Quantum Information, Game Theory, and the Future of Rationality
Games in Quantum Physics And The Missing Beef In Bozkashi
The literature on quantum information includes discussions of games in which Alice and Bob participate, but these are often casual, informal games rather than rigorous game-theoretic models. The primary motivation for framing the scenario as a "game" seems to be to create a more engaging narrative, rather than to contribute any novel insights from game theory. Even in instances where game theory is invoked, the often relaxed and imprecise application of the term "game" raises questions about whether any meaningful advancements in game theory have been made, or how, if at all, the use of game-theoretic frameworks enhances our understanding of physics.
Faisal Shah Khan, PhD
2/10/20253 min read
"Where's the beef?"—a legendary Wendy's commercial from 1984—featured a little old lady demanding more meat in her burger, taking a direct jab at competitors' skimpy patties. The phrase quickly transcended advertising, becoming a cultural catchphrase for calling out anything that is all talk and no substance—whether a weak argument, an empty promise, or a disappointing product. Even today, I still hear it used, especially among older generations. I wonder if it has enough rizz to stick around—that would be straight-up skibbidified.
This proverbial beef is precisely what I seek when reading quantum physics, especially quantum information theory papers that claim to use a "game" between two agents—typically Alice and Bob—to reveal new insights into physics or game theory. More often than not, however, the term "game" is used in an informal, superficial way rather than in a rigorous game-theoretic sense. The primary motivation seems to be making the discussion more engaging rather than contributing any substantive insights from game theory. Even when game-theoretic concepts are invoked, the lack of precision raises the question: Are these papers genuinely advancing game theory, or is the terminology just window dressing? More importantly, how—if at all—does framing these quantum scenarios as "games" deepen our understanding of physics?
A particularly problematic example is the CHSH "game," which is inspired by the 1969 work of Clauser, Horne, Shimony, and Holt. Their original result introduced an inequality that distinguishes quantum from classical correlations, but its game-theoretic reinterpretation is murky at best. The mathematical structures describing quantum mechanics and game theory do not align in a meaningful way, yet terms like players (Alice and Bob) and strategies (measurement bases) are casually borrowed without clear definitions. Is this supposed to be a competitive or cooperative game? If competitive, where is the value function, Nash equilibrium, or correlated equilibrium? If cooperative, what cooperative solution concepts—such as the Shapley value—are at play? I have yet to see a paper that treats the CHSH "game" as a cooperative game, and I am not surprised. Cooperative game theory remains largely unexplored in quantum game theory.
For a clear and well-structured discussion of the CHSH "game," I recommend this lecture note: https://www.cs.cmu.edu/~odonnell/quantum18/lecture07.pdf. However, even here, proper game-theoretic notions are absent; the term "game" is mapped onto a quantum communication protocol in a loose, almost metaphorical sense. By contrast, Eisert et al.'s seminal paper Quantum Games and Quantum Strategies (which I’ve written about extensively on this Qlog) extends the CHSH "game" into a proper, non-cooperative game-theoretic framework, connecting quantum physics to game theory through a quantum referee that facilitates superior Nash equilibria.
On the other hand, more recently, papers at the intersection of quantum physics (particularly quantum communication) and game theory have started to take the interplay between the two disciplines more seriously and systematically. For instance:
A Game Theoretic Security Framework for Quantum Cryptography: Performance Analysis and Application
Use of Nash Equilibrium in Finding Game-Theoretic Robust Security Bound on Quantum Bit Error Rate
One hopes this trend will continue. The bottom line for now: Adding bells and whistles to a toy train doesn’t teach us much about how locomotives or bullet trains work. Or, to recall an analogy from one of my older papers which is also the motivation behind the title of this post:
"Despite the fact that cooperative game theory is the motivation for the latter and other similar work, a formal discussion of cooperative games together with a formal mapping of the relevant physics to the requisite cooperative game is almost always missing. In fact, it would be accurate to say the word “game” is thrown around in this body of literature as frivolously as the headless carcass of a goat is thrown around in the Afghan game of Buzkashi; but the beef is nowhere to be found. This is not surprising since beef comes from cows! The point of this somewhat macabre analogy is that one should be just as disturbed when hearing the word 'game' used for an object that isn’t one, as one surely is when hearing the word 'beef' used for a goat carcass."