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Empirical game-theoretic analysis (EGTA) is a general framework for reasoning about complex games using agent-based simulation. Data from simulating select strategy profiles is employed to estimate a cogent and tractable game model approximating the underlying game. To date, EGTA methodology has focused on game models in normal form; though the simulations play out in sequential observations and decisions over time, the game model abstracts away this temporal structure. Richer models of extensive-form games (EFGs) provide a means to capture temporal patterns in action and information, using tree representations. We propose tree-exploiting EGTA (TE-EGTA), an approach to incorporate EFG models into EGTA. TE-EGTA constructs game models that express observations and temporal organization of activity, albeit at a coarser grain than the underlying agent-based simulation model. The idea is to exploit key structure while maintaining tractability. We establish theoretically and experimentally that exploiting even a little temporal structure can vastly reduce estimation error in strategy-profile payoffs compared to the normal-form model. Further, we explore the implications of EFG models for iterative approaches to EGTA, where strategy spaces are extended incrementally. Our experiments on several game instances demonstrate that TE-EGTA can also improve performance in the iterative setting, as measured by the quality of equilibrium approximation as the strategy spaces are expanded. 

An index-based exchange traded fund (ETF) with underlying se- curities that trade on the same market creates potential opportu- nities for arbitrage between price deviations in the ETF and the corresponding index. We examine whether ETF arbitrage trans- mits small volatility events, termed mini flash crashes, from one of its underlying symbols to another. We address this question in an agent-based, simulated market where agents can trade an ETF and its two underlying symbols. We explore multiple market configurations with active and inactive ETF arbitrageurs. Through empirical game-theoretic analysis, we find that when arbitrageurs actively trade, background traders’ surplus increases because of the increased liquidity. Arbitrage helps the ETF more accurately track the index. We also observe that when one symbol experiences a mini flash crash, arbitrage transmits a price change in the opposite direction to the other symbol. The size of the mini flash crash de- pends more on the market configuration than the arbitrageurs, but the recovery of the mini flash crash is faster when arbitrageurs are present. 

We present an agent-based model of manipulating prices in financial markets through spoofing: submitting spurious orders to mislead traders who learn from the order book. Our model captures a complex market environment for a single security, whose common value is given by a dynamic fundamental time series. Agents trade through a limit-order book, based on their private values and noisy observations of the fundamental. We consider background agents following two types of trading strategies: the non-spoofable zero intelligence (ZI) that ignores the order book and the manipulable heuristic belief learning (HBL) that exploits the order book to predict price outcomes. We conduct empirical game-theoretic analysis upon simulated agent payoffs across parametrically different environments and measure the effect of spoofing on market performance in approximate strategic equilibria. We demonstrate that HBL traders can benefit price discovery and social welfare, but their existence in equilibrium renders a market vulnerable to manipulation: simple spoofing strategies can effectively mislead traders, distort prices and reduce total surplus. Based on this model, we propose to mitigate spoofing from two aspects: (1) mechanism design to disincentivize manipulation; and (2) trading strategy variations to improve the robustness of learning from market information. We evaluate the proposed approaches, taking into account potential strategic responses of agents, and characterize the conditions under which these approaches may deter manipulation and benefit market welfare. Our model provides a way to quantify the effect of spoofing on trading behavior and market efficiency, and thus it can help to evaluate the effectiveness of various market designs and trading strategies in mitigating an important form of market manipulation. 

An index-based exchange traded fund (ETF) with underlying securities that trade on the same market creates potential opportunities for arbitrage between price deviations in the ETF and the corresponding index. We examine whether ETF arbitrage transmits small volatility events, termed mini flash crashes, from one of its underlying symbols to another. We address this question in an agent-based, simulated market where agents can trade an ETF and its two underlying symbols. We explore multiple market configurations with active and inactive ETF arbitrageurs. Through empirical game-theoretic analysis, we find that when arbitrageurs actively trade, background traders’ surplus increases because of the increased liquidity. Arbitrage helps the ETF more accurately track the index. We also observe that when one symbol experiences a mini flash crash, arbitrage transmits a price change in the opposite direction to the other symbol. The size of the mini flash crash depends more on the market configuration than the arbitrageurs, but the recovery of the mini flash crash is faster when arbitrageurs are present. 

We study learning-based trading strategies in markets where prices can be manipulated through spoofing: the practice of submitting spurious orders to mislead traders who use market information. To reduce the vulnerability of learning traders to such manipulation, we propose two variations based on the standard heuristic belief learning (HBL) trading strategy, which learns transaction probabilities from market activities observed in an order book. The first variation selectively ignores orders at certain price levels, particularly where spoof orders are likely to be placed. The second considers the full order book, but adjusts its limit order price to correct for bias in decisions based on the learned heuristic beliefs. We employ agent-based simulation to evaluate these variations on two criteria: effectiveness in non-manipulated markets and robustness against manipulation. Background traders can adopt the (non-learning) zero intelligence strategies or HBL, in its basic form or the two variations. We conduct empirical game-theoretic analysis upon simulated payoffs to derive approximate strategic equilibria, and compare equilibrium outcomes across a variety of trading environments. Results show that agents can strategically make use of the option to block orders to improve robustness against spoofing, while retaining a comparable competitiveness in non-manipulated markets. Our second HBL variation exhibits a general improvement over standard HBL, in markets with and without manipulation. Further explorations suggest that traders can enjoy both improved profitability and robustness by combining the two proposed variations. 

We study learning-based trading strategies in markets where prices can be manipulated through spoofing: the practice of submitting spurious orders to mislead traders who use market information. To reduce the vulnerability of learning traders to such manipulation, we propose two variations based on the standard heuristic belief learning (HBL) trading strategy, which learns transaction probabilities from market activities observed in an order book. The first variation selectively ignores orders at certain price levels, particularly where spoof orders are likely to be placed. The second considers the full order book, but adjusts its limit order price to correct for bias in decisions based on the learned heuristic beliefs. We employ agent-based simulation to evaluate these variations on two criteria: effectiveness in non-manipulated markets and robustness against manipulation. Background traders can adopt (non-learning) zero intelligence strategies or HBL, in its basic form or the two variations. We conduct empirical game-theoretic analysis upon simulated payoffs to derive approximate strategic equilibria, and compare equilibrium outcomes across a variety of trading environments. Results show that agents can strategically make use of the option to block orders to improve robustness against spoofing, while retaining a comparable competitiveness in non-manipulated markets. Our second HBL variation exhibits a general improvement over standard HBL, in markets with and without manipulation. Further explorations suggest that traders can enjoy both improved profitability and robustness by combining the two proposed variations. 

We propose an adversarial learning framework to capture the evolving game between a regulator who develops tools to detect market manipulation and a manipulator who obfuscates actions to evade detection. The model includes three main parts: (1) a generator that learns to adapt original manipulation order streams to resemble trading patterns of a normal trader while preserving the manipulation intent; (2) a discriminator that differentiates the adversarially adapted manipulation order streams from normal trading activities; and (3) an agent-based simulator that evaluates the manipulation effect of adapted outputs. We conduct experiments on simulated order streams associated with a manipulator and a market-making agent respectively. We show examples of adapted manipulation order streams that mimic a specified market maker's quoting patterns and appear qualitatively different from the original manipulation strategy we implemented in the simulator. These results demonstrate the possibility of automatically generating a diverse set of (unseen) manipulation strategies that can facilitate the training of more robust detection algorithms.