Game-theory is one of the sections of applied mathematics that deals with how participants use strategies and logical reasoning to make decisions in strategic situations like games. Game theory, along with Artificial Intelligence (AI), is not only implemented in online games and offline games but also some real-life applications as well. 

Concepts of game theory used in Artificial Intelligence

·   Nash Equilibrium

Different applications of Artificial intelligence use different concepts of game theory. One such game theory is the Nash Equilibrium. By Nash equilibrium, none of the players involved has an advantage if they change their strategy. Generally, to explain this theory, the Prisoners dilemma is used. In this case, we catch two prisoners who we cannot punish as there is lack of evidence. They are kept separately and are not allowed to communicate. If one of them accuses the other, he is set free, and the other stays prisoner stays in jail for ten years. If both do not confess, they both would have to spend one year in jail. And if both confess the crime of the other, they both would be imprisoned for five years. Now both prisoners can either stay silent because of which they will spend one year in jail, or both can give testimony against the other prisoner and get free. But more likely, the prisoners will choose to be free than spend one year in jail. When both prisoners give testimony against each other, then at that point, Nash Equilibrium is achieved.

·   Inverse game theory:

Another theory used in AI is the Inverse Game theory. Using Inverse Game theory games or strategic situations, are made based on the decisions and choices that the participants make. By this method, we try to determine why a participant made a particular decision. One such question can be: What was the thought process of the participant when he made the decision? Inverse Game theory, along with Nash Equilibrium, is used in applications of artificial intelligence. One such example is of the Generative Adversarial Networks (GANs). The further details of Generative Adversarial Networks (GANs) would be discussed later in the article.

·   MiniMax Algorithm and Alpha-Beta Pruning:

Another theory that we mainly use in AI is the MiniMax algorithm which uses backtracking to assess the moves of the players. In this one player is known as maximum whose scores maximum possible score while the other is known as Minimum who scores the minimum rating. The position in the board then decides which players out of the maximum or minimum will win and this would vary from game to game. We use this theory in games such as chess, tic tac toe, checkers, etc. After the MiniMax algorithm alpha-beta pruning algorithm is applied. We do this so that the branches in the Mini Max algorithm can be simplified further.

·   Mean field game theory: 

Mean-field game theory is a model created to smoothly deal with an environment where several participants are interacting with each other. This theory is a comparatively new concept in game theory as compared to the others. The main difference between the old game theories and this one is that the former used to deal with how two participants interacted with each other. In contrast, this one suggests how one participant deals with a group of others. Due to the complexity of interactions between participants, the former theory used to become nonapplicable to large groups. But with the introduction of mean-field game theory situations involving large groups like the scenarios of multi-agent reinforcement learning (MARL) can be solved quickly and easily. MARL is discussed further in the article.

Game theory in games

· Classification of games

Firstly, let’s talk about game theory in games. We classify the games into mainly five groups according to game theory. The first classification is of the cooperative and noncooperative games. In cooperative groups, participants can work together towards a common goal and in noncooperative they can’t. The second is symmetric games and asymmetric games. In symmetric games, players use the same strategy to play, and that determines the winner, whereas, in asymmetric games, the strategies are not the same. An example of a ‘symmetric game’ is chess, where the players have particular policies that players can use, which determine the winner. The efficiency of game theory, in that case, can be identified from the fact that in many games, humans were not able to beat the computer.

An example is the deep blue computer which defeated a player in 1996. Another example is of the game checkers where the computer Chinook defeated a human player in 1994. These were the first occasions where computers defeated the players in these games. After that, several events like this took place. The third category is of the complete information and incomplete information games. When we have complete information, we can guess the outcomes like a game of Tic Tac Toe. Whereas in incomplete information like a poker game or any other card game, a person cannot predict the results of other players due to incomplete knowledge like not knowing the cards of the other players. 

Fourth is the zero-sum category where when one player loses the other person gains something. An example of this is the rock paper scissors which children sometimes use to determine who will start a game. The fifth category is of the simultaneous and sequential games. In simultaneous games, the players make decisions without knowing the choices of other people, whereas in sequential game players take turns to make decisions. 

Game theory in real-life applications

·   Generative Adversarial Networks (GANs)

The inverse game theory is vital in creating an AI environment such as Generative Adversarial Networks (GANs). We use GANs in machine learning, where the program produces content by itself without being supervised. GANs consist of generative and discriminative networks. The generative model evaluates the data given to them and determines why a particular result was produced. While on the other hand, the discriminative model assesses them.

An example of this is in producing images. The generator model would take features as input and would create similar images based on them while the discriminator would evaluate them and reject the ones that are original or are not matching the given criteria.

Such generative models are widely used in the fashion industry and advertising so that professionals can produce imaginative models and the need of hiring actual models and their additional expenses like makeup, photography, etc. can be avoided. They are also used in science to improve scientific images and in video games to improve the resolutions of images. Besides this, we also use the technology to visualize items like shoes, bags and clothes in the fashion industry or scenes for computer games. This technology is beneficial for areas like fashion designing and interior designing, where visualizing items can be handy. 

They can construct 3-dimensional models, can change the appearance of photos by age or gender and recently, it has also been used in science to produce molecules that could treat diseases. We first tested these molecules on animals like mice. In GANs this process that generator keeps on producing images and the discriminator keeps assessing them continues until the Nash equilibrium is reached where both models are up to their most efficient level. Further, there is no room for improvement.

Multi-Agent Reinforcement Learning

Another application of game theory is in the multi-agent reinforcement learning (MARL) where we introduce an agent into the situation from which it can learn by interacting with it. MARL is used together with mean-field scenarios (MFS). These systems are advantageous in situations where humans cannot physically perform the task. An example of this is using robots or drones to go to places where humans cannot reach. It can also be used for satellites to collect information from outer space, for example, regarding the weather forecast. We can also use in traffic control and the context of self-driving cars to predict what things must be applied to restrict problems that may arise. 

To implement MARL successfully, we still need to solve some issues. One such factor is the complexity as the participants increase the model gets more complicated as it’s difficult to deduce all the ways a participant can interact with a system. The second problem is in the training as we have to train them in a way that different devices can coordinate. The third problem is that if two participants get to the same position together, it can be challenging to solve that situation. Maybe this model has not been implemented fully due to its complexity. However, still, there is room for developing it further, and its implementation can automate a large number of systems that cannot be automated today.

· Adversarial networks

‘Adversarial networks’ is an area of machine learning where abnormal or invalid inputs are given to a system to explore the vulnerabilities it has. If we don’t incorporate this into systems such as spam filtering or malware detection, it could lead to a security breach. So employing game theory concepts like that of inverse game theory the situation of a system and adversary are imitated. The adversary and the network aim to defeat each other. This practice allows taking care of adversarial attacks by providing robust countermeasures in a system machine learning and eliminating any possible chances of adversarial attacks. 

An example of an adversarial attack is the development of an image of a dog in 2017. It appeared as a cat to both humans and machines by Google brain! Another example of the three-dimensionally printed turtle developed by Massachusetts Institute of Technology that emerged as a rifle to the artificial intelligence systems of Google. These examples of adversarial attacks are enough to prove that machine learning systems still need a lot of modification.

Some Setbacks in Game theory

Though the game theory can be efficient in the scenarios where we assume things beforehand, there can be some minor issues as well. For example, in situations where we think that there is complete information, we believe that the participants have full information, including all facts, statistics, and data needed to make a decision. This condition might not be accurate in certain circumstances. 

Another assumption made in game theory is that all the players would make wise decisions. This assumption again is something that we cannot predict in many situations. Thirdly the limit of strategies cannot be determined. There can be a chain of strategy in a game, and predicting the threshold of the strategy is not possible in most situations. 

Another issue can be that when complexity increases, it might be challenging to apply the same theories. The theory might be made for one or two participants, and it might fail if a higher number of participants are involved. 

Lastly, we cannot predict all games using game theory. Some sports depend on human factors which are beyond the control of any machine.

We cannot implement many projects in the area of AI and machine learning as deducing all the outcomes in a real-life situation is a difficult task to do. Many answers for such queries reside in game theory. Game-theory is one of the sections of applied mathematics that deals with how participants use strategies and logical reasoning to make decisions in strategic situations like games. Game theory is still a less explored subject and holds answers for many applications. If explored fully, it can help the current issues AI and machine learning face, and this, in turn, would facilitate several breakthroughs in technology, which will be a big step in automation. Systems like those include self-driving cars, systems with drones and robots used to extinguish fires, technology including automated machines which mine coal and reserve dangerous tasks for robots, rather than humans. 

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