Game Theory

10 October 2016

The modern Game Theory was created in 1944 with the book “Theory of games and economic behavior” by Oskar Mogenstern and John Von Neumann. It was also developed a lot in the 1950’s with several studies by John Nash. After our seminary about negotiation we thought it would be very interesting to make some research about the Game Theory. Indeed, we made some researches on the Game Theory in our first year in IESEG in our economic classes. That is why we were a bit surprised to see that this theory could be also used in a negotiation process to analyze it.

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It seems to be obvious that using the concepts of that theory could change the course of a negotiation and be understood as a manipulation or just a skill to achieve the goals of the agents in a negotiation. We decided to divide our work in three parts. First, we will define the Game Theory and make some examples. Secondly, we will make an synthesis on how to act as a negotiator during a negotiation. Finally, on the third part we will talk about the limits and the interpretation we can make on that subject. Generally, we can say that our goal is to extend the concept of Game Theory.

Indeed, we imagined it only in an economic vision and we want to extend it to a negotiation vision. What is the Game theory? The Game theory is a method to study the strategic decision-making. More formally, it is «the study of the mathematical models of conflict and the cooperation between intelligent reasonable decision-makers. ” An alternative term suggested «as a more descriptive name for the discipline ” is the theory of interactive decision. The Game Theory is mainly used in the economy, the political science and the psychology, as well as the logic, negotiation and the biology.

The subject of the (landed) at first sent zero-sum games, such as the earnings(gains) of a person equal exactly the clear(net) losses of the other participant (s). Today, however, the Game theory applies to a vast range of relations of class and developed in a term of umbrella for the logical side of science, to include both man and non-people, as computers. Classic uses include the direction of the balance in numerous games, where every person found or developed a tactics which cannot successfully better its results, given the other approach.

Theory Making commitments: promises and threats The first assumption to be made is that the goal of any negotiation is to enlarge the pay off for both sides, and in most cases agreements has to be made in order to achieve getting a Win/Win situation. These agreements can be made by making either promises or threats. In both cases, the idea is to benefit from an enlargement of the total pie obtained by making commitments. Basic situation In the following example, both sides are looking forward to getting the better pay off.

At first sight, Neil seems to have a better hand since he is able to have payments by using both of his strategies while Bob can only win by using strategy 1. It is obvious that Neil would better use strategy 1 in order to maximize his payoffs expectations. But Bob would probably prefer using his second strategy than winning less than Neil, though it would result in a Loose/Loose situation. Bob will probably threatens to take strategy 2 if Neil chooses the first one. The only way to obtain a Win/Win situation though is for Neil to make a commitment: he must promise to choose 2 if Bob chooses 1.

This is the most basic commitment example. Unique Win/Win situation In the following one, there is one only scenario which allows the two player to win, but commitments must be made buy both sides in order to reach the best situation for both. Here, Neil will probably initially chose strategy 1 in order to avoid loss, but he won’t be able to gain anything though. Bob would probably choose to maximize his payoffs expectations by choosing the first strategy. Finally, neither Bob nor Neil will get payoffs, so that we obtain a Loose/Loose result, which is not acceptable.

They both have to promise to choose the second strategy in order to win. Commitments and side payments In this last example, it is not possible to reach a Win/Win agreement but by making side payment. Side payments allows to change the total pie, and though to reach the targeted situation. In this particular scenario, initially Neil would choose the first strategy, which is not acceptable for Bob in both cases. Moreover, Bob can’t threaten Neil to choose either a strategy or another. This is a very bad situation for Bob.

He will probably choose strategy 1 in order to minimize Neil’s payoffs, and though gain nothing. But, fortunately he can also promise side payments, which could change the total pie. As a matter of fact, if he pays $2 for Neil to pick strategy 2, we create a Win/Win situation which will allow both sides to get payoffs. Through this part we’re going to apply the concept of promises and threats into a concrete situation of negotiation. We set the situation, we have two participants, one will be selling an apartment two a possible buyer. At first sight, the man in power is the seller as he fixes the price.

Nevertheless, the buyer can use the threat technique, saying he won’t accept the offer. This decision would place our two actors in a lose/lose situation. Indeed, if the buyer is in the situation of losing the negotiation he will choose to make his opponent loose too. Thus in order to obtain a win/win situation, the seller must not be too greedy to convince his customer. In another way, if the seller wants to be sure to succeed, he can promise the buyer an offer that will automatically put the buyer in a state of winning. Prisoner’s dilemma The prisoner’s dilemma is one of the most famous games.

It is quite easy to understand and gives a good idea of different possibilities in negociation and the interest of cooperation. The main idea is that two burglars get caught by the police after a robbery, and they are interrogated separately. They have two options: either they say that the other guy is guilty or they say he’s not. Considering one’s interest separately, the best situation for him is to use the guilty option while the other chooses the not guilty option. In this case, the first guy will get only 1year of jail while the other one will get 5 years.

Therefore it is very risky to choose the not guilty option. If we consider the two as one, the most interesting situation is that both of them choose the not guilty option, whereas the worst is both choosing the guilty option. This is one of the simplest examples of a Win/Win, Win/Loose or Loose/Loose situation. They can both act individually using the guilty option, and get 3 years of jail each, or they can cooperate, use the not guilty strategy and get only 2 years both. The major thing to be remembered is that trust is crucial in negotiations.

It leads to the only Win/Win situation possible and credibility is needed to avoid defection. The Simplest Game: Two Person with a Fixed Pie When think of people negotiating, a very simple scenario comes into mind, where one person wins and the other fails to win. This is a very simple scenario and one of the first that game theory attempted to solve. Let’s take a very simple example where Nathan owes Barbara some money and they can’t decide on how much. Both of them have two options available to them, but the final decision depends not only on what strategy they choose, but also on what strategy is chosen by their opponent.

Nathan will choose to pay a minimum of 40 and Barbara will want to take the maximum of let’s say, 60. This is a very simple scenario and one can easily figure out that the outcome will be 50. 40| 50| 50| 60| However this illustrated a very important concept called the Minimax theorem which tells us to pick the strategy the minimizes the opponents maximum gain. Nathan will pick strategy 2 in order to not pay 60 while Barbara would pick strategy 1 to avoid only getting paid 40. The more variables one has, the more complex the game becomes to solve.

Therefore it is a good idea to have lesser number of variables, similarly we need to have a clear idea of what we need in order to reduce unimportant options. Reducing the number of variables one has is always a good idea, even if one is not really reducing the number of variables it is important to show to the opponent that you only have some variables to win. For example, when a customer asks for something one can refer to standardized guidelines or not having permission from the boss to reduce variables. Tacit Barganining. This term was first coined by Thomas Schelling.

Who did some experimental research and found out the following facts: * When asked to pick any number, 40% chose the number 1. * When asked to pick any amount of money almost all people chose a figure divisible by 10 * When people were told that they had to meet someone else – but had to guess the time – almost all chose noon. We often succumb to a lot of convections even without doing it consciously. It is normal for people to follow the laws of fairness and equilibrium; no one wants to be seen as deviating from the norm.

Therefore its usually a good idea to make the first move in a negotiation so that you can create the framework and make clear that you are precedent. In a negotiation, taking the initiative doesn’t seem to be the best thing to do when you start it. Indeed, when you ask somebody to start negotiations, generally he is reticent to do so. Nevertheless asking the first proposal allows you to be able to negotiate on this basis, that’s why you should do it first. Establish a precedence as we said before is a tool to start negotiating. The thing is, there is always a argaining whereas you don’t even notice it. It’s called the “tacit bargaining”. How to act during a negotiation Breakthrough Strategy In order to reach your goals through using the game theory to negotiate you will need to apply a strategy you will respect during the entire negotiation. That’s why we can use the breakthrough strategy. This breakthrough strategy is based on five steps and permits to solve issues during the negotiation process. Its aim is to offer the two parties the possibility to work together rather than appearing as two adversaries.

Nevertheless, this strategy needs to be remembered and followed as it wouldn’t be the intuitive reaction. These five steps are to firstly stay focused. In fact, the goal is to have your mind clear and not be parasite by your emotions. You need to have an overall view on the entire negotiation and to not get lose on a specific point. Then, you need to accept the counter-party. Indeed, being as empathic as possible is very important throughout the negotiation process as creating a climate of exchange is primordial to obtain a win/win situation.

This can be perfectly illustrated by the prisoner dilemma. Both parties searching for their proper interest without regarding his opponent situation will lead to lose/lose. Thereafter, the participant will reframe the negotiation. It is based on rephrasing the opponent arguments enhancing the common interest. This will permit that both side look for the fairest deal possible. Once again you need to look through the other negotiators eyes in building a “golden bridge. This means trying to understand if, in his situation, you will accept the deal as it is now.

You will therefore see when to finalize the negotiation in order that the counter-party doesn’t feel pushed in the conclusion. Finally, to make it hard to refuse by using the power game as threats or bluff is the most common mistake made at the end of the negotiation. In fact, by using lowering his chance to refuse you also lower his chance to accept the deal. Thus, by having used the four precedent steps, you have create a negotiation climate that will present your golden bridge as the best common interest for the parties. Tactics Tactic is about anticipating what the negotiator is going to do.

You have to prepare several strategies in order to obtain what you want from these negotiations. First, there are the behavioral tactics, whose aim is to differentiate the negotiation in its role of representation of a third person or a company and the person who plays this role. Negotiators when using these tactics can operate in many ways. They can use a spokesman for representation, or the executive person or a delegated representative. You have to create a positive frame if you want to obtain concessions from the person you’re negotiating with.

Moreover, you have to establish limits in your area of negotiation. Anchoring is a tool that has to be established in order to be able to make adjustments between the two parties in the future. Adjustments and anchoring are important because they have an impact on negotiators. They lead them to what is possible and doable during the negotiation. Another mean is to influence the negotiator as an individual. As if, the negotiator is using its unique and common sense during an argumentation. Some tactics can be based on ethic and morality.

If you think the proposition is unfair or contrary to the usual behavior or even illegal, you can use these tactics by pointing up the fact that the proposition is unethical. Tactics is not only about the human and the social part; there is also a part of a negotiation that is about the balance of power between the two parties. The main goal of this tactic is to let the other party know that accepting one request would have an important impact on the cost and that we are going to make them pay for that. The deterrence impact shouldn’t be ignored in a negotiation.

Commitment in a negotiation is of paramount importance. It is one of the three strategic strikes with bluff and threat. The thing is that negotiators have naturally the tendency to commit themselves into the negotiation. Instead of trying to develop its requirements and modifying its position, he will start conflict in order to put pressure on its opponent. It puts the opponent in a tough position; accept our request or he will have to face the failure of the negotiation. And that’s exactly what he wants to avoid. Otherwise, its role would be useless.

This tactic can lead to a dead-end, but it’s a stuck situation that doesn’t consider the balance of power between the two parties. Threats are different from commitment as they are more flexible and have a longer range of existence. They are various as they can be explicit or implicit. They are the direct consequences of the failure of negotiations and can be introduce by the company of the negotiator. They have to be used sparingly because threats without any actions discredited any negotiators and especially its company. In the future, it would have an impact on the approach of the opponent regarding the company.

Limits The study of a complex negotiation situation with the help of a model places two major complementary problems: the modeling itself (the passage of the reality to a version idealized of this reality) and the interpretation (inverse approach) The modelisation Modelisation is a very hard job. We can resume it as the stage of transforming reality problem into a matrix. The modelisation consists in creating a representation simplified by a problem: the model. But as every transformation, problems could be highlight. Some characteristics, some influence can be overestimated or less estimated. How to model the respective influences of the parameters (functional dependence, indeed if such or such parameter exercises one dominating influence or on the contrary, unimportant in first estimate, etc. ) * How measure the values of the parameters (variables of situation or history of the previous negotiations for example) and how fire of a model of the theoretical results (or of experimental simulation). And at least the human factor is very difficult to imagine and to predict. The process of modelisation tries doing it.

But through his experience, his character, his objectives or his approach, each human is different. So a model would try to simplify it but of course will make errors. The interpretation Indeed, we already possess a completely realistic model: it is the real world itself. Yet this model is too much complicated to be understandable. … It is only when a simplifying postulate ends in a model which supplies incorrect answers to the questions which it is supposed to answer that its lack of realism can be considered as an imperfection. … Otherwise, its lack of realism is then a virtue.

In that case, the simplifying postulate allows to isolate certain effects and to facilitate the understanding. How to interpret the results supplied by the model, suppose that there is (problem of adequacy of the model to the reality). Does such result of the model express suitably the real situation, in spite of the simplifications and the untidy parameters? Like the modelisation, Interpretation is a tuff job. The human factor is a hard to forecast. Game theoretic predictions may not be confirmed in experiments (the real life). Is this a fault of game theory? Yes: people are simply not rational … * No: maybe we get the information technology wrong (absentmindedness), or payoffs are not specified correctly (altruism). The advantage of assuming rationality is that we can think through situations (how can irrationality be modeled). The advantage of assuming selfish behavior is that it is “unique” (what means altruism, inequity aversion etc. ). Conclusion As a conclusion we have studied all the aspects about the Game Theory and that helped us to understand that it is a useful tool not only about economic classes but also for negotiation.

Indeed, we have made a link between the different sorts of Game Theory and the different cases you can face during a negotiation process. As it is often the case, we found that one of the strongest conditions to succeed in a negotiation is to be able to adapt your body language and attitude according to the characters and features of your contradictor(s). Using the Game Theory could help you to make a strategy and to adapt your goals to any case which is in front of you.

However, it is never possible to make a perfect prediction of how the person who is just in front of you and it is very important to be cautious enough, that means that you must rank the risks of any strategy you will try during a negotiation. We can take a final example: You start a meeting being sure you will use the theory of the prisoner’s dilemma because you thought you perfectly understood the mood of the other agent. Imagine one second that you made a very big mistake because you don’t know that the person in front of you has just been left by his wife (for example) and he is very upset.

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