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3

Adding to @soslow's answer: once you have an SPE, it should be easy to construct a non-subgame-perfect NE by modifying the off-equilibrium actions in such a way that 1) the players have no incentive to deviate to those actions and 2) the action profile is not a NE in any subgame. For example, one SPE of the game is play $(A,A)$ in stage 1, and play $(A,A)$ ...

4

Check for the Nash equilibria (pure or mixed) of the one-shot game. Repetition of the strategy profile of the Nash equilibria of the one-shot version yields one set of subgame perfect equilibria: For instance, play $(A,A)$ in the first stage and for any action profile played at the first stage, play $(A,A)$ in the second stage. The same holds true for the ...

5

Since you mention IEWDS, I presume by "dominant" you actually mean "dominated". Any strictly dominated strategy would satisfy the condition defining weakly dominated strategies and hence be called such. And yes, strictly dominated strategies can (and should) be eliminated in the process of IEWDS. The possible typo notwithstanding, any ...

0

I am not sure that I am able to fully answer your problem, but I can give you a short answer to your questions. "Aren't these games simultaneous games? Why would the players consider the choices made in the first game to play the second game?" I would refer to collusion and repeated games. Every stage game is simultaneous, but the fact that they ...

7

If in equilibrium, a player "chooses a mixed strategy" that plays $H$ and $T$ with positive probability, $H$, and $T$ must be both optimal choices. It is a standard result that for a (subjective or objective) expected utility maximizer, randomizing can only be optimal if it is over pure optimal choices. This is a direct consequence of expected ...

5

The real-life question is "how do you persuade people to use mixed strategies"? To stick with your example, Consider a person that has to make a binary choice $(H, T)$, and, after contemplation, they conclude that the optimal strategy is the mixed strategy $(2/3, 1/3)$. I have never know of anyone putting two red and one blue ball in a vase and ...

2

tl;dr: Short answer is that cardinal utility of rational person is in large part of a literature is derived from the von Neumann and Morgenstern expected cardinal utility framework. In such framework utility must be bounded by our definition of what rationality is. So in such framework the short answer is simply that utility has to be bounded for person to ...

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