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# Game theory bayesian updating

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Given its ability to typically select only a unique equilibrium in games, the BEIC approach is capable of analyzing a larger set of games than current games theory, including games with noisy inaccurate observations and games with multiple sided incomplete information games.

the belief a player holds about another player's type might change on the basis of the actions they have played.

By my reasoning, the posterior distribution is not straightforwardly uniform since it is formed from a non-conjugate prior. Does it make sense to say $\mathscr|\pi^ \ \sim Uniform[-1,\pi^*]$ or should some other distribution be specified?

Alternatively is it possible that the answer to the problem contains an error? Bayes formula: $$p(t|\pi^*) \propto p(\pi^*|t)p(t).$$ Since $p(\pi^*|t)$ is

the belief a player holds about another player's type might change on the basis of the actions they have played.

By my reasoning, the posterior distribution is not straightforwardly uniform since it is formed from a non-conjugate prior. Does it make sense to say $\mathscr|\pi^ \ \sim Uniform[-1,\pi^*]$ or should some other distribution be specified?

Alternatively is it possible that the answer to the problem contains an error? Bayes formula: $$p(t|\pi^*) \propto p(\pi^*|t)p(t).$$ Since $p(\pi^*|t)$ is $1$ only when $t\in [-1, \pi^*]$ and $0$ otherwise, you get the resulting posterior.

And either way, does that change anything about the question -- I am genuinely asking this (I know that internet comments can come off as defensive and rude, but that's meant to be my tone here)As I said in the answer, the posterior is not uniform.

The model is fully specified, implicitly, in econ language.

||

the belief a player holds about another player's type might change on the basis of the actions they have played.By my reasoning, the posterior distribution is not straightforwardly uniform since it is formed from a non-conjugate prior. Does it make sense to say $\mathscr|\pi^ \ \sim Uniform[-1,\pi^*]$ or should some other distribution be specified?Alternatively is it possible that the answer to the problem contains an error? Bayes formula: $$p(t|\pi^*) \propto p(\pi^*|t)p(t).$$ Since $p(\pi^*|t)$ is $1$ only when $t\in [-1, \pi^*]$ and $0$ otherwise, you get the resulting posterior.And either way, does that change anything about the question -- I am genuinely asking this (I know that internet comments can come off as defensive and rude, but that's meant to be my tone here)As I said in the answer, the posterior is not uniform.The model is fully specified, implicitly, in econ language.The lack of information held by players and modelling of beliefs mean that such games are also used to analyse imperfect information scenarios.

$only when$t\in [-1, \pi^*]$and the belief a player holds about another player's type might change on the basis of the actions they have played.By my reasoning, the posterior distribution is not straightforwardly uniform since it is formed from a non-conjugate prior. Does it make sense to say$\mathscr|\pi^ \ \sim Uniform[-1,\pi^*]$or should some other distribution be specified?Alternatively is it possible that the answer to the problem contains an error? Bayes formula: $$p(t|\pi^*) \propto p(\pi^*|t)p(t).$$ Since$p(\pi^*|t)$is the belief a player holds about another player's type might change on the basis of the actions they have played. By my reasoning, the posterior distribution is not straightforwardly uniform since it is formed from a non-conjugate prior. Does it make sense to say$\mathscr|\pi^ \ \sim Uniform[-1,\pi^*]$or should some other distribution be specified? Alternatively is it possible that the answer to the problem contains an error? Bayes formula: $$p(t|\pi^*) \propto p(\pi^*|t)p(t).$$ Since$p(\pi^*|t)$is$1$only when$t\in [-1, \pi^*]$and$0$otherwise, you get the resulting posterior. And either way, does that change anything about the question -- I am genuinely asking this (I know that internet comments can come off as defensive and rude, but that's meant to be my tone here)As I said in the answer, the posterior is not uniform. The model is fully specified, implicitly, in econ language. || the belief a player holds about another player's type might change on the basis of the actions they have played.By my reasoning, the posterior distribution is not straightforwardly uniform since it is formed from a non-conjugate prior. Does it make sense to say$\mathscr|\pi^ \ \sim Uniform[-1,\pi^*]$or should some other distribution be specified?Alternatively is it possible that the answer to the problem contains an error? Bayes formula: $$p(t|\pi^*) \propto p(\pi^*|t)p(t).$$ Since$p(\pi^*|t)$is$1$only when$t\in [-1, \pi^*]$and$0$otherwise, you get the resulting posterior.And either way, does that change anything about the question -- I am genuinely asking this (I know that internet comments can come off as defensive and rude, but that's meant to be my tone here)As I said in the answer, the posterior is not uniform.The model is fully specified, implicitly, in econ language.The lack of information held by players and modelling of beliefs mean that such games are also used to analyse imperfect information scenarios.$ only when $t\in [-1, \pi^*]$ and [[

the belief a player holds about another player's type might change on the basis of the actions they have played.

By my reasoning, the posterior distribution is not straightforwardly uniform since it is formed from a non-conjugate prior. Does it make sense to say $\mathscr|\pi^ \ \sim Uniform[-1,\pi^*]$ or should some other distribution be specified?

Alternatively is it possible that the answer to the problem contains an error? Bayes formula: $$p(t|\pi^*) \propto p(\pi^*|t)p(t).$$ Since $p(\pi^*|t)$ is $1$ only when $t\in [-1, \pi^*]$ and $0$ otherwise, you get the resulting posterior.

And either way, does that change anything about the question -- I am genuinely asking this (I know that internet comments can come off as defensive and rude, but that's meant to be my tone here)As I said in the answer, the posterior is not uniform.

The model is fully specified, implicitly, in econ language.

||

the belief a player holds about another player's type might change on the basis of the actions they have played.By my reasoning, the posterior distribution is not straightforwardly uniform since it is formed from a non-conjugate prior. Does it make sense to say $\mathscr|\pi^ \ \sim Uniform[-1,\pi^*]$ or should some other distribution be specified?Alternatively is it possible that the answer to the problem contains an error? Bayes formula: $$p(t|\pi^*) \propto p(\pi^*|t)p(t).$$ Since $p(\pi^*|t)$ is $1$ only when $t\in [-1, \pi^*]$ and $0$ otherwise, you get the resulting posterior.And either way, does that change anything about the question -- I am genuinely asking this (I know that internet comments can come off as defensive and rude, but that's meant to be my tone here)As I said in the answer, the posterior is not uniform.The model is fully specified, implicitly, in econ language.The lack of information held by players and modelling of beliefs mean that such games are also used to analyse imperfect information scenarios.

]]$otherwise, you get the resulting posterior.And either way, does that change anything about the question -- I am genuinely asking this (I know that internet comments can come off as defensive and rude, but that's meant to be my tone here)As I said in the answer, the posterior is not uniform.The model is fully specified, implicitly, in econ language.The lack of information held by players and modelling of beliefs mean that such games are also used to analyse imperfect information scenarios.$ otherwise, you get the resulting posterior.

And either way, does that change anything about the question -- I am genuinely asking this (I know that internet comments can come off as defensive and rude, but that's meant to be my tone here)As I said in the answer, the posterior is not uniform.

The model is fully specified, implicitly, in econ language.