prices accordingly. First, we show how the multi-period model with finitely many pure strategies can be reduced to a (static) social system in the sense of Debreu (1952) and prove the existence of a sequential Kyle equilibrium, following Kreps and Wilson (1982). This works for any probability distribution with finite support of the noise trader’s demand and the true value, and for any finite information flow of the insider. In contrast to Kyle (1985) with normal distributions, equilibria exist in general only in mixed strategies and not in pure strategies. In the single-period model we establish bounds for the insider’s strategy in equilibrium. Finally, we prove the existence of an equilibrium for the game with a continuum of actions, by considering an approximating sequence of games with finitely many actions. Because of the lack of compactness of the set of measurable price functions, standard infinite-dimensional fixed point theorems are not applicable. ...