5
So $h$ is just some history of the game.
Consider the following game, where Player 1 first decides Heads or Tails, then depending on his choice, a coin is flipped whose outcome and probabilities depends on the choice of Player 1.
An example of a history $h$ is $h = Heads$, i.e. after heads is chosen.
Consider the very beginning of the game, before Player 1 ...
4
Bayes Correlated Equilibrium characterizes (by Theorem 1 in the paper) what can happen in a Bayes Nash Equilibrium in which the players might have more information than is specified in the Bayesian game.
One way to think of it is that some "omniscient mediator" figures out what the agents would do with the additional information and simply tells ...
3
There is no guarantee that a random game can be solved by an easy trick. (For an example see Kuhn poker.)
Did you study something like this in class? If yes, was there a step-by-step method the teacher followed? Perhaps the steps were not designated as steps, but if you look back on it, you may realize that is what they were? If yes, you should probably ...
2
A direct revelation mechanism is one in which a player's type space is also their action space ($X_i=T_i$ for all $i$) and the outcome function is the same as the social choice function ($a(t)=f(t)$ for all $t\in T_1\times\cdots\times T_n$).
1
Perfect recall means that every player remembers her own history.
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