Definition:Card Game with Bluffing

Definition
The card game with bluffing is a class of games which is exemplified by the example whose mechanics are as follows:

There are two players: $A$ and $B$.

First it is $A$'s move.

$A$ receives one of two possible cards: either the high card or the low card.

If he receives the high card, he must bid $2$ credits.

If he receives the low card, he has two options, either:
 * $A (1): \quad$ He may pay $1$ credit, and the play is complete.

or
 * $A (2): \quad$ He may bid $2$ credits.

If $A$ has bid $2$ credits, it is $B$'s move.

$B$ has two options, either:
 * $B (1): \quad$ He may pay $1$ credit

or
 * $B (2): \quad$ He may challenge $A$'s bid.

If $A$ had the high card, $B$ must pay $2$ credits to $A$.

If $A$ had the low card, $A$ must pay $2$ credits to $B$.

The play is complete.

Payoff Table
The payoff table of the card game with bluffing is as follows: