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        riddles >> general problem-solving / chatting / whatever >> 2 problems in decision making 
        
(Message started by: BenVitale on Sep 19th, 2009, 10:55am)
Title: 2 problems in decision making
Post by BenVitale on Sep 19th, 2009, 10:55am
I'm currently working on 5 problems in game theory: 4 problems in decision making theory and 1 in auction theory (I'm in the process of constructing the problem in auction theory).

Decision making, Problem #1 :

Imagine that you have decided to see a play where admission is $20 per ticket. As you enter the theater you discover that you have lost the ticket. The seat was not marked and the ticket cannot be recovered. Would you pay $20 for another ticket?

Result: 54% of people asked said 'No'

Imagine that you have decided to see a play where admission is $20 per ticket. As you enter the theater you discover that you have lost a $20 bill. Would you still pay $20 for a ticket to the play?

Result: 88% of people asked said 'Yes'

But in both problems, the final outcome is the same if you buy the ticket: you have the same amount of money and you see the play. Why should these cases differ?

Decision making, Problem #2 :

Imagine that you are about to purchase a jacket for $250, and a calculator for $30. The calculator salesman informs you that the calculator [jacket] you wish to buy is on sale for $20 [$240] at the other branch of the store, located 20 minutes drive away. Would you make the trip to the other store?

Results:

- 68% of people are willing to make extra trip for $30 calculator
– 29% willing to make extra trip for $250 jacket

Note that you save same amount in both cases: $10. Why is there a discrepancy?


Note also that choices in games should always reflect what is best for the decision maker, i.e. what will maximize the decision maker’s payoff
Title: Re: 2 problems in decision making
Post by towr on Sep 19th, 2009, 3:09pm

on 09/19/09 at 10:55:12, BenVitale wrote:
Imagine that you have decided to see a play where admission is $20 per ticket. As you enter the theater you discover that you have lost a $20 bill. Would you still pay $20 for a ticket to the play?
Money is fungible. Loosing $20 is not the same as loosing the twenty dollar reserved for the theater ticket. Additionally, it may only be misplaced; if found again the money retains its value. A Theater ticket is only worth anything at the moment it can be used, if misplaced at that time it is worth nothing ever after.
Of course the reality of it is more likely just psychological impact. Which has little or nothing to do with game theory or rational decision making.
Try functional MRI to find out what's really going on in people's brain when they think about these things.


Quote:
Note that you save same amount in both cases: $10. Why is there a discrepancy?
If you buy $240 worth of calculators, you'll safe $80.
It is better to safe 33% on things you buy than 4%. Although factoring in the cost of driving for 20 minutes, it is almost certainly not worth it in either case. (Gas, wear and tear on the car, time lost which could be spend doing something else)
Title: Re: 2 problems in decision making
Post by BenVitale on Sep 21st, 2009, 3:46pm

on 09/19/09 at 15:09:36, towr wrote:
Of course the reality of it is more likely just psychological impact. Which has little or nothing to do with game theory or rational decision making.


Well, I'm sorry to disagree with you.


Quote:

Try functional MRI to find out what's really going on in people's brain when they think about these things.

Ouch! Should I just stop posting such questions/puzzles?
Title: Re: 2 problems in decision making
Post by towr on Sep 22nd, 2009, 1:37am

on 09/21/09 at 15:46:12, BenVitale wrote:
Well, I'm sorry to disagree with you.
What can I say; it's what neurological and psychological research shows. These aren't rational decisions; most likely the mind has made up its mind before you think about it.


Quote:
Ouch! Should I just stop posting such questions/puzzles?
I'm not sure what's "ouch!" about that statement. People's brains are just wired in strange and wonderful ways. Strange because they don't work as rational theories prescribe, wonderful because they work very well and efficiently in most circumstances.
I suspect the decision about the theater ticket and ticket-money are not even made in the same brain regions. Which is why I say, look at it with fMRI. Then you can see which part of the brain is making the decisions here.
When seemingly similar problems are dealt with by different parts of the brain, then you're likely to get different results. That's also why people are bad at dealing with abstract logic problems, but fairly good at solving the same problem in a social context. A canonical example of this is the Wason selection task (http://en.wikipedia.org/wiki/Wason_selection_task).
Title: Re: 2 problems in decision making
Post by BenVitale on Sep 23rd, 2009, 12:38pm
Yeah, and adding to your post.

I'm posting keywords to help whomever might be interested in behavioral economics and mathematical economics.

- Behavioral economics (http://en.wikipedia.org/wiki/Behavioral_economics)
- Logistic function, the S-Shaped curve (http://en.wikipedia.org/wiki/Logistic_function)
- Utility (http://en.wikipedia.org/wiki/Utility)
- Expected utility hypothesis (http://en.wikipedia.org/wiki/Expected_utility_hypothesis)
- The Prospect Theory (http://en.wikipedia.org/wiki/Prospect_theory)
- Read the Experimental demonstration: Framing (social sciences) (http://en.wikipedia.org/wiki/Framing_(economics)#Experimental_demonstration)

These 2 problems/scenarios deal with the abovementioned concepts.

The Expected utility theory assumes rationality, and that the net benefit, or utility, we gain from an outcome is the weighted sum of the utilities of the outcomes, multiplied by their probability of occurrence.
But this model fails to provide a good description of how people make choices in many circumstances

Unlike expected utility theory, prospect theory says that we value gains and losses differently.

These 2 problems are also an illustration of the concept "Framing" ... The way in which the question is worded or "framed" can affect the outcome of choice problem, as shown in the "Experimental demonstration" (wikipedia article, posted above) ... A problem framed (as a gain or loss) can cause us to deviate from the behavior predicted by expected utility theory.

In the "Experimental demonstration" (wikipedia article), notice how the framing makes the difference. A and C are the same, and B and D are the same.

Consider this: GoodYear and Dunlop (http://www.fountaintire.com/) are offering 4 tires for the price of 3.

What if the offer was : one free with three purchased.

Would consumers behave differently?


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