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bio website jeremybejarano.wordpress.com
location Provo, UT
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visits member for 1 year, 11 months
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Jun
4
comment The potential function of Prisoner's Dilemma
I'm not sure what you mean by potential. The numbers here refer to the length of the sentence, e.g. years in prison. So, each player wants to minimize what they get.
May
12
comment How do we determine the saddle point in game theory?
Yeah, that's backwards.
Apr
1
accepted Variance of Martingale Difference Sequence
Apr
1
comment Variance of Martingale Difference Sequence
Agh. I'm sorry, I should have seen that. Thanks for the help.
Apr
1
asked Variance of Martingale Difference Sequence
Mar
21
comment Strictly Convex and Strictly Monotonic Preferences
And no problem. If you're satisfied with the answer (and the answer of the other question), just be sure to press "accept". ;) Thanks!
Mar
21
comment Strictly Convex and Strictly Monotonic Preferences
I am not raising every dimension of the vector. The expression $t x + (1-t) y \leq x$ is correct as it stands. $<$ would not make sense because $x$ and $y$ are vectors. $<<$ would make conform to the fact that these are vectors, but like you mentioned, I am not raising every dimension. So $\leq$ is appropriate. As for the definition, Martin has pointed out that the definitions vary a lot. So, my proof is careful to provide the definition that it relies. on. The proof would work just as well with the alternative definition that you gave, after adjusting the assumptions.
Mar
21
revised Strictly Convex and Strictly Monotonic Preferences
small typos
Mar
20
comment Markov chain problem, Help!
You are supposed to choose p0. The question asks you to "how does your answer depend on the initial state." That means, choose a couple different values of p0 and see what happens.
Mar
19
revised Strictly Convex and Strictly Monotonic Preferences
added 920 characters in body
Mar
19
comment Strictly Convex and Strictly Monotonic Preferences
You're right about strong monotonicity. It is correct, however, in my solution below. However, I think there is definitely agreement between strict and strong, as the same concepts appear elsewhere and more generally in mathematics. (Check me if I'm wrong.) See wikipedia. I believe the idea is that strongly convex means that strictly increasing the quantity of at least one good strictly increases utility. Strict convexity means all goods must be increased to guarantee strictly more utility. en.wikipedia.org/wiki/Convex_function#Strongly_convex_functions
Mar
19
answered Strictly Convex and Strictly Monotonic Preferences
Mar
19
comment Strictly Convex and Strictly Monotonic Preferences
Also, just to note, a "preference" relation is usually defined as a binary relation that is complete and transitive. The other properties are assumed so that we can derive "demand functions." We want the consumer's constrained maximization problem to produce a unique solution that is continuous in prices (among other properties).
Mar
19
comment The implications of Completeness and the Continuity axiom for utility representation
Cool, no prob. Glad it helps. Also, if the answer looks ok, could you "accept" it?
Mar
18
comment Strictly Convex and Strictly Monotonic Preferences
What you call "strictly monotonous" should instead read "strongly monotonic." Preferences that are strongly monotonic state that when $x \geq y$ and $x \neq y$, then $x \succeq y$. Preferences that are strictly monotonic when $x \geq y$, then $x \succeq y$ and when $x >> y$, $x \succ y$.
Mar
17
comment The implications of Completeness and the Continuity axiom for utility representation
Like I said, consider "Lexicographic preferences." For example, say there are two categories of goods, $x$ and $y$. I like $B_1 =(x_1, y_1)$ better than $B_2 = (x_2, y_2)$ when $x_1 > x_2$. When $x_1 = x_2$, I like $B_1$ more when $y_1 > y_2$. Certainly these preferences are complete. I can compare any bundle. However, they're not continuous. For all $n \geq 1$, $(2 + 1/n, 0) \succ (2,1)$. But $(2 + 1/n, 0) \xrightarrow{n} (2,0) \prec (2, 1)$. So the set $\succeq (2, 1)$ is not closed.
Mar
12
answered The implications of Completeness and the Continuity axiom for utility representation
Dec
4
comment When can we interchange the derivative with an expectation?
Where could I find information about when such an operation is ok?
Nov
25
comment Nash Equilibrium in Cournot Duopoly
I added an edit that should help. You can write the maximization problem out so that it's not in matrix notation. But it helps to see the general principle. Hope this helps!
Nov
25
revised Nash Equilibrium in Cournot Duopoly
Added hint.