Question

write an essay about Game Theory, types of games and the Nash Equilibrium?

Answer 1

Game theory can be called modeling the potential interactions between two or more Rational Agents or players. I will emphasize the keyword "Rational" here, because it serves as the cornerstone of Game Theory. But what does Reason really mean? We may simply call rationality an awareness that each agent knows all the others are just as logical and have the same degree of understanding and knowledge as they do.

Rationality would also refer to the fact that agents will still choose the higher reward / payoff taking into account what other agents are going to do. In short, each agent is selfish and will seek to maximize the reward. Now that we know what rationality means, let 's discuss some other keywords that are related to game theory:

Game: A game usually consists of a collection of teams, actions / strategies and the final payoff. Example: Chess, Politics, Auction, etc.

Players: Players are rational entities which take part in any game. For instance:
Auction bidders in setting
Children who play rock-paper scissors

Politicians who take part in elections etc.

Payoff:  : Payoff is the compensation that players get when any result is obtained. If it's positive or negative. Every agent is selfish, as we discussed before, and wants to maximize their payout.

The Nash Equilibrium in Game Theory

Nash equilibrium is the "Bedrock" approach to Artificial Intelligence in game theory. Nash Equilibrium is an action chosen by each player to: No player wishes to change their action. Changing their action from Nash Equilibrium means that they don't behave optimally "Given that all other agents are rational and take the right action for me is the best response curve. No player can increase payoff by making changes to decisions within their set of actions. We may also think of it as "no regrets" in the sense that once a decision is taken, the player should have no regrets about decisions taking into account the consequences. To see Nash Equilibrium in motion, let 's address the most common question in Game Theory, The Dilemma of the Prisoner. We have two inmates in this game, Alan and Ben, who were arrested for the same crime and are being held in two different rooms for questioning. We have had two choices:

1. Stay silent
2. Confess to the crime

Let’s say that each of them is given two choices. So, there would be 4 outcomes in total:

• {Silent, Silent}
• {Confess, Silent}
• {Silent, Confess}
• {Confess, Confess}

And these 4 outcomes can be conveniently represented as a game matrix:

The payoffs are depicted in this depiction in the form of (Alan's Payoff, Ben's Payoff). Across the line, we have Alan 's actions and we've got Ben's actions in the columns. I recommend you take a closer look at these payoffs. Why do you find payoffs to be negative? This is because they'll get a predetermined number of years of incarceration based on their actions.

Following the results of the outcome:

1. If both of them remain silent, both of them get imprisonment for a year
2. If either one of them confesses, the confessor walks free and the other prisoner gets 15 years of imprisonment
3. If both of them confess, both of them receive imprisonment for 10 years

The problem comes about as neither inmate knows what the other inmate did. So, what do you think of this problem as the Nash Equilibrium action? It is very natural to think inmates should cooperate and remain silent.

But then we do recognize that prisoners have obvious self-interest in reducing the imprisonment they receive. So even though they're all quiet, they 're all having a year in jail each. Now, Ben would be thinking about this, too. If we concentrate on the matrix of the game, then the process of thought will make complete sense:

1. n the case where Ben confesses, Alan’s best choice is to confess. This will lead to lesser punishment of 10 years rather than 15
2. In case Ben stays silent, Alan is still better off confessing as he will be a free man instead of facing one-year imprisonment if he also stays silent

And this structure of the game is completely in line with what Alan feels. Now, if Ben thinks the same thing as well, the matrix of the game will look like this for him:

Let's presume Ben goes through the cycle of logical thought like Alan too. Ben also concludes that whatever Alan chooses, he'll always benefit from confessing. Now, if we combine these two p's logical thought

And looking at the results, {Confess, Confess} comes out to be the best strategy. Even if either of them tries to deviate from this action, playing this action makes them worse off than they get. Therefore, {Confess, Confess} is a technique of Nash Equilibrium. Will meaning make perfect sense, right? We can conclude for Nash Equilibrium that this is a "No Regret" solution for any game but not necessarily  the most optimal one.

types of games

Through game theory, various types of games help to evaluate different types of problems. The various types of games are developed on the basis of the number of players participating in the game, the structure of the game and the interaction between the players. there are five types of games in game theory:

Cooperative and Non-Cooperative Games:  Cooperative games are those in which players are convinced to follow a common strategy by discussions and agreements between players. Let us take the example cited in the prisoner's dilemma of understanding the idea of cooperative games. In the event that John and Mac had been able to reach each other, they had to agree to remain anonymous. As a result, their negotiation would have helped to solve the problem. For pan masala organizations, another example may be cited. Suppose pan masala organizations have high ad-expenditures that they want to reduce. However, they are not sure whether or not other organizations would follow. This creates a situation of confusion for pan masala organizations. The law, however, limits the advertisement of pan masala on television. It will help to reduce the ad-expenditure of pan masala organizations. This is an example of a cooperative game. However, non-cooperative games apply to games in which players agree on their own plan to maximize their profits. A prisoner's dilemma is the best example of a non-cooperative game. Non-cooperative games produce reliable results. This is because a very deep study of the problem takes place in non-cooperative games.

Normal Form and Extensive Form Games: Standard type games apply to the game definition in the form of a matrix. In other words, when the payoff and the strategy of a game are represented in a tabular form, they are referred to as regular form games. Standard form games help to recognize the dominant approaches and the Nash equilibrium. Under normal game form, the matrix displays the tactics followed by the various players under the game. On the other hand, the comprehensive form games are the ones in which the definition of the game is rendered in the form of a decision tree. Extensive type games aid in the depiction of things that might happen by chance. These games consist of a tree-like structure in which the names of the players are reflected in different nodes. Therefore, the feasible acts and pay offs of each player are also provided within this framework. Using an example let 's explain the idea of extensive type games. Suppose organization A decides to reach a new market, while on that market organization B is the current organization.

Organization A has two strategies; one IS entering the market and struggling to thrive or not joining the market and remaining deprived of the income it can produce. Similarly, organization B also has two methods for either battling for its life or cooperating with organization A.

Simultaneous Move Games and Sequential Move Games:  Simultaneous games are the one where two players pass at the same time (the tactic followed by two players). During simultaneous transfer, players have no knowledge of other players' movements. Sequential games, on the contrary, are the one in which players are conscious of the actions of players who have already implemented a strategy. Nevertheless, the players do not have a strong knowledge of other players' tactics in sequential games. For example, one player assumes that the other player will not use a single strategy, but he / she is not sure how many strategies the other player could use. Simultaneous games are depicted in normal form while detailed sequential games are depicted. Using an example let 's explain the application of simultaneous moving games. Suppose companies X and Y want their marketing operations outsourced to reduce their costs. They are, however, afraid that outsourcing marketing efforts will result in the other competitor 's profits growing. The strategies they can adopt are to outsource the m or not. the table show the simultaneous game.

now we look the sequential game tree.

Constant Sum, Zero Sum, and Non-Zero Sum Games: Constant sum game is the one where all the players' sum of outcome remains constant even if the outcomes are different. Negative sum game is a type of constant sum game where the sum of all players' outcomes is zero. In zero sum game, different player strategies can't influence the resources available. Additionally, in zero sum game, one player 's gain is always equal to the other player 's loss. On the other hand, non-zero sum game is the games where the sum of all players' results isn't null. The introduction of one dummy player will turn a non-zero sum game into zero sum game. Dummy player losses are overridden by player's net earnings. Examples of zero sum games include poker and chess. For such games one player 's benefit results in the other player 's loss. Cooperative games, however, are an example of non-zero games. This is because, either every player wins or loses in cooperative games.

Symmetric and Asymmetric Games: For symmetric games both teams follow the same strategies. Symmetry can only occur in short-term games, as the number of choices decreases with a player in long-term games. For a symmetric game the decisions depend on the tactics used, not on the game players. In symmetric games, except in the case of exchange of teams, the decisions remain the same. Examples of symmetrical games include prisonner dillema. On the other hand asymmetric games are the one in which players follow various strategies. In asymmetric games, the strategy that gives one player benefit may not be equally beneficial to the other player. However, decision making in asymmetric games depends on the different types of strategies and decision of players, Asymmetric game example is the introduction of new company into a market as different companies follow different strategies for entering the same market.