$A$ and $B$ are playing a dice game. They both roll a standard 6 sided dice once, but they cannot see the outcome. Then, there is a box containing money equal to the sum of the outcome of the two dices. Then $A$ and $B$ need to bid to buy the box.
For example, if $A$ rolls 3 and $B$ rolls 4. Then the box will contain 7 dollars. However, for now, without knowing any outcome of their rolls, $A$ needs to give a price to buy the box. Then $B$ can give another price. The one with the highest price will get the box and dollars in the box. Do you want to be the first to bid or the second to bid? What is the optimal strategy?
If now $A$ and $B$ can see the outcome of their rolls respectively, but cannot see the other player's outcome. Do you want to be the first to bid or the second to bid? What is the optimal strategy?
I suppose for the first scenario, being the first to bid is advantageous since you can bid 7, which is the expected value of the sum of two dices and there is no reason for the second player to bid a price higher than this.
For the second scenario, being the second to bid seems advantageous since you can obtain information from the bid of the first player.