Fighting Games: More Fighting or more Game (Theory)?
As with all competitive video games, fighting games display a deeper level of game theory that most people give them credit for. Here, we investigate the underlying theory behind decision making in the video game Super Smash Bros. The articles I will be referencing use Street Fighter, another popular fighting video game, to illustrate these concepts, but the ideas are the same.
Let’s take a specific scenario where two players have three options to select from: Attack, Block, and Grab. The three options form a relationship similar to that of Rock-Paper-Scissors – Attack beats Grab but loses to Block, Grab beats Block but loses to Attack, Block beats Attack but loses to Grab, and the same selection results in a tie. From here, we can create a 3×3 matrix with rows representing the option Player 1 selects, and columns representing the option Player 2 selects. Note that instead of using words like “Win” or “Lose” to describe the relationships, we quantify them, using -1 in place of losing, 1 in place of winning, and 0 in place of a tie
While this may seem simple enough, there is another dimension of depth that is rarely mentioned – that is, the payoffs of each scenario may be different. For example, the payoff for winning by attacking may be greater than the payoff for winning by blocking. If we arbitrarily adjust the above matrix to represent this, we might see something more like
Now, the matrix is unbalanced in a sense, and player decisions really boil down to unpredictability and/or guessing their opponent’s moves. For instance, assuming that Player 2 does not have information to this chart, Player 1 might want to always Attack since the expected payoff is positive. But, since both players are in the same position and form a chart like the one above in their mind, Player 2 will counter Player 1’s constant Attacking by constantly Blocking. In a similar manner, Player 1 might suspect this and will counter Player 2’s counter play by himself opting to mix in a few Grabs to remain unpredictable.
Essentially, video games such as Super Smash Bros are really just a glorified and repeated version of Rock-Paper-Scissors. Each player may have general information on the payoffs of certain options but will not always choose the “best” option as a means of remaining unpredictable.
Sources:
http://suburbanlion.com/blog/2010/04/22/street-fighter-mathematics/
https://www.polygon.com/2014/7/7/5876983/how-to-play-street-fighter-fighting-game-primer