With my best wishes of well-being and successes in the pilgrimage of this prestigious platform. The study of Game Theory is extensive, it is about learning the models to handle the great administrative problems that arise daily, through quantitative procedures, judgment, experience, leads us to make the best selection thinking about the greater benefit, that is to say it is the main guide to perform the calculations through its logical results for the decisions.

Game theory as a descendant of mathematics helps in making strategic decisions based on the interaction between individuals playing a large role in the application of problems, using two key elements such as reason and logic. The importance of learning to make decisions is to look for solutions to problems by considering alternatives and thus discard what does not help in the decision by selecting what is useful and beneficial at a given time, both for us and for others, that is to say What to do the analysis taking into account what you think others will do, given the situation or problem you face.

As a consequence, the factors involved in a resolution are systematically considered in the decision-making process, structuring the change in an organized and coherent manner with the objectives pursued. However, the participation of those involved in the problem is sometimes cumbersome if you do not have the right tools. There are several theories, but the prisoner's dilemma, in game theory, is the most successful, because whatever the variation is always the decision-making depends on the decisions of the other and vice versa.

With the great boom and technological growth today, decision-making has been automated, in fact it helps to improve administrative problems faster. With this, the linear programming would be discovering the problem of an organization through variables controlled by the administrators, to make the setting of numerical values, and with it the decision making with the expected optimal result. Mathematical models based on programming under any system suitable for operation are able to select the data inserted by the user, to process them, and analyze them in search of an expected result.

Many times our life is compromised and depends on the type of decisions. A manager always has to consider a number of people to make a decision. Therefore, making decisions is a science that systematically teaches us to consider the factors involved in a resolution, and above all to structure the change in a more organized and coherent way with the objectives pursued. That is why the theoretical models on decision making are very useful for various sciences, especially to anticipate the behavior of people in rational decision making.

The game theory model is useful, its application depends not only on the decision of a single person, but also on the decisions made by the interaction of individuals, who face conflicts of interest and in which damages are obtained or benefits considering what we think others would do.

From the business point of view, decisions are studied in order to achieve a balance being beneficial to organize competitive behaviors among economic agents. The applications of game theory are endless and apply to all types of companies, where the domain is based on decisions in search of success, where it will not only be based on experience and intuition to choose the best decision, such as all the scenarios that are presented to us, since life is full of small decisions, what dish I will choose for food, what brand of soap I will use, on the weekend I will go to the cinema or stay at home, in short it is all about an election.

The decision-making specialists point out that if the process develops with error in one of the steps, it goes back, the process begins, the internal pressure to reach a decision and the external elements, together with the ability to remake You can study the possible solution options, choose one of them, strategically take action at the right time. The optimal strategy, advances predicting the strategies of the rest, so that decisions are more reliable reason why it relies on mathematics because if the decision is wrong, we know that the action was correct, but they are always exposed to external factors that divert the selected strategies with the Game Theory.

We will explain it with an Example: two families decide to meet to make a sancocho as a family, and each one decides if one brings the meat and the other the vegetables (Problem of Decision Making) or adds all the expenses generated by the sancocho, it is divided between both families in equal parts (Strategic Problem). In this line, consider the disagreement between a decision-making problem regarding a strategy problem, where there are always two alternatives.

Within this framework, game is defined as any structured situation in which pre-established rewards or incentives can be obtained. As in every game, it is made up of at least two players, you must have a set of strategies for each player. It is understood that the game is described as an interaction between two or more parties, with rules, in which those involved use reason and logic, as a result the strategies affect the result.

Many researchers analyze the behavior of people in situations with conflicts of interest, to create patterns on which to choose the strategies that lead to optimal effects, where all participants win. On the other hand, game theory allows us to more accurately verify the social environment by emphasizing general patterns of behavior, so that people are aware of the most precise rules of action being very frequent situations in which in games, Its result depends on the conjunction of different decisions.

In the day to day game theory has been a model that has helped us a lot especially to make rational or strategic decisions, usually it has been study of several disciplines mainly by mathematics being an advantage for us to have knowledge of it because He has shown great lightness in solving problems, now for the economy and business his study has been to maximize the benefits.

Nash's equilibrium is part of game theory is one where the optimal result is achieved individually for each player in the game. That is to say, it is a scenario in which all the players put in dexterity a strategy that maximizes their particular gains, given the strategies of the others. As an effect, no player has incentives to individually modify their strategy.

It is important to note that a Nash equilibrium participants seek to achieve the best result for each of them, but individually. That is, each competitor performs the best strategy given the movements of the others. Although it is not the best for all competitors

If we start as would be the application to the economy, it would be a balance of imperfect competition that analyzes the situation of several competitors for the market of the same good and that they can opt for profit maximization. As a consequence of this, a game can have multiple Nash equilibria or none

Possible Decisions to achieve Nash equilibrium:

• Competitors seek to maximize (profit).

• Competitors establish a series of strategies according to their preferences.

• Competitors determine their own balance and estimate that of the other competitors participating in the game.

• Any competitor can modify their strategy, thinking about what others will do, to consider their own strategies.

In this sense, the importance of Linear Programming is that it is a financial tool that has great utility in the business world such as investment analysis, budget control, production operations, product mixes, inventory control, production , sales prediction, among others. It is then, when profits are maximized or costs are minimized, that it can help companies to make decisions.

The Prisoner's Dilemma is based on two individuals involved in a robbery. The police capture them and place them in separate cells. In each problem the strategies can change, depending on each person. If we think as managers for decision-making on this problem from a cooperative point of view, we must start by analyzing each of the options and it would begin that both think about the benefit of not ending up blaming the other partner, so the penalty will be Minor. However, if we perform the analysis of this situation individually, then several situations will be reflected.

Because one can decide to give away, thinking about their own interests regardless of the situation of the other. Since you don't get the trust in the other partner because it can help you sink into jail. Unquestionably the best decision for both of them is to speak and tell the truth which will lead to a situation of equilibrium 3.3 where each prisoner will see his sentence diminished. Faced with this situation that arises where each one will have to pay a 3-year sentence is what is known as the Nash equilibrium.

In this game Nash's equilibrium is Delatar-Delatar because none of the competitors has stimuli to change his decision thinking what his partner will do. Both will think about placing themselves in another balance but they cannot do it because the optimal action for each of them, considering the payments and the possible action of their partner is to betray. Before the described, when the rules change the conditions of the game it is possible to reach other scenarios or Nash equilibria

The analysis of the Prisoner's Dilemma is how the survival game mankind ends with extinction or survives. It is a dual game, where you always have a logical solution, that is if the participants play with the truth, the game is beneficial for both competitors. But if the player is illogical he will always have two options, deceive the honest and convince others. However, people can choose not to cooperate, even if that decision goes against their interests.

The argument of the valuation of the common good based on individual interest does not diminish the problem but rather increases it, since in cases such as that of the Prisoner's Dilemma and the like, individual players face the use of the joint benefit of cooperation with interests. found: the interest of each individual is, on the one hand, that all others act altruistically, and on the other, act selfishly with respect to all others. In fact, in every game based on the conflict of interest, even greater general altruism will increase the benefits of those who act selfishly.

In our life there are always situations that lead us to make decisions complex, whether for ourselves that we think there are a number of factors and conditions that lead us to opt for not so logical decisions. Obviously, to carry out an adequate analysis, it is necessary to deepen and select the strategies that can give greater benefits or decide between following a selfish strategy or instead, in solidarity with other players.

Generally, in the prisoner's dilemma the only correct result happens when all competitors decide to be honest telling the truth. On the other hand when someone of the participants cheats, manipulates, the solution will always be wrong because each prisoner will want their own benefit. So both will choose to speak ill of the other partner to be benefited in the decrease of the sentence. Therefore, it is to suspect that the other partner thought the same and ended up giving away. The inconsistency of all of the above is that in order to achieve individual benefit, it is necessary to respect the common good. Selfishness finally converges on the worst decision.

Decisions in the Prisoner's Dilemma

• The decisions, depends on the decisions of both prisoners

• Neither of the two betraysOne of them betrays.

• Both decide to betray their partner.

Made the above considerations. The implementation of linear programming is a simple technique, being applied to solve various numbers of economic problems as long as the assumptions that they require are met. It should be noted that, with the implementation of technologies and computing, manual linear programming, considerably improved its use and speed, generating a better optimization for users and the most important thing is that with just the fingering of some data their results They are what allow decision-making measures.

It is necessary to describe the importance of linear programming as a method to solve certain problems in industry, economy, among others. We must have judgment and analysis in the correct interpretation of the statements and in the approach to the problem. To facilitate the approach of a linear programming problem it is important to build a summary table, with the problem data. Decision making plays a very important role in the business field where the applicability of linear programming is essential to choose the best solution. In the problems of linear programming not only can be checked by the graphic method but also for greater security it can be done by the simplex method

Bibliography:

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@exqueila

Specialist in Commercial Law Mention: Human Talent Management
Graduated from the Universidad de los Andes