Game theory models how agents trade in a risky asset considering price impact and a common signal.
problem Modeling how financial agents liquidate assets in a risky market with price impact and a common signal.
method Formulated and solved a multi-player stochastic differential game and mean field game.
result Equilibrium strategies reveal how agents adjust the predictive trading signal to price impact.
Just as war is sometimes fallaciously represented as a zero sum game -- when in fact war is a negative sum game - stock market trading, a positive sum game over time, is often erroneously represented as a zero sum game. This is called the "zero sum fallacy" -- the erroneous belief that one trader in a stock market exch…
Paper extends Mean Field Game for portfolio trading, revealing trading flows impact on correlations.
problem Understanding how trading flows affect perceived correlations in portfolio trading.
method Extends Mean Field Game model to portfolios, analyzes real stock data, proposes calibration model.
result Closed-form formula linking observed correlations to underlying and initial imbalance of orders.
Generalizes insider trading model to multiple assets.
problem Modeling informed trading in a multi-asset context.
method Formulated an infinite-dimensional Bayesian trading game.
result Obtained a parsimonious equilibrium with closed-form solutions.
Model explains periodic trading in financial markets through game theory.
problem Understanding periodic trading activities in financial markets.
method Mean-field liquidation game with major-minor players.
result Existence and uniqueness of Nash equilibrium established.
Study on market entry timing in stock liquidation with trading constraints.
problem Optimal timing of market entry and exit in portfolio liquidation with trading restrictions.
method Mean-field game approach to model N-player and mean-field games of optimal portfolio liquidation. result Existence of unique equilibrium in both mean-field and N-player games. Study examines how traders optimize in a market with differing beliefs about price formation.
problem Optimizing trading actions in a market with heterogeneous beliefs about price formation.
method Analysis of mean-field game limit of a stochastic game with non-standard forward-backward SDEs.
result Nash equilibrium found through a non-standard vector-valued forward-backward SDE, with solutions constructed using expectations of filtered states.
We study multistep Bayesian betting strategies in coin-tossing games in the framework of game-theoretic probability of Shafer and Vovk (2001). We show that by a countable mixture of these strategies, a gambler or an investor can exploit arbitrary patterns of deviations of nature's moves from independent Bernoulli trial…
We introduce a new formulation of asset trading games in continuous time in the framework of the game-theoretic probability established by Shafer and Vovk (Probability and Finance: It's Only a Game! (2001) Wiley). In our formulation, the market moves continuously, but an investor trades in discrete times, which can dep…
Game theory model for optimal trading with end-of-day constraints.
problem Optimal trading strategy in a game between slow and fast traders.
method Coupled stochastic control problems, Fredholm integral equation solution.
result Explicit solution to the game with profitable strategies for both players.
The study examines how brokers' identity affects their trading strategies on the Toronto Stock Exchange.
problem Impact of anonymous trading on brokers' optimal execution strategies.
method Formulated a stochastic differential game and mean-field game to analyze the optimal execution problem of anonymous and identity-revealed trading.
result Obtained a closed-form solution for the optimal strategy under Almgren-Chris price impact framework.
Solves a game between brokers and informed traders using stochastic differential equations.
problem Optimizing wealth in a game between brokers and informed traders with private signals.
method Closed-form solutions to a mean-field game using forward-backward SDEs.
result Optimal trading strategies for both brokers and informed traders are found.
The paper analyzes trade execution strategies for large traders in a stochastic market environment.
problem Analyzing trade execution strategies in a stochastic market with price impact.
method Formulated a Markov game model and used backward induction method of dynamic programming.
result Explicit closed-form execution strategy at Markov perfect equilibrium.
Study on HFTs' interactions with a large trader using mean field game theory.
problem Interactions between high-frequency traders and a large trader executing assets at discrete times.
method Modeling HFTs' behavior using a jump process and solving the equilibrium through mean field game approach.
result Inventory-averse HFTs lower LT's costs when market impact is large.
Two strategic agents track their portfolios, influencing each other's trading targets.
problem Strategic competition in portfolio tracking with price impact.
method Stochastic linear quadratic differential game with terminal state constraints.
result Unique open-loop Nash equilibrium strategies emerge based on price impact types.
Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where all agents filter the latent states of the world, and their trading actions hav…
The paper analyzes trading strategies in a competitive market with incomplete information.
problem Strategic trading under uncertainty when firms lack full knowledge of competitors' strategies.
method Bayesian games framework to incorporate uncertainty and derive optimal trading strategies.
result Uncertainty significantly impacts trading strategies compared to complete information scenarios.
An evolutionary game model analyzes e-commerce and traditional retail trends during the pandemic.
problem Understanding the dynamics between e-commerce and traditional retail during the pandemic.
method Developed an evolutionary game model to study consumer-producer interactions on e-commerce platforms.
result Investment in logistics and warehouses in e-commerce led to faster delivery and consumer trends.
Study shows how multiple traders can trade together without excessive price impact.
problem Coordination issues in trading to exploit a common signal.
method Closed-loop Nash competition model for stochastic differential games.
result Excessive trading reduced but not significantly for practical parameters.
Deep Q-learning is investigated as an end-to-end solution to estimate the optimal strategies for acting on time series input. Experiments are conducted on two idealized trading games. 1) Univariate: the only input is a wave-like price time series, and 2) Bivariate: the input includes a random stepwise price time series…
Modeling pollution from competing firms using mean-field games.
problem Pollution regulation of competitive firms producing similar goods.
method Developed a mean-field game model with cap-and-trade regulation.
result Explicit solutions found through Riccati differential equations.
We study analytically and numerically Minority Games in which agents may invest in different assets (or markets), considering both the canonical and the grand-canonical versions. We find that the likelihood of agents trading in a given asset depends on the relative amount of information available in that market. More s…
Deep Q-Learning method for Nash equilibria in stochastic games.
problem Model-free learning for multi-agent stochastic games, especially for general-sum games.
method Data-efficient Deep-Q-learning using local linear-quadratic expansion parametrized by deep neural networks.
result The algorithm learns optimal actions for stochastic games without experiencing all state-action pairs.
Study optimizes SREC generation and trading in solar energy markets.
problem Optimizing solar energy generation and trading in SREC markets.
method Mean-field game approach to solve stochastic game with heterogeneous agents.
result Characterized firms' optimal controls and equilibrium SREC price.
Paper solves a trading game for stocks that jump and diffuse, finding the Kelly rule is optimal.
problem Trading game for stocks that can jump and diffuse.
method Solves a zero-sum game with a payoff kernel, finding the Kelly rule for jump diffusions.
result The Kelly rule is the optimal strategy for outperforming traders in a trading game.
New discrete-time model shows insider trading dynamics.
problem Modeling insider trading with discrete time and noise traders.
method Formulated as a game with three types of traders, including an insider, noise traders, and a market maker. Proved existence of sequential Kyle equilibrium for various distributions and information flows.
result Equilibria exist in mixed strategies but not in pure strategies, unlike in Kyle's original model.
Brokers and an informed trader compete for liquidity, affecting trading costs and inventory risk.
problem How brokers and an informed trader manage liquidity and trading costs.
method Sequential Stackelberg game, solving for trading strategies, numerical solutions.
result Equilibrium strategies and liquidity prices determined, not Pareto efficient.
The paper analyzes optimal stock position-building strategies in competitive markets.
problem Optimal stock position-building in competitive markets with market impact.
method Developed a game-theoretic framework to find best-response strategies.
result Closed-form solutions for equilibrium trading strategies were derived.
A game-theoretic analysis of DEX competition through dynamic trading fees.
problem Competition between decentralized exchanges (DEXs) and their impact on trading fees and slippage.
method Characterization of an approximate Nash equilibrium via coupled system of partial differential equations and closed-form expressions for equilibrium fees.
result The equilibrium trading fees shift from the oracle price to a weighted average of the oracle and competitors' exchange rates under competition.
This paper makes a small step towards a non-stochastic version of superhedging duality relations in the case of one traded security with a continuous price path. Namely, we prove the coincidence of game-theoretic and measure-theoretic expectation for lower semicontinuous positive functionals. We consider a new broad de…
Study examines large banks' role in interbank markets using game theory.
problem Understanding systemic risk in interbank markets with large banks.
method Mean-field game framework, convex analysis, Monte Carlo simulations.
result Large banks can positively or negatively impact market stability.
New framework for portfolio management using binomial markets and game theory.
problem Investment behavior in competitive and incomplete markets.
method Introduces PRFPP framework, constructs and analyzes for both finite and mean field games.
result Relative performance concerns do not always lead to more risky asset investment.
Optimal trading strategies identified in electricity markets with a major player.
problem Price formation and optimal trading in intraday electricity markets with strategic interactions.
method Stochastic control theory and mean field games with a major player.
result Nash equilibrium identified in closed form for the asymptotic case.
Investors with asymmetric information play a game to optimize their portfolios.
problem Two investors with different information levels compete in portfolio selection.
method Modelled as a Stackelberg game with entropy-regularized mean-variance objectives.
result Equilibria exist where follower's strategy depends on leader's actions.
Study on optimal trading in a finite population with market frictions and asymmetric information.
problem Optimal trading in a finite population with market frictions and asymmetric information.
method Investigates stochastic differential games with asymmetric information and market frictions, proving existence and uniqueness of Nash and Stackelberg-Nash equilibria.
result Existence and uniqueness of Nash and Stackelberg-Nash equilibria in both unconstrained and constrained trading scenarios.
Study shows how wealth distribution leads to volatility clustering in speculative markets.
problem Volatility clustering in financial markets.
method Agent-based model of financial markets with heterogeneous wealth distribution and round-trip trading.
result Heterogeneous wealth distribution induces volatility clustering through market wealth redistribution.
Players choose rebalancing rules to maximize their wealth relative to others in a continuous-time trading game.
problem Optimizing wealth in a continuous-time trading game between two players.
method Players choose rebalancing rules to maximize their expected wealth ratio, using the Kelly rule in equilibrium.
result The Kelly rule emerges as the optimal strategy in both short and long time intervals.
Study shows how capital constraints can lead to systemic crises in financial systems.
problem Impact of regulatory capital constraints on fire sales and financial stability.
method Mean field game model with banks adjusting holdings via trading strategies under regulatory constraints.
result Capital constraints can lead to simultaneous defaults in a substantial proportion of the banking system.
We study partial hedging for game options in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the maximum between proportional transaction costs and a fixed transaction costs. We prove that in the continuous time Black--Scholes (BS) mo…
Agents learn to outperform in trading by using past and current prices.
problem Optimal trading performance beyond theoretical limits.
method Two-agent Almgren-Chriss liquidation game, schedule-learning, DDQN architectures.
result Agents with access to past and current prices achieve supra-competitive outcomes.
Study optimal execution in a transient price impact model with multiple traders.
problem Optimal execution among multiple traders with transient price impact.
method Analyzed N-player optimal execution games in an Obizhaeva--Wang model with and without regularization. Derived equilibrium solutions and explained their behavior. result Existence of equilibrium restored with a specific time-dependent cost on block trades, and equilibrium is tractable.
Study optimal trading strategies with differing views and market prices.
problem Maximizing portfolio value with subjective asset value vs market price.
method Mean-field game approach to analyze interactions among agents with differing signals.
result Cross-sectional distribution of agents' inventories and price distribution dependence on shared information.
Investors' strategic trading affects asset prices, modeled as a game.
problem Investors' trading rates influence asset prices in dynamic markets.
method Model as a non-zero sum singular stochastic differential game, establishing equivalence between best-response and auxiliary control problems.
result Unique Nash equilibrium is deterministic with a closed-form solution.
Extends trading framework to incorporate real-world constraints.
problem Trading strategies in multi-player non-cooperative games with constraints.
method Re-framed as quadratic programming problem, constraints readily incorporated.
result Two-trader equilibria calculated dynamically.
Study analyzes non-Markovian effects in financial markets over multiple years.
problem Understanding non-Markovian dynamics and trader interactions in financial markets.
method Empirical analysis of self-response functions and trade sign correlators for different stocks over multiple years.
result Significant variations in traders' interactions over time, indicating changes in market mechanisms.
The \$-Game was recently introduced as an extension of the Minority Game. In this paper we compare this model with the well know Minority Game and the Majority Game models. Due to the inter-temporal nature of the market payoff, we introduce a two step transaction with single and mixed group of interacting traders. When…
This paper examines transitions in sniping behavior among algorithmic traders, finding new profitable strategies.
problem Understanding transitions from sure to probabilistic sniping in competitive algorithmic trading environments.
method Reinterpretation and extension of Menkveld and Zoican's stylized game, analysis of repeated games, sequential statistical testing.
result Probabilistic sniping can be profitable in certain conditions, resembling the prisoner's dilemma.
Study analyzes portfolio liquidation games influenced by self-exciting order flow.
problem Analyzing portfolio liquidation strategies with market order dynamics.
method Mean-field control problem, novel FBSDE system, sufficient maximum principle.
result Existence and uniqueness of open-loop Nash equilibria proved.