# Game theory bayesian updating

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.

on their available strategies or payoffs), but, they have beliefs with known probability distribution.

A Bayesian game can be converted into a game of complete but imperfect information under the "common prior assumption". Harsanyi describes a Bayesian game in the following way.

I was working through a signaling game problem recently and the proof suggested the following: Actor A has a type: $\ \mathscr \sim Uniform[-1,1]$ Actor A gives signal $\pi^*$ that perfectly seperates types at $\pi^$.

In other words, $pr(\pi^*|\mathscr\in [-1,\pi^*])=1\ \&\ pr(\pi^*|\mathscr\in [\pi^*,1])=0$ (this is the likelihood) Actor B observes $\pi^*$, yielding posterior beliefs about actor A: $\mathscr \sim Uniform[-1,\pi^*]$. It appears that this process, as i read it, has the same prior and posterior distributions (uniform), yet the likelihood distribution is unspecified and the uniform is not a conjugate prior for any common distribution.

But if she decides to hunt for deer, she faces the possibility that her partner abandons her, leaving her without deer or hare. Two people playing chess is the archetypical example of an interactive situation, but so are elections, wage bargaining, market transactions, the arms race, international negotiations, and many more. Its fundamental idea is that an agent in an interactive decision should and does take into account the deliberations of her opponents, who, in turn, take into account her deliberations.

In addition to the actual players in the game, there is a special player called Nature.

Nature assigns a random variable to each player which could take values of types for each player and associating probabilities or a probability mass function with those types (in the course of the game, Nature randomly chooses a type for each player according to the probability distribution across each player's type space).

Consider the following situation: when two hunters set out to hunt a stag and lose track of each other in the process, each hunter has to make a decision.

Either she continues according to plan, hoping that her partner does likewise (because she cannot bag a deer on her own), and together they catch the deer; or she goes for a hare instead, securing a prey that does not require her partner’s cooperation, and thus abandoning the common plan.