Game Theory in Video Games (Blog Post II)
I wanted to provide an example of how game theory is applied today that is relatively simple to understand.
So, as most of you may know, Pokemon is pretty lit. For those who’ve been living under a rock their entire lives, Pokemon is a turn-based battling game where where two players, each with 1–6 pokemon, pit their magical animal-things against each other until one team beats the other into complete unconsciousness. Usually, the pokemon face off in 1-on-1 battles with the player having the option to either attack or switch the active pokemon with another on the team, given he has more than one pokemon.
Each individual pokemon owns a type (or combination of types), like Water type or Ghost/Fire type, and is assigned a set of four moves meant to damage the other pokemon or manipulate the dynamic of the battle. Damaging moves are labeled as “not very effective,” normally effective, or “super effective,” denoting their strength when they strike a pokemon of a certain type. Water, for instance, is “super effective” against Fire type pokemon, so water moves do more damage against Fire types, but are “not very effective,” or are weak against Grass type pokemon.
The other player may or may not know what pokemon compose the other player’s team, depending on the context of the battle. However, neither player knows the move sets of the opponent’s pokemon until the moves are used in battle.
These are just some of the rules in place that make Pokemon a strategy game. Hence, game theory can be applied here. To provide an example, let’s say we have a Ground Type pokemon facing off against a Water/Electric type pokemon: The players each have another pokemon of a different type in the party.
Each value in the payoff table represents the benefit granted to Player 1 given the chosen actions of both players. For simplicity’s sake, I made this a zero-sum game where the benefit of one player is equal to the losses of the other. Accordingly, the negative of each value in the table represents the payoff of player two in that given scenario. It should also be noted that this assumes both players have learned each other’s movesets.
At first glance, it seems unclear who has the advantage. Player 1, a ground type pokemon, has an advantage over Player 2, a water/electric type, since ground is super effective against electric and electric moves don’t affect ground pokemon. Steel moves, though, are not very effective on both water and electric types, making the move nearly useless to use against the water/electric pokemon. Both of Player 1’s other moves are normally effective against water/electric.
Player 1’s ground typing essentially renders Player 2’s electric move useless, lowering the amount of viable actions Player 2 can make. On the other hand, Player 2 is a water type pokemon, which is super effective against ground types. It also has an ice move, which would also do double damage against the ground pokemon, and a healng move, which restores the same amount of damage that a normal move would do. It can be concluded that Player 1 has preferable typing, but Player 2 has an advantage in its movepool.
Recall that each player also has the option to forfeit their option to attack for a chance to switch in to their other pokemon. One can tell by looking at the table that this is where Player 2 has another huge advantage. Since flying pokemon are immune to ground moves, switching into the flying pokemon would be the wisest move on Player 2’s part as it eliminates a viable move on Player 1’s end.
However, if Player 1 knows that Player 2 has a flying pokemon, he could instead use a rock move, which would normally do normal damage to the water/electric type but would be super effective to the flying type. So he might take the risk of lowering possible damage to the water/electric type to potentially maximize damage to the flying type.
So yeah, that’s an example of game theory and how it’s applied.
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