Game Theory

Game theory is a framework for conceiving social situations among competing players. In some respects, game theory is the science of strategy, or at least the optimal decision-making of independent and competing actors in a strategic setting. The trailblazer of what we consider modern game theory was the famed mathematician John von Neumann and economist Oskar Morgenstern in the 1940s. Mathematician John Nash is regarded by many as providing the first significant extension of the von Neumann and Morgenstern work.

Components of Game Theory

In any given situation with two or more players that involve known payouts or quantifiable consequences, we can use game theory to help determine the most likely outcomes. Let's start by defining a few terms commonly used in the study of game theory:

• Game: Any set of circumstances that has a result dependent on the actions of two or more decision-makers (players)
• Players: A strategic decision-maker within the context of the game
• Strategy: A complete plan of action a player will take given the set of circumstances that might arise within the game
• Payoff: The payout a player receives from arriving at a particular outcome (The payout can be in any quantifiable form, from dollars to utility.)
• Information set: The information available at a given point in the game (The term information set is most usually applied when the game has a sequential component.)
• Equilibrium: The point in a game where both players have made their decisions and an outcome is reached

At its elementary level, game theory is the study of how people, companies, or nations (referred to as agents or players) determine strategies in different situations in the face of competing strategies acted out by other agents or players. Game theory assumes that agents make rational decisions at all times. There's some fault in this assumption: What passes for irrational behavior by most of society (a buildup of a nuclear arsenal, for instance) is considered quite rational by game theory standards.

However, even when game theory analysis produces counterintuitive results, it still yields surprising insights into human nature. For instance, do members of society only cooperate for the sake of material gain, or is there more to it? Would you help someone in need if it hurt you in the long run?

Applications of Game Theory

Game theory's development ould be said to have taken an acceleration during World War II. Though its intent was more towards economics, both the United States and the Soviet Union quickly saw its value for forming war strategies.

Early in the Cold War, the Eisenhower administration viewed nuclear weapons as any other weapon in the arsenal available for use [source: Spence]. Game theorist Thomas Schelling convinced officials that nuclear weapons were only useful as deterrents. Additionally, he proposed that the U.S. should have a variety of responses it could call upon concerning the size of the offense against it.

A balance was struck in which neither nation could gain advantage through nuclear attack -- the reprisals would be too devastating. This was known as Mutual Assured Destruction (MAD). This balance required open acknowledgment of each nation's strengths and vulnerabilities. However, as a prisoner's dilemma showed us, both players must assume the other is only concerned with self-interest; therefore, each must limit risk by adopting a dominant strategy.

If one nation changed the balance of power (by building a missile-defense shield, for instance), would it lead to a strategic blunder that resulted in a nuclear war? Governments consulted game theorists to prevent such imbalances. When one nation built missile silos, the other nation targeted them. The Soviet Union and the U.S. then spread out and hid their launch sites around the globe, which required both nations to commit more missiles to a potential first strike to diminish the retaliatory abilities of the other. They also kept nuclear-armed aircraft aloft in the skies at all times to provide a deterrent if the silos were destroyed. As another deterrent, they established nuclear-armed submarines. This allowed them to cover all bases: ground, air, and sea.

The atmosphere was tense, and there was a constant threat of miscommunication leading to disastrous results. Amid such massive distrust, even a purely defensive move could be interpreted as provocative. Building fallout shelters, for instance, makes it look like you're expecting a confrontation. Why do this, unless you're planning on starting it?

By no rational or mathematic measure would it make sense to launch nuclear weapons after your nation has already taken a significant hit. What would be the point? World destruction for the sake of revenge? But if revenge isn't a deterrent, what keeps either nation from launching a first strike? To counteract the threat of a first strike, American and Soviet leaders sometimes used a "madman strategy" or released rumors that they were mentally unstable or blind with rage to keep the other off guard.

Weapons control and disarmament negotiations were essentially repeated games that allowed both parties to reward cooperation and punish defection. Through repeated meetings and increased communication, trust and cooperation led to (some) disarmament and less strategic posturing. This was also due in no small part to the resources required to maintain an ever-growing nuclear capability.

Fortunately, neither nation was willing to play the final stage of a game in which the best possible outcome involved a victory that could only be celebrated by a handful of survivors underground.

In another application of game theory called an evolutionary theory, each player is viewed as a strategy himself or herself. That is, you represent the result of your ancestors' decisions. If your ancestors chose to steal from their neighbors, you're the walking embodiment of that survival strategy. As these strategies compete for dominance, certain strategies will dominate and replicate, in the form of children. Eventually, these will dominate other strategies by sheer numbers.

A scenario called public goods tests players' rationality. In this game, a group of six players is given $20 each. They are then told that any money contributed to a general pool will be tripled and divided evenly among all players, regardless of how many contribute or how much. The rational course of action is to defect and benefit from whatever dividend may come your way. Fortunately for us, in real-life situations, people sometimes deviate from the rational course and contribute to the pool. One real-life example of the public goods game is the environment. Whether or not an individual invests money or effort into environmental stewardship, that individual will benefit from any contribution made by others.

Game Theory as it Affects AI

On the other hand, people often debate about the carryover of Machine Learning and Deep Learning research over to real-world use cases. Since real-world cases are often incomplete information games, most Machine Learning and Deep Learning approaches struggle there.

Game Theory approaches are gradually gaining momentum because of their generalizability in real-world use cases. Its application can be as far-reaching as providing tools for Public Safety

Wildlife Conservation, Public Health, etc. 

Let’s imagine we are trying to improve the traffic flow in a given town using a group of AI-powered Self-Driving Vehicles. On their own, each of the cars can perfectly interact with the external environment but things can get more complicated if we want to make the cars think as a group. For example, a car might get in conflict with another one because both of them are most convenient to follow a certain route.

This situation can be easily modeled using Game Theory. In this case, our cars would represent the different players and the Nash Equilibrium the equilibrium point between the collaboration between the different cars. This is just one practical example and is by no means a standalone case.