Extracting irl morality solutions from solving games... - Page 3 - Religion, God, and Theology

Pareto optimal seems to be about distributing a finite number of goods. I'm not sure if it can be applied to PD since that game has unbounded resources.

It's a standard part of game theory in general and Prisoners Dilemma specifically.

http://www.cs.umd.edu/~nau/cmsc421/game-theory.pdf

Quote:

[where C = co-operate and D = defect]
The Prisoner’s Dilemma
 (C,C) is Pareto optimal
 No profile gives both players
a higher payoff
 (D,C) is Pareto optimal
 No profile gives player 1 a higher payoff
 (D,C) is Pareto optimal - same argument
 (D,D) is Pareto dominated by (C,C)
 But ironically, (D,D) is the dominant strategy equilibrium

As I say, the whole interesting part about non-iterative PD is that the Nash equilibrium strategy (both defect) is not Pareto optimal (both co-operate). Which is why I'm confused about what 'superrational' means and how it is different from the Pareto optimal strategy (at least as far as Prisoners Dilemma is concerned). From what RollWave has said it looks like 'superrational' is a subset of Pareto efficiency, but I'll probs have to do some more reading to get a proper handle on it.

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05-30-2013 , 12:20 PM

#52

RollWave

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Originally Posted by zumby

From what RollWave has said it looks like 'superrational' is a subset of Pareto efficiency,

intersecting sets, not a subset.

An example of a game where they do not intersect would be like prisoner's dilemma except 1 person defecting doesn't punish the cooperator.
5,5 5,10
10,5 -10,-10

In this case, CC is not pareto optimal as in the normal prisoner's dilemma since either player can defect without hurting the opponent. CD and DC are now pareto optimal. However CC is still superrational since it is clearly superior to DD. A superrational strategy will never lead you to CD or DC since without communication you can never determine whether its you or the other guy who is supposed to choose either different choice.

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05-30-2013 , 12:28 PM

#53

newguy1234

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Is there a better strategy for irl than everyone works together as a team?

Which does that fit under? Co operative? Is Pareto Optimal? Super rational?

I am having trouble understanding how people can think its not optimal and why they think defecting from it could yield better results for the individual.

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05-30-2013 , 12:31 PM

#54

newguy1234

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Quote:

Originally Posted by RollWave

A superrational strategy will never lead you to CD or DC since without communication you can never determine whether its you or the other guy who is supposed to choose either different choice.

I can't tell if this is a stupid question or not but what if they each flip a coin so they sometimes choose cc dd cd or dc?

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05-30-2013 , 12:43 PM

#55

RollWave

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Quote:

Originally Posted by newguy1234

Is there a better strategy for irl than everyone works together as a team?

yes

Quote:

Originally Posted by newguy1234

Which does that fit under? Co operative? Is Pareto Optimal? Super rational?

'real life' is sufficiently complex that none of these categories can adequately describe it. Or maybe more precisely that all of might be better, just in different ways.

Quote:

Originally Posted by newguy1234

I am having trouble understanding how people can think its not optimal and why they think defecting from it could yield better results for the individual.

this is because you are oversimplifying and applying inaccurate analogies/scenarios/scoring.

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05-30-2013 , 12:48 PM

#56

newguy1234

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Quote:

Originally Posted by RollWave

yes

Which is the better strategy than the world working together as a cohesive unit?

Quote:

'real life' is sufficiently complex that none of these categories can adequately describe it.

With everyone on the same team working together and no defectors, the situation is too complex?

Quote:

this is because you are oversimplifying and applying inaccurate analogies/scenarios/scoring.

Its not an analogy or scenario and there is no scoring mentioned. I just simply mean the world works together as a whole. Or maybe you can explain what you mean?

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05-30-2013 , 12:49 PM

#57

RollWave

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Originally Posted by newguy1234

I can't tell if this is a stupid question or not but what if they each flip a coin so they sometimes choose cc dd cd or dc?

Sometimes a mixed strategy can be appropriate for games, but that's not the point I was trying to illustrate so feel free to change the DD result to Death instead of -10 to remove that from your consideration.

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05-30-2013 , 12:51 PM

#58

zumby

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Quote:

Originally Posted by RollWave

Thanks

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05-30-2013 , 12:58 PM

#59

Aaron W.

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Quote:

Originally Posted by zumby

It's a standard part of game theory in general and Prisoners Dilemma specifically.

http://www.cs.umd.edu/~nau/cmsc421/game-theory.pdf

Thanks. The wiki page wasn't very clear.

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05-30-2013 , 01:09 PM

#60

RollWave

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Originally Posted by newguy1234

there is no scoring mentioned. I just simply mean the world works together as a whole.

exactly. 'the world works together as a whole' is not uniquely defined. it could mean any number of different strategies, all with different results, but all which could be considered teamwork without defection. So your claim that it is the best doesn't make sense since you are simultaneously describing a large number of completely separate strategies as better than each other.

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05-30-2013 , 01:17 PM

#61

newguy1234

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Quote:

Originally Posted by RollWave

We should go into this aspect a little I think. Applying the strategy and the resulting applications are debatable, in the way you describe.

But the concept or strategy of working together as a team doesn't need to be defined further to show that it is superior.

How can you show there is a better strategy than total teamwork for this world?

Or lets say the world is already in a state in which everyone sees them self on the same team, how might they change this view to better serve the whole or the individual?

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05-30-2013 , 01:44 PM

#62

RollWave

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Originally Posted by newguy1234

But the concept or strategy of working together as a team doesn't need to be defined further to show that it is superior.

How can you show there is a better strategy than total teamwork for this world?

Yes it does need to be defined. Which of the following is the result for A and B working together?

1. A=10, B=10
2. A=9, B=20

Working together for the betterment of the team is completely ambiguous. #1 is better from a maximin pov of teamwork. #2 is better from a cumulative sum pov.

Whichever you choose as being the result of total teamwork - the better strategy is the other one.

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05-30-2013 , 01:56 PM

#63

newguy1234

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Quote:

Originally Posted by RollWave

Both of these strategies are working together as a team, not being able to pick the best one does not show they are inferior to individualistic type strategies.

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05-30-2013 , 02:00 PM

#64

RollWave

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Originally Posted by newguy1234

Both of these strategies are working together as a team, not being able to pick the best one does not show they are inferior to individualistic type strategies.

No, both of those strategies are individualistic - that's the point, there's no such thing as ultimate teamwork.

#1 is individualistic for Player A. He benefits from that strategy at B's expense.
#2 is individualistic for Player B. He benefits from that strategy at A's expense.

They are both better for the team in some aspect, but both result from one player being greedy and hurting the other.

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05-30-2013 , 02:11 PM

#65

newguy1234

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Quote:

Originally Posted by RollWave

No, both of those strategies are individualistic - that's the point, there's no such thing as ultimate teamwork.

I don't know how the word ultimate nullifies teamwork, but irl there is certainly ability to see ourselves as a team and to work together to attain superior results that cannot be achieved without teamwork.

This isn't dependent on math not being able to represent it.

Isn't the issue that we don't know what this kind of 'teamwork' means?

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05-30-2013 , 02:21 PM

#66

RollWave

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Originally Posted by newguy1234

irl there is certainly ability to see ourselves as a team and to work together to attain superior results that cannot be achieved without teamwork.

and also the exact opposite, to work individually and to achieve superior results not attainable through teamwork.

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05-30-2013 , 02:27 PM

#67

newguy1234

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Quote:

Originally Posted by RollWave

and also the exact opposite, to work individually and to achieve superior results not attainable through teamwork.

You cant show this without showing first that we are not on the same team. We are not talking about a game.

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05-30-2013 , 02:32 PM

#68

RollWave

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Originally Posted by newguy1234

You cant show this without showing first that we are not on the same team.

This step is trivial. "we aren't on the same team". there, done. though i think your claim is actually false, and that it can be shown even for players on the same team.

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05-30-2013 , 02:36 PM

#69

newguy1234

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Quote:

Originally Posted by RollWave

This step is trivial. "we aren't on the same team". there, done.

I'm not talking about that level. That step can stand.

I am saying in observing models, the mathematician comes from the belief we are not all on the same team, this assumption clearly taints the mathematically validity of the models

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05-30-2013 , 02:47 PM

#70

RollWave

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Quote:

Originally Posted by newguy1234

I am saying in observing models, the mathematician comes from the belief we are not all on the same team, this assumption clearly taints the mathematically validity of the models

if you want to change the assumption to be for a team instead of an individual - that doesn't mean the individual's strategy won't still be optimal, just that it won't necessarily still be optimal.

the individual strategy still could be optimal even as a member of a team.

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05-30-2013 , 02:53 PM

#71

newguy1234

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Quote:

Originally Posted by RollWave

Yes, we cannot show that a non team strategy is better without making the individualistic assumption. And we don't need to define team or non team to show this.

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05-30-2013 , 03:00 PM

#72

RollWave

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Originally Posted by newguy1234

Yes, we cannot show that a non team strategy is better without making the individualistic assumption.

Are you just trying to make a head in the sand argument? That if people just play as a team and don't even try to play for themselves, then they will all do better because they don't even realize what they are missing?

If not, I fail to see the relevance of your current line. what's your point? Who care's if they have to make a different assumptions in order to compare different strategies?

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05-30-2013 , 03:01 PM

#73

newguy1234

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Quote:

Originally Posted by RollWave

Its shows you cannot extract morality from solving games in this manner.

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05-30-2013 , 03:07 PM

#74

RollWave

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Originally Posted by newguy1234

Its shows you cannot extract morality from solving games in this manner.

no it doesnt. if you think it does, please reconnect those dots because you have definitely skipped a few steps somewhere.

--
edit: oops, thought i was talking with someone else, didn't realize it was the op. nevermind, shoulda bailed long ago.

Last edited by RollWave; 05-30-2013 at 03:14 PM. Reason: doh