I'd be curious to hear how they have been useful to you: just in teaching you about the topic for curiosity's sake, or in achieving some practical outcome?
Depends on what you want. Just want to map the maths to code? Python is a good choice. Easy to understand and visualize too.
But Game Theory models can easily blow up in huge n-dimensional matrices very quick, so performance can be an issue. You might be tempted to go to something like C. But then again, Python has numpy.
Having minored in this, I’d put it in the category of “abstract framework” at the moment. Though perhaps that’s also due to my exposure more to theory and math, and less to application.
This paper is funny if you actually understand game theory because you can see how the author either chose to withhold key applicable information for applied game theory or inadequately researched famous game theory principles and developments.
This is a much easier and more realistic introduction to game theory principles:
Game theory is often explained as a math problem involving humans and a specific scenario that requires a choice, from humans.
The scenarios are fun thought experiments and about as useful as the famous trolley problem [1][2]
In reality humans have many more variables affecting decisions than the pure rational equations can clearly define. Often the undefined variables are within the context of communication theory and reputation or auditing systems.
In the case of the famous prisoners dilemma, the real solution is establishing a secret out of band communication channel prior to the dilemma, alongside a known reputation and retaliation penalty for abusing the mutual trust.[3] [4]
The famous "tragedy of the commons" rational resource optimization game is often cited as justification for machiavellian exploitation, yet humans being social creatures are subject to reputations, and have sophisticated communication, cooperation, and retaliation abilities.
[4]
Elinor Ostrom's "Rules, games, and common-pool resources" and Robert Axelrod's work "The Evolution of Cooperation" both explain game theory in the context of human scale realities. Of particular interest to the hacker community would be Ostrom's Common Pool Resource principles, which are applicable to adhoc decentralized communities. :)
At the core of game theory, and human civilization is communication and trust. The abuse of mass media to manipulate populations knows the power of communication and cultural narratives, and we're witnessing what's often described in terms such as "hypernormalization" or "accelerationism" [6][7][8][9]
For a better applicable human scale game theory primer, check out Bruce Schneier's (yes, the same legendary cryptographer Bruce), "Liars and Outliers"
As someone that studied Game Theory (and philosophy, for that matter) at graduate levels, there's quite a lot wrong with this post, and I just want to reiterate what @georgeglue1 said: Matt Jackson is quite literally a leading expert and the paper is actually very good for how terse it is. The kinds of exercises you'd do in a Game Theory class are pretty on par with what you see in the paper itself. You would end up answering questions like: What are the dominant strategies? Do any equillibria exist? What's the Nash Equilibrium? What outcome is Pareto optimal (if any)? What's the expected utility of a particular pure strategy? Mixed strategy? Etc.
Anyway, to address your comment, just on a very basic level, Phillipa Foot's "Trolley Problem" is unequivocally not a game theoretic problem. It's in the family of ethical "no-win" puzzles a la "Sophie's Choice" and has little to do with the actual study of game theoretic strategies, outcomes, and equillibria. The "Tragedy of the Commons" is also not game theoretic. There have been some attempts at turning it into an iterated game (in the formal sense), but -- again -- it's not technically a game theoretic problem, and rather a question on social policy. Elinor Ostrom famously provided a non-game theoretic solution to the Tragedy, so bringing her up is just confusing.
> At the core of game theory, and human civilization is communication and trust. The abuse of mass media to manipulate populations knows the power of communication and cultural narratives, and we're witnessing what's often described in terms such as "hypernormalization" or "accelerationism"
And I have no idea what the hell this means. It looks like gibberish and has nothing to do with the (relatively narrow) scope of Game Theory as a field.
The pure math of von Neumann style modeling is an incomplete and inapplicable system that has mostly been rendered obsolete when applied to human situations [1] and has been surpassed with behavioral game theory [2] and sociological modeling which is dependent on variable input from field research into actual human activities (which often vary widely by regional, cultural, temporal influences). Attempts to describe this can be found with Knightian uncertainty, dynamic inconsistency, bounded rationality [3], anchoring bias, decision theory, applying bayesian models, and complex system modeling theories which generally also involve models using statistical sampling from reality instead of presumptive theoritical models based on the early primitive von Neumann concepts.
For computational optimization, the von Neumann game theory terms are applied to actual logic systems and we end up with computer vision optimizations and video/audio codec best guess optimizations, or some interesting applications of evolutionary computing [4] in verifiable applications like signal optimization in antenna design [5] or industrial manufacturing techniques and structural integrity or architectural optimizations via generative design [6] in software [7] like generative computer automated design, ie Fusion 360 or Grasshopper [8].
Rudimentary modeling with von Neumann game theory fails to account for variables in reality, like the ambiguity effect and in applications like optimization of social choices like economic modeling or voting i.e. Gibbard's theorem. There's often situations where game theory fails to account for an adversarial evasion of the rule set - https://en.wikipedia.org/wiki/Metagame_analysis
If the primitive von Neumann game theory models were used to train an artificial intelligence system that controlled military weapons, there would have been global thermal nuclear winter in several decision making "games" like the 1983 Soviet nuclear false alarm situation.
Matt Jackson is one of the most respected game theorists at probably the best game theory department in the US.
His goal is just pretty different. He's presenting the mathematical / intuitive foundation that underly more advanced models (probably for the purposes of academic classes).
A lot of commonly understood stuff you mention (like reputation) is hard to define in the rational math of game theory, especially when you start layering real-world complexity like incomplete information.
See Kreps Milgrom Roberts Wilson (1981) for a fun example from two recent Nobel Prize winners on how hard this gets (and why it's useful to understand Matt Jackson's intro if you want to get into academic / theory stuff)
https://www.sciencedirect.com/science/article/pii/0022053182...
Imagine posting this and not idk, googling the author to find he's one of the most well-respected game-theorists in the world.
But sure, anonymous internet bro knows more about game theory than the Stanford econ PhD who teaches at Stanford econ department and edited the leading game theory academic periodical...
Aside from the first paragraph’s claims of inadequate research, I thought GP’s post was actually a pretty good critique of some of game theory - especially when you try to break out of the neat mathematical formulations it espouses and apply it to the real world.
Your post, on the other hand, reads like an argument from authority.
There is some notation you must know (product, sum, set, etc) but the math is very straightforward, which makes sense, game theory in its most basic form is relatively straightforward logic that one can reason through with needing complex mathematical tools or abstractions.
Ditto on this. Game theory is what people put into practice through play. Any rules more complex than being turn-by-turn decisions or game-length strategy tend to not find their way into interesting models.
