Mario Kart–Game Theory and More
Mario Kart is racing video game. However, it is not that simple–scattered along the course are boxes with question marks on them, which once a player drives through them, provide them with either an offensive or defensive item that will help them get ahead. In this article William Spaniel, a postdoctoral fellow at Stanford, discusses the multiple aspects of game theory behind Mario Kart, from prisoner’s dilemma circumstances to auctions.
One of the topics Spaniel discusses is the game mechanics behind picking which race course to use. In the Mario Kart system, each player submits their choice for what race track they want to play, and then the system randomly selects a player and everyone plays the course that the chosen player selected. Thus, Spaniel asserts that picking your favorite course is a dominant strategy: “you don’t have to worry about what everyone else will pick. After all, if the game randomly selects your choice, then you are best off picking your favorite track; and if it chooses anyone else, then your selection is irrelevant.” This is is somewhat similar to the situation of an ascending bid auction–in that scenario, the dominant strategy is to bid your value, regardless of what the other bidders are doing because if you lose, your bid did not matter anyway but if you win you stand to make a positive payoff. Likewise in Mario Kart, it is every player’s dominant strategy to simply cast their vote for their favorite race course because their vote only matters in the event that they win.
Game theory also comes into play when players consider what to do when approaching item blocks. Spaniel states, “item blocks give better items as a player’s position increases. So . . . there is a great incentive to gently press the brakes, fall back to fourth, and get three mushrooms instead of the banana peel instead.” In this scenario, since both players wants a better item, the dominant strategy for both is to slow down a little so that they are in last place within their group of two, regardless of what the other player is doing. Thus, they both slow down and both fall further behind. This is an example of how people will play their dominant strategy, even if it is to the detriment of both of them. This is analogous to the prisoner’s dilemma, where confess is a dominant strategy and both of the prisoners should play it even though they would both benefit more from not confessing. And in Mario Kart, both players would benefit from not falling behind, but they both do it because it is better than if one of them does slow down to get the better item and the other one does not.
Lastly, the format of Mario Kart racing demonstrates the Structural Balance Theory and the Balance Theorem. In Mario Kart, the configurations of the different players gravitate to a balanced state. For example, in a race with three competitors, the network begins as one with three negative edges between all three nodes, but as soon as one of the players pulls into the lead, the other two form an alliance and team up against the first place racer, showing how the unstable configuration of three negative edges transitions into a stable one, with one positive edge and two negative edges denoting two allies and a mutual enemy. Balanced networks are also seen in team races in Mario Kart, where players are divided into two teams and compete against each other. Here, it is a balanced network because each player has a positive edge to every other player on their team but a negative edge to every player in the opposing team, satisfying the balance theorem.