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If you draw the corresponding game tree, you will see that "equivalent to simultaneous move game" implies that the game has no proper subgame and the only subgame is the whole game.
This is because the information set of the second player covers every move of the first player.
Therefore, every Nash equilibrium is trivially also subgame perfect.
6
Disclaimer: My academic coming of age was in an environment where behavioral economics played only a minor role. My research is theoretical, both "behavioral and non-behavioral", economcis.
I believe it is incorrect to say that game theorists (or economists) in general are not convinced by behavioral economics. You can easily see it is considered ...
5
There is also no NE which sustains coopration for more or less the same reason as in the SPNE case.
Consider, a PD played twice. A strategy contains five actions, one for each decision node: one in the beginning (empty history) and one for each of the four period-2 histories (CC,CD,DC,DD). I claim that any strategy other than (D;D;D;D;D) is dominated.
...
5
There are a lot of game theorists quite open to many versions of behavioral economics. That being said, I think there are some reasons why these are still fairly separate areas. I will focus in particular on the issue of rationality.
Parts of behavioral economics simply do standard economics with somewhat different preferences, such as other-regarding ...
4
Just for sake of acknowledgement, please note that the game described in the question is a variation of the famous Ultimatum game. Knowing this can help you get a ton of literature on such games.
Further note that your professor has made an extremely important point that coming up with answer is sufficient, solving is not necessary. My answer is also limited ...
4
I know a bunch of people who teach behavioral economics using Erik Angner's book.
I love Rani Spiegler's book on behavioral economics in IO called "Bounded Rationality and Industrial Organization." Both books will introduce models that can be applied to poker.
Perhaps a little lighter but still scientific readings would be Kahneman's "Thinking,...
4
The two (pure) Nash equilibrium in this game is (Betray, Silent) and (Silent, Betray).
Let us see why (Betray, Silent) is an equilibrium.
Let us look at person A.
Person B is playing Silent.
If she plays Betray, she gets $2$.
If she deviates to Silent, she gets $1$. So she would not play Silent.
Now consider person B.
Person A is playing Betray.
If she ...
4
Take any $a\in(0,3)$.
Since $a>0$, X is a best response (BR) to x. Since $a<3$, Y is BR against y, and Z is BR against z.
Similarly, x is BR against X, z against Y, and y against Z.
Hence, your only pure strategy NE is (X,x). The latter is also true if $a=3$.
If $a>3$, X and x are strictly dominant strategies such that (X,x) is the unique NE.
Now ...
4
Yes. There are no proper subgames then, so all NE are trivially SP.
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It's well known that if $\succsim$ satisfies independence, then it is also convex.
Since $\succsim$ satisfies independence,
$L\succsim L^{'} \iff \alpha L$ $+$ $(1-\alpha)L^{''}$ for all $\alpha \in \left[0,1\right]$ and $ L, L^{'}, L^{''}\in \mathfrak{L} $
Convexity requires:
$L\succsim L^{''}$ and $L^{'}\succsim L^{''} \Longrightarrow \alpha L$ + $(1-\...
3
If a sequential game can be validly represented in the 'normal form' then that means the game has only one sub-game - the whole game. In that case any NE is also SPNE.
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This depends on the kinds of beliefs players can have about their opponents’ play. If opponents' strategies can be correlated, then the strategies surviving IESDS are exactly the rationalizable ones. But if you only allow opponents to choose independently (this is the standard approach in most textbooks), then these two sets are identical for 2-player games ...
2
You are making the mistake of looking at the problem, seeing some numbers, and thinking those are the payoffs. It's a common mistake for novices in game theory to treat the numerical gain as being the same as utility. The payoff for a result in this game is not the number of yards gained, but the probability of a win. That is, for each square in the payoff ...
2
It seems that there is already some prior work on theory of gamification from game theory perspective. For example, Easley & Ghosh (2016), provide theory on optimal badge design even explicitly mentioning sites like StackOverflow and their paper seems to be highly cited. Hamari, Huotari & Tolvanen (2015) have article titled "Gamification and ...
1
The trick for finding a mixed strategy Nash Equilibrium is that given everyone else's strategies, all players will be indifferent between each of the options their randomizing over (ie. those options will yield the same payoff). So all you need to do is write an expression relating each player's expected payoffs for each strategy, and solve for the ...
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