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        riddles >> general problem-solving / chatting / whatever >> Game Theory: discussions
        
(Message started by: BenVitale on Jul 17^th, 2009, 12:49am)

Title: Game Theory: discussions
Post by BenVitale on Jul 17^th, 2009, 12:49am

Take this simple test ... and find out how rational you are :

Imagine that each of your three fabulously wealthy cousins offers you a choice of two Christmas gifts. In each case, choose the one you'd prefer.

1. Cousin Snip offers you a choice of :

A. $1 million in cash.

B. A lottery ticket. The ticket gives you a 10-percent chance of winning $5 million, an 89-percent chance of winning $1 million, and a 1-percent chance of winning nothing at all.

2. Cousin Snap offers you a choice of :

A. A lottery ticket that gives you an 11-percent chance of winning $1 million.

B. A lottery ticket that gives you a 10-percent chance of winning $5 million.

3. Cousin Snurr offers you a choice of :

A. $1 million in cash.

B. A lottery ticket that gives you a 10/11 chance of winning $5 million.

P.S. "Rational" does not mean "risk-neutral"

Title: Re: Game Theory: discussions
Post by pex on Jul 17^th, 2009, 1:49am

http://en.wikipedia.org/wiki/Allais_paradox

Title: Re: Game Theory: discussions
Post by Grimbal on Jul 17^th, 2009, 6:40am

Is it allowed to buy an insurance against loosing?

Title: Re: Game Theory: discussions
Post by BenVitale on Jul 17^th, 2009, 5:47pm

on 07/17/09 at 06:40:44, Grimbal wrote:

Is it allowed to buy an insurance against loosing?

The problem as stated does not ask us to consider "buying an insurance"

It is interesting though, we could add that element, as we could add other elements, such as 'regret' because you're asked to choose between a sure thing and running the risk to lose by choosing a not-so-sure thing.

Title: Re: Game Theory: discussions
Post by BenVitale on Jul 17^th, 2009, 5:52pm

on 07/17/09 at 01:49:52, pex wrote:

http://en.wikipedia.org/wiki/Allais_paradox

Yes, but there's more to it ...

Economists and game theorists seem to disagree on this problem.

Here's the same problem stated a bit differently:

A is the certainty of winning 100, and
B is a 10% chance of winning 500

do you prefer A over B?

C is an 89% chance of winning 100; and
D a 1% chance of winning nothing

do you prefer C over D?

Earlier analysis of game theory had suggested that in the following example, the preference of A over B should entail a preference of C over D.

Allais stated, however, that many sensible people who wanted A over B would choose D or C, suggesting a paradox