Game Theory — The Ultimate Analytical Tool for Game Developers

You must have played video games at least once in your lifetime. What makes a game stand out from the rest? Is it their beautiful graphics or breathtaking map design? Is it an engaging plot that makes you crave for more content?

When playing a game of Valorant, you might think about saving your weapon so that you have something to rely upon the next round. There are many Candy Crush fanatics out there that will tell you to save up your power ups to get out of difficult levels. Human Psychology plays a big role in converting a game from a bunch of assets put together to making it an industry standard game.

Game Theory emphasizes on analyzing the human brain and simplifying the complex decisions they make while playing the game. This data is essential to how you structure your game and make it enjoyable. Game theory takes a grandstanding upon one philosophical concept, Nash’s Equilibrium.

Nash’s equilibrium : A Paradoxical Situation

It was named after John Forbes Nash Jr. , one of the most well known mathematicians in the game industry. Nash’s Equilibrium discusses a scenario in which no person in a non cooperative game has anything to gain by changing only their strategy.

This situation is excellently described by “Prisoner’s Dilemma”, a real life setting where two accomplices to a crime are stuck in a jail cell and have two options to go about it. Fess up and reduce their sentences, stay quiet and rely on their partner to not out them.

Regardless of what the other decides, each prisoner gets a higher reward by betraying the other . The reasoning involves analyzing both players’ best responses:

Prisoner B will either cooperate (stay silent) or defect. If Prisoner B cooperates, Prisoner A should defect, because going free is better than serving 2 years. If Prisoner B defects, Prisoner A should also defect, because serving 2 years is better than serving 3.

So, either way, Prisoner A should defect since defecting is Prisoner A’s best response regardless of B’s strategy. Parallel reasoning will show that Prisoner B should defect.

Defection always results in a better payoff than cooperation for both parties but the ideal choice is for both A and B to cooperate, thus fulfilling Nash’s equilibrium.

Do we even use game theory that often?

You have surely heard or seen rock-paper-scissors. Have you ever wondered why one of the two people playing wins more than the others?

Nash’s Equilibrium comes into play in this 20th century hand game in a discrete way.

As per theory, a person should choose each option exactly one-third of the time to have an “equal” game. If one of the two players picks an option more than the others, the other player has the tendency to exploit the tendency.

This concept is so prevalent across games and in real life that we face the prisoner’s dilemma subconsciously. Resource management, “coordination game” featuring bank runs and currency crisis , and many more theories revolve around Nash’s equilibrium.

“The Walking Dead” is a well known post-apocalyptic scenario game that involves decision making and focuses on correct choices rather than things like aiming mechanism and skill. The game revolves around survival among the “undead” and the decisions you make have both payoffs and rewards, which make the game interesting from the get-go and increase its replay value by a long way.

Levying the downsides

Over usage of Nash’s equilibrium is also a problem many game developers face. Nash’s equilibrium is a concept reliant on decisions based on BOTH the players in a non cooperative game. Although the most effective way is to concede to a point where both players gain the most, the human brain is tricky and everyone does not think in the same manner.

Suppose you are the inmate in the Prisoner’s dilemma scenario. What would you do? Would you really cooperate and stay silent or would you defect to the police and get away for free?

Dominant strategy is a concept where a person in a non cooperative game thinks about personal gain regardless of whether the other person is being harmed or not. The cases where Prisoner A or Prisoner B face no jail time are examples of dominant strategy and showcase the downside of Nash’s equilibrium in games as it can be frustrating for the losing side to play the game.

Final Words

The pros of the paradox far outweigh the cons and is a must for game developers, strategy makers and gamers alike. Nash’s equilibrium is a fun concept showcasing what could or could not happen depending upon your actions. Maybe Prisoner A after betraying Prisoner B gets out of jail a few years early, only to face redemption from Prisoner B later on.

This paradox can be used on and off throughout your lifetime or inside a game. Will you be using this newly learnt tool in your next bright idea?

Written by Biswajit Roy (Member at ACE)