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2

Would be strange to write it that way. If you had to define something like that, just do the following: Start with a type space $(T,\mu)$ with probability measure $\mu$. Let $\sigma: T \rightarrow \Delta(A)$. Then $\mathbb{P}(a) =\mu(\sigma^{-1}(a))$.


5

First, the Sonnenschein-Mantel-Debreu theorem has nothing to do with demand functions. It is a result about excess-demand functions, which represent demand minus supply. They are formulated in the context of an exchange economy in which no production happens. The result says that if one only looks at prices that are not too close to zero, any continuous ...


6

So recently I have been thinking a lot about this fundamental question: Does the Sonnenschein-Mantel-Debreu theorem disprove the "Law of Demand"? It contradicts law of demand as a general law but it is worth noting that the law of demand is for over a century not considered actual general law but just a special case that is simply applicable to ...


3

You take $p$ to be the corresponding correlated equilibrium with $A_k$ being the strategy space of player $k$ Conditions 1. and 2. mean that each player can compute the prescribed action they should play and that they do not know more than this prescription would give them. This is exactly what a correlated equilibrium requires (together with optimality, of ...


4

You got to the quadratic equation $$ \lambda^2 - (\rho - n)\lambda + \frac{c^\ast f''(k^\ast)}{\varepsilon} $$ The discriminant is given by: $$ \Delta = (\rho - n)^2 - 4 \frac{c^\ast f''(k^\ast)}{\varepsilon} $$ So the two roots are: $$ \lambda_1, \lambda_2 = \frac{(\rho - n) \pm \sqrt{(\rho - n)^2 - 4 \frac{c^\ast f''(k^\ast)}{2}}}{2} $$ As $f''(k) < 0$ ...


4

To answer the first part of your question, we do not need any more assumptions for the comparison of experiments (besides some measurability issues). Before going on, I'll fix some notations to ones that are standard in the game theory literature, and for the sake of my convenience. An experiment (or informtion structure) is defined as a tuple $(S,\pi)$ for ...


0

So if I understand it correctly, the cryptocurrency basically represents a certain amount of your physical asset. Assuming you/your team is not seeking to reinvent the wheel, you could use an ERC20 (or higher) token protocol to implement this, though you would need an oracle to gather data from the non-blockchain world, which could be difficult depending on ...


1

Looking at the numbers again plan B is simply worse (assuming a non-negative interest rate). In any specific month you look at, you have to pay no less under plan B than under plan A.


0

I think I understood your question. You want a mechanism through which the government and the owner of the non-monetary asset interact in such a way that the tax charged is "fair", right? If this is correct I think the issue here is to define what would be a "fair" tax, and in your question you are assuming that fairness will be for the ...


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