Game Theory and the reasons for filing Lawsuits

It is a great opportunity for us to write in an interesting topic titled “Game Theory and Law: A study of the reason for filing Suits”. At the time of preparing this term paper we have gone through different books and websites which helped us to get acquainted with new topics. We are actually focusing on those topics which are important for us to understand about this subject easily. We would Ilke to thank Dr. Bimal Patel for giving acknowledge with gratitude to Professor Dr Ranita Nagar and

Hitesh Thakkar, my respective teachers, who have always been sincere and helpful in making me understanding the different concepts of the relation between law and economics and importance of intellectual property rights. Apart from me this paper will certainly be immense importance for those who are interesting to know about law and economics. We hope It will be comprehensible. We have tried hard and soul to gather all relevant documents regarding this subject. We don’t know far we are able to do that.

Furthermore we dont claim all the information in this term paper is included perfectly. There may be shortcoming, factual error, mistaken opinion which are all mine and we are responsible for those but we will try to give a better volume in future Game Theory analysis the two or more parties, who interact with each other and choose strategies and policies in the same manner. For example Government, law and firms. The basic element of Game Theory includes players who determine their different actions and strategies to tackle market and other firm of same sector.

The new element Is payoff table of a game which shows different strategic options for firm to apply and the effect on them. The answer why to choose game theory is to determine their own goal and to determine their opponent’s goal because any firm while active in market cannot deny other side because their decision may collude with the firm’s goal. While playing game in the field of law, assume that your opponent will surely think for his or her benefit. A player has two option always either go by Dominant strategy or by Nash equlllbrlum (non co-operative strategy).

Either firm can collude or co-operate, but the Government initiative to table anti-trust law and reason behind it is that two firm may co-operate on higher prices and can exploit consumer. Sometimes, non co-operative behaviour may harm as such they can harm other elements of surroundings and they start believing that winners take all-game. Founding Fathers Game Theory was founded by John von Neumann and Oscar Morgenstern and published in Theory of Games and Economic Behavior (Princeton University Press, Princeton, N. J. , 1980) in the year 1944.

Definition Game Theory: An analysis of situation involving two or more decision makers with at least partially conflicting interest. It can be applied to the interaction of oligopolistic markets as well as to bargaining situations such as strikes, conflicts, punishments, ar, union-management disputes, countries trade policies and international environment agreements. Concept Strategic Thinking is the art of outdoing an adversary, knowing that the adversary is trying to do the same to you. Avinash Dixit and Barry Nalebuff Basic Concepts: Now we will illustrate the basic concept by analyzing a duopoly price game.

This is a situation where the market or institution is supplied by two firms/persons that are deciding to engage in warfare or to cooperate. Let start understanding game theory with the economic concept. Normal Price Amazing Price nEwBooks Price Price War Analysis:2 A useful tool for representing the interaction between two firms/people is a two-way payoff table. A payoff table is a means of showing the strategies and the payoffs game of the two players. For example nEwBooks can choose between its two columns and Amazing can choose between its two rows.

In this example, each firm decides whether to charge its normal price or to start a price war by choosing lower price. Combining the two decisions gives four possible outcomes, which are shown in the four cells of table. Cell A, at the upper-left shows the outcome when both the firms choose the normal rice; Cell D, is the outcome when both choose to conduct a price war; and Cell B and C results when one firm has a normal price and one firm has a war price. For example, in Cell C Amazing plays “price war” and nEwBooks plays “normal price” the result is that Amazing earns profit of -$100 while other firm earns profit of -$10 as a whole.

Thinking through the best strategies for each players leads to the dominant equilibrium in Cell A. Alternative Strategies: The new element of the game theory is to think that or to work out keeping in mind the decision of your opponents to achieve goals by that particular opponent and onsidering its action towards achieving goals. But you must remember that opponent may try hard to bit you. Let’s know apply this strategy to above mention example. First, the two firms earn the same amount of profit and highest Joint profit in Cell – A. Each firm earns $10 by following normal price strategy.

On the other end both follows price war which leads to cut prices and runs a big loss. In between two strategies were played from both the sides. For example, the outcome of the Cell clearly shows that Amazing engages in a price war and on the other hand nEwBooks follows normal price strategy which results into a loss for Amazing but akes most of the market by selling products or goods below cost; on the other hand nEwBooks is actually applying normal price strategy which helps to earn a good amount of profit but fails to take most of the market.

There are basically two types of strategy/equilibrium: 1. Dominant Strategy 2. Nash Equilibrium3 Dominant Strategy: strategy the other player follows. In our example, consider the options open to Amazing. If nEwBooks declares normal price, nEwBooks will earn $10 of profit, if Amazing plays normal price strategy but losses $10 if Amazing declares economic warfare. If nEwBooks declares warfare then they will lose $100 while Amazing losses only $10. Therefore, no matter what strategy the other firm follows, each firm’s best strategy is to follow normal price.

Charging the normal price is the best price for the any firm not keeping in mind other firms strategy or price war game. Nash Equilibrium: In above mentioned example, both the firms earn huge profit or Joint profits in cell A. Situation A would surely come if both the firm colludes for price of the products. In our example in Cell B Amazing follows normal- price strategy4 and nEwBook follows igh- price strategy so in reality consumer would tend towards low price products so no doubt normal-price strategy would win over high-price strategy.

On the other hand in the Cell C Amazing follows high-price strategy and nEwBook follows normal- price so nEwBook will take lead over Amazing in earning profit. So now whether it is better to play high-price or normal-price strategy? The answer would be simple to follow the strategy what our rivalry follows and to be at his shoes is better option because you should set your strategy on the assumptions that your opponent will act in his or her best interest. This is known as Nash Equilibrium or No cooperative equilibrium where firms do not take care of consumers or for the welfare of society but keeps price strategy what they think it as best.

In our example if nEwbook follows normal-price and then turns to high-price which leads to earn more amount of profit but if Amazing increase price but doesn’t follows high-price which may help them to earn more profit than nEwBook. Now let’s consider cooperative equilibrium If say both the firms are following high-price strategy soon Amazing slightly reduces price which affects profit margin of both the firm in which Amazing would earn more rofit after then nEwBook would be affected by low profit margin so it will lead them to decrease price of products i. . cell D. Government is so keen to table antitrust law is because of this reason that two firm may decide monopolistic price of product and may sell it which leads to mbalance in market so Government would charge high penalties for such a illegal act. Moreover competitive equilibrium is Nash Equilibrium as such no firm would change price strategy until and unless other changes. In perfectly competitive economy, non co-operation behavior helps to maintain economic efficiency.

In earlier example we saw that sometimes Nash and Dominant strategy is useful for economic balance but it is rather very important to compare law and Game Theory and especially with Prisoner’s Dilemma. 5 In above mentioned example District Attorney investigates to criminals. District Attorney said both of them separately about the crime they have done and threatened them that he has sufficient evidence to prison them at least for 1 year. Now he gave offer that if any one of them s confess then he would be Jailed for only 3 months while other would be punished for 10 years but if both of them confesses then both will be punished for 5 years.

So now prisoner’s are facing dilemma that who will confess and who is not going to? If any one of them confesses will lead to imprisonment of 3 months who confessed and 10 years to other one Confess Knuckles No Confess Analysis Molly Now there are four probabilities which are shown as above. imprisoned for 1 year. This cell is result of selfishness among both of them. Any one of them doesn’t want to sacrifice for the other one. Both want to get less imprisoned and this clearly shows competitive mind. It may be result of Dominant Strategy where the one doesn’t care of the other. 2) Cell B: In this case both are co-operative to quite extent. Over here one confesses while other remains silent over the matter. So any one of them will suffer Jail term of 3 months while other will imprisoned for 10 years. This is result of keeping eye over what other do in this matter. Molly may confess thinking that Knuckles would not and it happens due to certain reasons. (3) Cell C: It is result totally opposite what is of Cell B. Over here Knuckles keep eye over Molly and confess what he has done while on the other hand Molly remains silent.

So one sacrifices for the other or may be not because one may have thought the other one might have followed him but it was not as per his expectations. 4) Cell D: In the last cell both of them shows their co-cooperativeness over this matter. In this the period of criminals remaining in the Jail is quite higher as such no one of them confesses what they have done. They both simultaneously pass 5 year in the Jail and this is result of co-cooperativeness and if it happens in number of cases then numbers of criminals would be in Jail for more years than what if one confess and other remains silent Overview: What should Molly do?

Should she confess and hope to get a short sentence? Three months are preferable to the year she would get if she remains silent. But wait. There is an even better reason for confessing Suppose Molly doesn’t confess but Knuckles then it would imprisoned her for 10 years, so it would be better to confess either it would result 1 or5 year Jail imprisonment Knuckles is also in the same dilemma. The significant result here is that when both prisoners act selfishly by confessing, they both end up with long imprisonment. Only if both act collusively they end up with shorter imprisonment. Implication of Game Theory in various fields of Law The economic analysis of law is an interdisciplinary subject that brings together two reat fields of study and facilitates a greater understanding of both. Economics helps us to perceive law in a new way, which is extremely useful for the people who are connected to the field of law. The law frequently confronts situations in which there are few decision-makers and in which the optimal action for one person to take depends on what another actor chooses. These situations are like games in that people must decide upon a strategy.

A strategy is a plan for acting that responds to important. Game Theory helps in enhancing the understanding of some legal rules and regulations. By using the principles in game theory, many legal aspects and proceedings can be better learnt and understood. Game theory can be extremely useful in understanding why a plaintiff sues the other party anyway? What is the thought process that the party who sues goes through before suing and what are the factors that the party considers before filing a suit? It also helps in understanding the agency game in contracts.

So, let us begin with the first and foremost aspect: Why does one party sue the other party? For any wrong committed by a person against another person, the law provides a emedy for the aggrieved party. The aggrieved party has the option of going to the court and asking for a remedy which is the inception point of all other legal formalities and proceedings. But still, not all the disputes go to the court. People don’t knock on the doors of the Court of Justice for each and every grievances incurred by them. Now, why is this so? When law provides a remedy of going to the court, why do people not go to court for every dispute resolution?

There are certain factors which determine whether the case is worthy of going to trial or not. Those factors are as following: l. Computing the value of a claim: Before filing any case in the court of law, the complainant must keep in mind the expected value of the claim8(hereinafter referred to as EVC). It depends on what the complainant thinks will incur after the suit goes to trial. To decide upon the fact whether the plaintiff should file a complaint or not, it must take into account the probabilities and payoffs to these events. 9 The EVC can be computed taking various equations. 0 First, we shall start with the least possible option, which is after the trial, aggrieved by the decision of the Court the complainant goes for an appeal. First, we will determine the EVA in appeal and then gradually reach the first stage. Suppose the plaintiff who wants to go for an appeal after losing in the trial has to pay Rs. 20 to appeal the case. On appeal, the plaintiff stands a chance of winning Rs. 100 with a probability 0. 1 and losing with the probability of 0. 9. Thus, the EVA can be calculated as following: EVA= 0. 1(100) + 0. 9(0) – 20 = -10 The EVA here is negative.

Any rational plaintiff who finds out that the chances of winning are thin and the cost is likely to be more than the earnings would most certainly not go for an appeal. Now, we can compute the value of the first trial. The plaintiff only goes to trial if he fails to settle with the defendant. In this case, as both the parties failed to settle, we can safely assume that according to both the parties, the minimum chances of them winning should minimum be 0. 5. Now, to go for trial, one must pay Rs. 20. The plaintiff stands to win Rs. 100 at the probability of 0. 5 and lose with the probability of 0. . If the plaintiff loses, as established in the previous paragraph, he will not go to trial. So, he will receive the payoff equal to Rs. O. So, the EVT is: EVT= 0. 5(100) + 30 As we have now computed the value of trial, we shall now compute the value of bargain before the trial. After the exchange of information, both the parties pretty much realise the chances of them winning or losing. The plaintiff can now bargain to the defendant settles for Rs. 50 and the plaintiff pays a settlement cost of Rs. 1. If the bargain fails, then the case goes to trial in which case the value of the trial is Rs. 0. 11 By combining these numbers we can get the expected value of settlement bargain(EVB): EVB= 0. 7(50-1) + 0. 3(30) = 43. 30 The fact that the settlement value is positive, the plaintiff reaching this stage will be appy to bargain and avoid the hassles of the Court! Now we can compute the expected value of the legal claim when the complaint is filed. Even after the suit is filed, the parties can still settle outside the court as in some cases it might even be a win-win situation for both the parties. The plaintiff who files a complaint settles immediately with the probability of 0. in which case he receives Rs. 50 and pays Re. 1 in settlement cost. Alternatively, the plaintiff fails to settle with the probability of 0. 3 and proceeds to the exchange of information which costs Rs. 3. 30. Even after the xchange of information, the process of bargaining between the parties continues incessantly. We have computed the EVB which is 43. 30. By combining these numbers we can obtain the expected value of the legal claim when the plaintiff initiates the suit by filing a complaint in the court of law: EVC= 0. 7(50-1) + 0. 3(43. 30-3. 30) = 46. 0 The filing cost (FC) includes the cost of hiring a lawyer, drafting the complaint and paying the filing fees assessed by the court. Let’s say the FC here is Rs. 10. The plaintiff gets Rs. 46. 30 from filing the suit and after paying the FC, the payoff from filing equals Rs. 36. 30. When the expected net payoff is positive, the rational plaintiff is expected to file a complaint. EVC FC – files a legal complaint EVC Injuries that trigger disputes 2. The cost of filing a complaint 3. The expected value of the claim To see these causes at work, consider how the increase in damages awarded at trial would affect the filing of legal complaints. 12 An increase in damages awarded at trials will increase the EV’T13, which in will lead to increased EVC and thus leading to ore filing of the claims by complainants. To illustrate this point, if the cost of filing a suit is Rs. 500, and the damages awarded are Rs. 1000 and the probability of winning is 0. , then the 0. 5(1000) + 0. 5(0) – 501 = -1 . No one will file a suit in this situation but if the damages awarded are Rs. 2000, then EW will be Rs. 499, a really big incentive for the aggrieved parties to file a suit. But, increase in the awarded damages can have its effects in an opposite direction as well. If the amount of damages paid is high, the potential defendants will be more cautious as to they don’t n the decrease in negligence thus, bringing down the number of cause of action for filing the suits itself.

For example, the manufacturers would try to avoid the liability by doing quality control. The chart above suggests that the number of suits increases with the amount of damages awarded and after one point, it starts decreasing as the defendants start taking more precautions and avoid negligent act. Ill. Filing Cost: In some civil law countries, the cost of filing a civil suit is borne by the government itself. But, in common law countries like India, the cost of filing a suit is borne by the arties to the suit themselves, the situation arises where the filing costs have to be determined.

The cost has to be proportionate in such a way that it doesn’t become too great a burden on the parties filing it. This section concerns how to set the filing fees. In the figure below, the horizontal axis indicates the EVC and the vertical axis indicates the number of potential plaintiffs. Out of these claims, only some of the plaintiffs have worthy claims. Now how to draw the line between worthy and unworthy claims? The line indicating filing costs partitions the distribution of potential plaintiffs into two groups.

For those plaintiffs to the left of FC, the filing cost exceeds the expected value of the legal claim. So these plaintiffs don’t sue. For the plaintiffs to the right of the FC, the expected value of the legal claim exceeds the filing cost, so the plaintiffs file the suit. Thus, filing costs are the filter for disputes. Only those to the right of the FC have a higher probability of suing. If the authorities increase the filing cost, it will cause a shift in the above given chart and thus making the border line worthy suits unworthy and as a result of that, causing a decrease in the number of cases. V. Supply of Legal Services: Here, in this section the point kept in centre is how an increase in the number of lawyers affects the filing of legal claims. The effect of the increase in number of lawyers depends upon the organisation controlling it i. e. the bar council of each country. In the country like India, where the lawyers are given the freedom to contract with their clients and decide the fees accordingly, it results in lowering the cost of filing the suit. To elaborate on this point, suppose that a lawyer charges contingency fees14.

Suppose that the plaintiff expects to win Rs. 1000 with the probability of 0. 5. the contingency fees is 0. . So, the expected value of the claim to the plaintiffs lawyer would be = 150. If the case takes two hours of preparation, then the hourly gain for the lawyer is Rs. 75. The profit maximizing lawyer will not take this case to the court if he has any other alternative paying him more than Rs. 75 per hour. But the increase in the number of lawyers would mean decrease in opportunities for an average lawyer.

But since the number of lawyers is high and the opportunities scarce, they will also take those cases to the court which they previously wouldn’t have. But this notion does not apply in all the countries. The Bar of some countries has insulated itself from the law of demand and supply and has been regulating the legal market to a great extent. V. Agency Problem: whether to put the valuable asset in the hands of the agent and the agent decides whether to cooperate or not. In lawyer’s case, Lawyer is the agent of their clients.

He provides his client with advice. So, what are his incentives to provide service and advice to the client? Lawyer’s incentives to work on a case are the contingency fees. To maximize the Joint payoffs, the lawyer should work on the case until the marginal cost equals the marginal benefits for both the parties. The marginal cost of the lawyer’s time spent on a suit equals in its value in the best alternative use. 1 5 Usually the lawyers focus upon three factors such as time spent working, service performed and the outcome of the dispute.

Hourly billing, as popularized by the giant law firms, externalizes the cost of working on a case. It also gives them an incentive to devote too much time on one case. This pattern of hourly billing can have some adverse effects as well. Now comes into picture the lawyer’s incentive to give information. Suppose a plaintiff approaches the lawyer for an advice regarding the suit and the FC xceeds the EVC. But the lawyer being paid by the hour might get induced in giving false information and exaggerating the value of the claim.

A lawyer being paid on contingency basis may be induced to misguide the clients. The lawyer internalizes all cost of filing the claim and one-third value of the claim. Even if the EVC exceeds the FC, the lawyer may not take up the case if the marginal benefit for him is not so great. Conclusion The insights of Game Theory include events of everyday life, economy, law, trade, social science. Game Theory can explain law with the of Prisoners dilemma whether o confess or not to confess with the help of their opponent’s strategy.

Basically Game theory helps to determine competition among different foreign firm. A key feature is to gain credibility is one must consistent with the incentives of the game. For example Judges can give Judgement by following the principles of not becoming bias and following natural law principles. These few example provide a small taste from the vast harvest produced by game theories over the last centuries. This field is very much useful for lawyers and Judges where numbers of people are being informed about various legal principle existing society.