Game of Spreads: How to Build Better Trading Algos With Game Theory
By Eunice Xu, APAC AES Coverage, Credit Suisse
As you start on this article, look around; you’re likely surrounded by poker players, if not one already yourself.
What’s with this poker frenzy among traders? Adrenaline rushes aside, this seemingly simple game bears an uncanny resemblance to trading — a multi-party environment fraught with the perils of imperfect information.
The key to competing was once thought to be acquiring an information edge to act in a more informed way. To this end, poker players have gone to great lengths to identify a ‘tell’ — a subtle action that provides an informative hint about a player’s cards. A classic example of this is in the movie Rounders, where Matt Damon’s character defeats his opponent in a large hand after spotting his cookie bluffing tell.
While cookies are not usually available on poker tables, players used to resort to HUDs (Heads Up Display) software for an information edge. HUDs collect and display historical data about opponents’ past actions. These statistics allow players to strategize based on an opponent’s historical behavioral tendencies. For example, if you see someone fold almost 100% of the time when facing a raise, you probably want to raise more often even with suboptimal hands.
HUD was close to a gold standard until Libratus appeared. Libratus is an artificial intelligence program created by Carnegie Mellon University that employs the Game Theory Optimal (GTO) strategy. It defeated four of the best poker players in the world in 2017, the first time AI ever trounced human players in poker. Human adopters of its GTO strategy, such as Linus Loeliger, ascended rapidly in high stakes poker and they are now widely considered to be some of the best players in the world.
To understand what GTO is, we need to begin with game theory. Game theory is a study of interactive decision-making, in which the effectiveness of one agent’s decision is influenced by the decisions of other actors. GTO poker strategy builds on its principles to construct tactics that minimize the possibility of the player being taken advantage of by other players.
Game theory is by no means a foreign concept to finance professionals. The Keynesian beauty contest, where contestants are rewarded for voting the most voted, beautifully explains how the stock market works from a game theory perspective. George Soros’s interpretation of game theory — a trading philosophy of ‘fallibility and reflexivity’, detailed in his The Alchemy of Finance, demonstrated its use to establish a track record of beating the market.
In the field of algorithmic trading in APAC markets, one of the biggest challenges we face nowadays is an over-reliance on historical data in the same way poker enthusiasts used to rely on historical statistics collected by HUDs. Researchers collect historical data on stock price, volatility, trading volume, and spreads, and plug them into mathematical models to produce clues that will forecast future market movement.
In a competitive environment like the stock market, countless participants who possess cutting-edge technology and vast stores of historical data come together to compete for a few basis points. However, relying purely on historical data yields a narrower and narrower competitive advantage. This is accentuated when algorithms are restricted from reacting to signals or forbidden from a particular trading action by a set of pre-set parameters.
While the industry generally acknowledges the importance of having algos that can react intelligently to the live order book and real-time market events, most prediction models do not go far enough to reach beyond analytics based on historical data. Game theory, however, provides a new perspective that could transcend the confines of preexisting paradigms.
When approaching trading from the perspective of trading rules, the stock market could be viewed as a centralized auction market, where activities take the form of either a continuous auction or a batch auction. Through this lens, the execution algo’s role becomes deciding when, where, how much, and at what price to engage in a series of mini auctions, with a goal of maximizing the payoff from the aggregation of small positive results in all auctions participated.
Auction theory is one of game theory’s applications in economics. The 2020 Nobel Memorial Prize in Economic was awarded to economists Robert Wilson and Paul Milgrom for their achievement in this field. Extensive research in auction theory, from private value and common value models to the Revenue Equivalence concept, provides invaluable insights that can be applied to algo slicing and pricing logic, especially when it comes to optimizing placement in the order book.
The application of auction theory needs to be combined with a thorough understanding of market structure nuances across APAC markets. In a liquid market with a fast-moving book, for example, an outsized quote in a reasonably sized spread should trigger a strong take signal, instead of a hold signal based on the belief that there might be more behind.
Another important concept in game theory is Nash Equilibrium, which refers to the optimal solution in a multi-party non-cooperative game where no agents are incentivized to change their strategy. In the multi-party non-cooperative game called trading, stock exchange trading rules play a major role in determining ecosystem equilibrium.
Market structure equilibrium is fluid. Even a slight change with regards to tick sizes, timings, or short sale rules could have unforeseen or unintended consequences. When the Taiwan Stock Exchange moved from frequent batch auctions to continuous trading, research showed that market efficiency in mid-cap and small-cap names improved, while liquidity and efficiency in large-cap names declined1. To gain an upper hand in algo trading, it’s crucial to understand game theory, keep track of any potential changes to the equilibrium state, and fine tune algo parameters accordingly.
The equilibrium state in game theory may also be helpful to stock exchanges and regulators when deciding on trading rules. While most research on the effects of policy rely on ex post empirical data, game theory provides a useful tool for ex ante modelling in the quest for optimal policy design.
In this short article that barely scratches the surface of game theory, we have discussed ideas about how to build better trading algos with auction theory and Nash Equilibrium. Auction theory could help algos to better respond to live order book and unexpected events, and the Nash Equilibrium could help algos set optimized parameters based on market structure equilibrium.
The beauty of game theory is that it is profoundly scientific and philosophical at once. One implication of game theory is, “freedom of choice of any one state is limited by the actions of the others”, as commented by Kenneth Waltz in Man, the State, and War2. Of all the complexities algorithmic trading faces, this is one simplicity that won’t change.
Lee, Yi-Tsung and Riccò, Roberto and Wang, Kai, Frequent Batch Auctions vs. Continuous Trading: Evidence from Taiwan (November 19, 2020). Available at SSRN: https://ssrn.com/abstract=3733682 or http://dx.doi.org/10.2139/ssrn.3733682
Kenneth N. Waltz, Man, the State, and War: A Theoretical Analysis (1959)