Identify this card game, where you have to beat previous cards put on the table

Question

I remember playing this card game using a regular card deck but I don't remember the exact rules and also don't know what it's called. If it helps, I live in the Netherlands so it might not be known anywhere else. If the Dutch name of the game is known that would also be great.

This is what I remember.

• I think it must be played with at least 3 people, but the more the better I think.
• Everyone is dealt an amount of cards. (I don't remember what amount)
• The player whose turn it is lays down a card. Or multiple cards with the same rank.
• The next player should then put a higher card on the table and when there are multiple cards he should put the same number of cards that are all of the same rank and of course higher.
• At any time before the next player responds to some cards any other player may throw in a card of the same rank to make it harder for the player to beat it.
• I can't remember what exactly happens if you can't beat it. But I believe that it just meant that the player that won is able to lay down the next card(s) on the table to start a new chain.
• I also don't remember what the exact goal of the game was and when (if even) a player could draw new cards.
• I also believe the terms "attack" were used but I'm not 100% sure

Example with 4 players (as I remember it):

1. player one lays down a 7.
2. player two lays down a 8.
3. before player three responds player one throws in another 8
4. player three lays down two 10s. (to be able to beat two 8s)
5. and so on

I can also imagine this is a game that has multiple rules variations. If anyone knows what this game is called and what the exact rules are , that would be great.

Answer 1

It is called President and goes by many different other names, most of which are better not mentioned here. A rule you forgot to mention is that the winning player(s) from last round get the best cards of the loosing player(s).

Here you can find all the details with many variants

Answer 2

There's a similar game in Japan that goes by the name daifugo.

The two main differences versus your description are that

1. people cannot jump in randomly (proceeds clockwise unless people pass because they cannot play).
2. playing four cards of a kind causes a reversal of the winning hands (from 3 up to A, 2 becomes from 2, A up to 3).

Separately, there are lots of variants. In daifugo, 8s often have a special meaning of leading to a stop.