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MayCaesar

Game theory is a field in mathematics that studies rational behavior of actors with mutually conflicting interests. One of the weird consequences of such behavior is that groups of people can behave in such a way that every member of the group stands to lose from it, and yet that behavior is perfectly rational from the individual viewpoint. 
The reason for this is that the individuals can never trust each other to act for the mutual benefit.

Consider the "thief paradox". Someone stole a goat in a village, and nobody admits to it. The mayor calls up all the residents and says, "Whoever admits his guilt will lose $100. If nobody admits the guilt, then each person will lose $50." Nobody wants to lose $100, hence nobody admits the guilt, and every person ends up losing $50.
What would be a better collective behavior? It would be for someone to admit the guilt, and then for the entire village to put the money together to pay the $100 fine. Every single resident of the village would end up better off. If, say, the village has 20 residents, then every resident would end up losing only $5, rather than $50.
However, since the person who admits the guilt can never rely on his fellow residents to help him with paying off the fine, this does not happen.

Consider another situation. Due to a misunderstanding, two individuals are pointing guns at each other. None of the individuals wants to end up dead.
The rational collective behavior would be for both individuals to put their guns down and walk away.
However, neither individual can put their gun down and trust the other individual to do the same. There is a chance that, as soon as one individual puts their gun down, the other individual will use the moment and shoot them. Hence, the individuals keep pointing guns at each other, even though neither one wants to maintain the status quo.

With regards to the elections, the "median voter theorem" is illuminating. 
Consider the election with two candidates. 80% wholly support every policy of candidate A, and 20% wholly support every policy of candidate B - and each group absolutely hate the policies of the candidate they do not support. If candidate A is elected, then 80% people will be happy and 20% will be unhappy, which is a pretty good result.
Now, candidate B, realising he is losing the election, shifts his policies more to the middle. He gets to the level where the 20% still mostly support him, and the other 80%, while not really supporting him, do not mind his policies that much.
Candidate A is now afraid of losing the voters to Candidate B, and becomes concerned with the opinion of those 20% that absolutely hate his policies. So he also slightly shifts his policies to the middle, to gain their support. But now the 80% are less excited about his policies.
In the end, whoever wins the election does so by promoting the middle-ground policies, which nobody really wants. But everybody is afraid of the worse alternative, hence they compromise on this. And rather than having 80% happy and 20% unhappy people, we have 100% people who are somewhere in between, which, by most reasonable metrics, is a worse outcome.

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Game theory essentially destroys the idea of natural collectivism at its root. Collectivism suggests that all people are a part of the collective that works for the benefit of every individual. The game theory illustrates that, while it would indeed be better for everyone if that was how it worked, in reality there is no collective, there is only a group of individuals, each of which is after their own gain. And it is not necessarily because these individuals are selfish, but it is because these individuals, however altruistic and sharing-loving they can be, simply cannot rely on others being so.
Even one individualist in a collective society will quickly make the system unsustainable, as he/she exploits others' trust for their own gain.

One could say that game theory paints humanity in very dark lights, humans being proven to be beings who constantly harm themselves by not willing to cooperate for mutual benefit. Even when everyone stands to gain by working together and lose by not doing so, people still rationally do not do so.

I, on the other hand, think that it offers a good practical guidance for cooperatives. Whenever people want to cooperate for mutual benefit, they need to make sure that everyone is incentivized to do so. The mere notion that "if we work together, we will all be better off" is not sufficient for a productive cooperation. 
In this regard, I like the system of individual bonuses in private companies. When one strongly contributes to a group project, then, regardless of the outcome of that project, that person receives a bonus to their salary. This ensures that everyone personally benefits from cooperating with other people, even if the other people do not want to cooperate with them.

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On this note, when talking about collectivist economical systems, such as socialism or corporatism, I feel like some crucial ingredient is missing. Game theory states that a system which expects everyone to cooperate voluntarily for no immediate benefit is going to fall. Real socialist and corporatist systems attempted to "incentivize" people to cooperate by punishing them for not doing so, but that led to the minimal amount of cooperation required just to not be punished, which obviously could not be sufficient to produce a sustainable economy.

On the other hand, a collectivist system could work if people personally profited from cooperating with others. For example, a collective-owned farm could reward people daily proportionally to the amount of harvest they have collected.
Of course, the question still remains on how to organise such a system and how to make sure that those who oversee these rules, in turn, do not try to use them to their sole benefit at the expense of others. And regardless, there exist countless moral and preferential objections to such a system. I personally, for one, would rather have my own farm, even if it was less productive than a collective-owned farm with incentives, as I like my freedom and independence.

But still, the notion remains: advocates for collectivist economies would stand on a much solid ground if they ditched the implausible ideal of "everyone happily cooperates with each other for the mutual gain" and replaced it with a more pragmatic incentive-featuring cooperation. One does not have to care about others to want to work with them, and, in fact, as game theory shows, the only way cooperation can work long-term is when every cooperator pursues their own selfish interest.
So make it a selfishness-based pragmatic collective, and then such an economical system, at the very least, would not be so glaringly incompetent, as the ones most modern collectivists like to promote.

Plaffelvohfen

Interesting but there are multiple game types in "Game Theory"... I'm not convinced every game type "destroys" the idea of natural collectivism, it's certainly true of non-cooperative games and zero-sum games obviously, but not so sure about the many other game types... Still interesting and informative though!

Oppolzer

Game theory is neither a hypothesis or assertion and therefore cannot substantiate as right or wrong. The theory is merely a simplification of the complex reality we live in, and any simplification will not be decisively accurate. Game theory heavily relies on presumptions and probability and will be less reliable in certain circumstances. The ideas put in motion by game theorists may be right or wrong and therefore materializes as speculation. Albeit, the field as a cohesion would still be adequate.

Game theory is utilized as an analytical tool to consider plausible outcomes. It's synonymous with statistics. For example, if you apply statistical samples to reality, and reality doesn't equal with all of the samples, it doesn't imply that statistics is wrong. It merely signifies that the odds were against you.

billbatard

there is no black no white only shades of grey there is no collective no private only mixtures of the two life is about balance

MayCaesar

Plaffelvohfen said:

Interesting but there are multiple game types in "Game Theory"... I'm not convinced every game type "destroys" the idea of natural collectivism, it's certainly true of non-cooperative games and zero-sum games obviously, but not so sure about the many other game types... Still interesting and informative though!

I would say that Game Theory considers a fundamental problem with any collective, in that the goals of every individual are at odds with the goals of other individuals, and no matter how much everyone agrees that cooperation is mutually beneficial, it is simply impossible to organise it in a reliable way without some extra actions. 

It, of course, does not mean that collectivism is absolutely disfunctional. There can even be natural collectives that work without any manually introduced incentive. It is long-term stability of such collectives that is under question, however. People can cooperate voluntarily with no special incentives, but eventually someone will start using the product of the cooperative in a way that disadvantages other its members. And at that moment the entire cooperative may crumble.

That said, as @Oppolzer noted, Game Theory does not necessarily describe the real world perfectly, and as you pointed out, there are many different game types, some of which may lead to other outcomes.

Oppolzer said:

Game theory is neither a hypothesis or assertion and therefore cannot substantiate as right or wrong. The theory is merely a simplification of the complex reality we live in, and any simplification will not be decisively accurate. Game theory heavily relies on presumptions and probability and will be less reliable in certain circumstances. The ideas put in motion by game theorists may be right or wrong and therefore materializes as speculation. Albeit, the field as a cohesion would still be adequate.

Game theory is utilized as an analytical tool to consider plausible outcomes. It's synonymous with statistics. For example, if you apply statistical samples to reality, and reality doesn't equal with all of the samples, it doesn't imply that statistics is wrong. It merely signifies that the odds were against you.

As any other model in mathematics, it is an idealised description of some observable trends. It assumes that every individual seeks to maximise their personal outcome by minimising the risk/reward ratio, which in practice does not always have to be the case.

Within the scope of Game Theory, everything is perfectly logical, and theorems are strictly derived from previous results. However, as any other mathematical field, it is built upon a set of axioms which are selected somewhat arbitrarily. In fact, one of the consequences of Godel's Incompleteness Theorem is that any possible system of axioms is necessarily limited in its scope and cannot describe everything there is to be described.

I really like your comparison with statistics! It is a good example that something that, in itself, is correct does not necessarily lead to correct predictions.

K_Michael

billbatard said:

there is no black no white only shades of grey there is no collective no private only mixtures of the two life is about balance

Not technically true. There are models and practices of total collectivism and total individualism. I'll give a few examples. 

If your teacher promises a 5% markup in grade for everyone if everyone in the class turns in the homework on time, this is an example of total collectivism. No matter what you do, you cannot get that grade boost unless everyone meets the requirements. You are dependent upon all of your classmates' decisions. You have no freedom of choice.

Conversely, if your teacher promises a 5% markup in grade for each individual that turns in his/her homework on time, then it is an example of total individualism. You now get to make decisions for yourself, receive the earned benefits and consequences of your actions.
 
The funny thing is that if all the students decide they want the boost and obtain it, the situations will have the exact same outcome. 

K_Michael

K_Michael