Is this improvised card game is a known game?

Question

I'm looking for the name of the improvised card game for two players with the following rules:

• Each player gets 13 cards numbered from 1 to 13 (These could also be from Ace to King).
• Both players play a card and place it upside down on the middle of the table, and then turn their cards. The player with the higher number wins the round and scores one point. If the values are equal, no one scores a point. The player with the most points at the end of the game wins.

I have tried searching by description (''card game the card with the higher number wins''), but without success.

Answer 1

Since players choose their next card it is a variant of Colonel Blotto game (unlike in War where players just pick the top card in their deck).

In Colonel Blotto, players are tasked to simultaneously distribute limited resources over several battlefields. The player devoting the most resources to a battlefield wins that battlefield. The player that won the most battlefields wins the game.

In your variant, players contest over 13 battlefields. Each side poses 1+2+...+13=91 resources (armies), however they must assign the resources to battlefields in set amounts (the value of cards).

Answer 2

What you describe sounds very similar to 'War' or 'Battle'. There seems to be many different versions of this game such as this here and other examples on wikipedia.

The basic rule in these games is player simultaneously reveal a card and the highest ranked card get a point/ cards added to their deck which is what you described.