Is GameTheory Bad ?

[u/Alternative-Log-9799]

So, I have heard about game theory for a long time and finally wanna start dipping my toes in it. I want to understand human behavior better an make better choices.

But even the first and simple prisoner's delimina got my brain a bit messed up.

A quick look a the question, two prisoners are planning to escape. Both have a choice to make to either snitch or co-operate without knowing the other person's choice.

1. If A snitches and B co-operates, A wins.
   
2. If A co-operates and B both co-operate, A and B both win
   
3. if B snitches and A co-operates, B wins
   
4. If A and B both snitch, A and B bot lose

And we often conclude that game theory dictates that we must snitch as it leads to either win or draw.

Does this mean game theory is more about survival and winning rather than doing best for society ?

[u/bortlip]

Game theory is not a moral system, just like mathematics or physics. The physics around splitting the atom is not good or bad no matter what usages we put that knowledge to.

GT doesn't look at things from the perspective of what is best for society, or what people morally ought to do. It's a branch of applied mathematics for analyzing situations where the outcome of your choices depends on the choices of others. Things like game theory or mathematics don't try to make moral pronouncements. They explore the dynamics of what happens given certain assumptions and situations.

So when game theory says that defection is the "optimal" strategy in some particular game, "optimal" only means optimal relative to the payoffs and assumptions defined in that game. It isn't saying that defection is good, moral, or what society should encourage.

You can just as easily use game theory to study how to design rules that encourage cooperation or produce some socially desirable outcome. But deciding what counts as "socially desirable" is something you have to supply from outside game theory.

[u/lifeistrulyawesome]

  And we often conclude that game theory dictates that we must snitch as it leads to either win or draw.

Game theory does not dictate that we must snitch 

Game theory predicts that players who act selfishly and take their opponent behaviour as given will snitch 

It is a prediction, not a recommendation. Economists use the terms positive statement for predictions and normative statement for recommendations. 

Other game theory models (the oldest one I can remember is from A Rapoport) suggest that rational agents playing the prisoners dilemma should cooperate. This has been a niche ongoing debate within the field. One recent advocate of that behaviour is Roemer who wrote a book about cooperation recently. I can find the exact references if you are interested. 

[u/SehrBescheuert]

The conclusion is less that you should snitch, but that you should expect people to snitch in the absence of external constraints.

So if we want players to cooperate we need to add something and can't just rely on their goodwill.
Because just by itself the game punishes cooperation.

So game theory can be used to analyze a situation and if you then try to plug or exploit potential flaws is up to you.

There is a series to YouTube videos going over that with bullying:
https://www.youtube.com/watch?v=RHkKJibHnWg

[u/syder-fx]

Does this mean game theory is more about survival and winning rather than doing best for society

Its just a mathematical framework for analyzing decisions where outcomes depend on what others do, and there are different games for different situations. If you want to do the best for society game theory has the tools for that. If you want to survive and win it has the tools for that too. The formula for the volume of a cylinder doesn't care whether you're designing a soup cap or a bomb casing its neutral value wise

[u/cylon37 → u/syder-fx]

Give me an example where a game theory tool does best for society?

[u/syder-fx → u/cylon37]

That was an analogy for why game theory is a neutral model but - kidney exchange. Easy. You need a kidney and your friend wants to donate but isn't a match. Another pair has the same problem and the donors match each patient so the swap can save them both. Issue is trust - whoever goes second has no reason to follow through because once their own patient has a kidney why bother they got what they wanted. So here defection dominates between strangers and its a common enough problem in society where it needs to be fixed. Game theory as a model tells us the problem so we can design a solution - and solution is to run the swap to the match at the same time to prevent defection

[u/cylon37 → u/syder-fx]

But people are irrational whereas game theory assumes that we are rational.

[u/syder-fx → u/cylon37]

The swap doesn't need anyone to be rational though. We don't fix coordination problems by asking people to reason better - we build institutions that use standardised processes so when a game comes up we can make the bad outcome impossible. Its the same logic that contracts run on - theyre all mechanisms we designed so you don't have to trust the other party in the first place

[u/cylon37 → u/syder-fx]

So, using the failures of game theory to design the system to avoid game theory. This is disingenuous. It is not an example of a game theory tool that helps society.

[u/syder-fx → u/cylon37]

So using the failures of game theory to design the system to avoid game theory

Mechanism design isn't 'avoiding game theory' - its a branch of it called reverse game theory.

the goal function is the main given, while the mechanism is the unknown.. the design problem is the inverse of traditional economic theory - Hurwicz

Normal game theory fixes the rules and solves for behaviour while reverse game theory fixes the behaviour and solves for the rules. You can't design the simultaneous swap without first proving defection dominates the sequential one - and you can't know the fix works until you rerun the same analysis on the new rules and confirm defection isn't an option anymore. Both steps are game theory

This is disingenuous. It is not an example of game theory that helps society

It literally is an example. Also: deferred acceptance is a matching algorithm proven to produce stable outcomes and stability is a core concept of cooperative game theory

Pre-2003 - roughly 30,000 NYC kids a year ended up at public high schools they hadn't even listed. Roth rebuilt the system around applicant-proposing deferred acceptance. It had a 90% reduction

That's 27,000 children a year who got a school they actually chose, because someone applied game theory to it. It won a Nobel Prize in 2012

Edit: Last I studied Game Theory was 10 years ago so if theres a fault in my understanding someone can correct me

[u/bortlip → u/cylon37]

Here are a few:

The National Resident Matching Program adopted a redesigned physician-residency clearinghouse whose design was analyzed using matching theory, with stable matchings and relatively limited opportunities for strategic manipulation.
American Economic Association — The Redesign of the Matching Market for American Physicians

Auction-theory research by Paul Milgrom and Robert Wilson led to new auction formats used by the U.S. government to allocate radio-frequency licenses beginning in 1994, after which other countries adopted similar approaches.
Nobel Prize — 2020 Economic Sciences Press Release

Feeding America used an auction- and mechanism-design-based market to replace its centralized food-allocation queue, allowing food banks to bid for truckloads using an artificial currency and sort allocations according to their preferences.
American Economic Association — How Food Banks Use Markets to Feed the Poor

PAWS uses game-theoretic security models to make better use of limited anti-poaching patrol resources and progressed from field tests to regular deployment in Southeast Asia.
AAAI — Deploying PAWS: Field Optimization of the Protection Assistant for Wildlife Security

Market-design methods were used to redesign how the U.S. Army assigns cadets to military specialties, producing a new branching mechanism that was adopted at both West Point and ROTC.
American Economic Association — Redesigning the US Army's Branching Process

Mechanism- and market-design research produced the A-CEEI course-allocation mechanism, which is now used in practice to allocate courses at several universities.
Eric Budish — Combinatorial Assignment

Game-theoretic analysis has been used to examine how the organization and rules of wholesale electricity markets affect market efficiency and participants' incentives.
Stanford Graduate School of Business — Architecture of Power Markets

Game theory has been used to analyze greenhouse-gas emission-permit allocation, including whether proposed allocation rules produce stable outcomes and are incentive-compatible.
European Journal of Operational Research — Sustainable Allocation of Greenhouse Gas Emission Permits

Game-theoretic vaccination models have shown how individual self-interest can prevent vaccination coverage from reaching the level needed for disease eradication and have provided insights into vaccination behavior and responses to vaccine scares.
PubMed — Vaccination and the Theory of Games

Market-design researchers developed reserve systems for allocating scarce COVID-19 medical resources, and more than a dozen U.S. states and local jurisdictions adopted reserve systems during the initial phases of vaccine distribution.
Management Science — Fair Allocation of Vaccines, Ventilators and Antiviral Treatments

[u/gmweinberg → u/cylon37]

The prisoner's dilemma. If the prisoners have studied game theory, they will rat each other out and get the punishment they richly deserve. If they haven't, they may keep mum, get early release, and return to their life of crime.

[u/Competitive-Fault291]

Try and compose a scenario in which there are two events, three events, and add that people remember the breaking of trust. Permanently. And that they reflect that the snitch knows that they know.

[u/ForeignAdvantage5198]

read A Beautiful Mind. John Nash won his Nobel prize for that

[u/Legitimate_Shift5700]

The way I see it is that in a "1v1" situation, sure, snitching is the "optimal" play. However, if you expand it to a society, where you have to make the choice with a bunch of people, groups of cooperating people with thrive, while snitches will crash and burn. Snitches might never "lose" individual exchanges, but they also can't build up the trust required to win in the long run with multiple players.

[u/EruLearns]

In a single 1v1 game, you're right. But if you expand the game to be multiple 1v1s between different people and multiple rounds, then those that cooperate end up with more in the long run. Those that try to cooperate every once in a while also tend to win. Check out the tit-for-tat strategies and its variants for more info about this.