When we hear the word ‘game,’ we usually start thinking of some fun and amazing activities that one plays, but the ‘game theory’ is the study of the mathematical and scientific model of strategic decision making, which focuses on analyzing the various cost and benefits involved in any situation (game) and trying to make the best possible solution that offers the maximum benefit and minimum or zero lose. The economist Oskar Morgenstern and the mathematician John Neumann first formulated the game theory in 1940, and another mathematician John Nash further advanced their work and modernised the game theory. The game theory comes into play whenever the person tries to make any decision by understanding the several rules of the game, wherein each of the players receives the payoff according to the effectiveness of his/her decision. Nearly 12 professional economists and researchers have been bestowed with the Noble Prize in Economics for contributing to the advancement of the game theory. The game theory finds its applications in several areas, which include finance, business, psychology, political science, social sciences, computer science, mathematics, and philosophy. An understanding of the game theory can help the person in making a clear analysis of the problem, and finding the best possible solution to any given problem. Here in this article, we’ll learn about the game theory and the various real-life examples of the game theory.
Five Types of Games in Game Theory
1. Cooperative and Non-Cooperative Games
There are several types of games in the game theory, however, the two commonly known types of game theory are cooperative and non-cooperative games. In cooperative games, the players have to follow a specific strategy by negotiating with the other players. The problems are solved by following the agreement based on the mutual discussion among the players. The cooperative game theory focuses on the interaction of the cooperative groups and coalitions when the players are only aware of the payoffs. The cooperative game theory also questions how do the groups formulate and how the payoffs are distributed among the players. Let us understand this type through an example, suppose company X which manufactures alcohol has to spend a huge amount on the marketing of its product, hence the management decides to reduce the high ad-expenditure. But, the problem is that there is not any surety that the other companies who produce the same product will also do the same and spend less on marketing. Hence, a dillemma is created among the cigarette manufacturing companies that whether they should lower their budget on marketing or not because if one company does not follow the agreement and spends more on marketing then that company may get the profit while others who follow the agreement are likely to face the losses. However, if the authorities or the government passes a rule that restricts cigarette advertisement, it would be helpful for company A in reducing its advertisement budget. Here, even though the government may take the decision for the health of the people but it worked as cooperation for company A, hence it is an example of a cooperative game. Contrary to cooperative games, in non-cooperative games, the player focuses only on their profits and makes the strategies for their own maximum profit. Non-cooperative theory deals with how do the players think rationally and deal with the other players to achieve their targets. Rock-paper-scissors are a prominent example of a non-cooperative game. It is a strategic game, wherein the outcome is based on the combination of various sets of choices.
2. Normal Form and Extensive Form Game
When the description of the game, i.e., the strategies of the players and the payoffs are represented in the tabular or matrix form, it is called normal form games. These types of games help to find the Nash equilibrium and the strategies that can dominate the other players. The matrix in the normal game form represents the type of strategies used by the players and the possible outcomes associated with those strategies. While in the case of the extensive game forms, the description of the game is given in the form of a decision tree. In the case of the extensive game, the naturally occurring event in the game can be easily represented. The representation forms a tree-like structure, and the player’s names are defined on the nodes. Also, the possible actions and the payoffs of the players are also represented in the structure. To understand the extensive form of games, let us consider an example, suppose company A is an older organization with around a decade of experience, and company B is in the initial phase and wants to enter the market. Company B has two strategies, the first is that enter the market and face a strong challenge from the existing company B, and the second option is that avoid the chance to earn more profit by not entering the new market. Company A also has two strategies, i.e., either to face the competition from company A and risk its existence or help organization B in entering the new market and both companies cooperate with each other. The figure below represents that company B takes the first step and this step is later followed by company A. The payoff of company B will be zero if it does not enter the market, but if the company decides to enter the market the payoff would depend upon the situation of the market which is controlled by company A. If both the companies decide to compete with each other, both of them are likely to face a loss. But, if company A cooperates with company B, then both the companies can make an equal profit. Hence, the best suitable strategy, in this case, would be that company B enters the market and company A helps company B.
3. Symmetric and Asymmetric Games
The main feature of symmetric games is that all the players in these games adopt the same strategies. This is usually applicable in the short-duration games because in the long-duration games the players get a more number of options. In symmetric games, the decisions do not depend upon the player, in fact, it is based on the type of strategies used. The decisions in the symmetric games remain the same even if the players are interchanged in the game. The prisoner’s dilemma is a prominent example of the symmetric game. This example is discussed further in this article. In the case of asymmetric games, the decisions depend upon the players. In these games, if a particular strategy provides benefits to one player, it does not assure that the other player will also get equal benefits. A prominent example of asymmetric games is the decision of the company to enter the new market.
4. Simultaneous Games and Sequential Games
Those games in which the two or more players simultaneously play the move (adopt strategies) are known as simultaneous games. In simultaneous games, the players are not aware of the moves of the other players, while in the case of sequential games the players know about the moves of the other players if they already have applied any particular strategy. However, the players do not have a deep understanding of the type of strategies that may be used by the other players, for example, the player has the knowledge that the other player may not use only a single strategy, but he/she does not know that how many strategies the other player may adopt. We can represent the sequential games in the extensive form, and the simultaneous games in the normal form. The application of the simultaneous move game can be understood through the following example.
Suppose company A and company B both want to outsource their marketing budget. However, the companies have a fear that if they outsource their marketing budget, the other companies that are spending huge on marketing will gain more profit. Hence companies A and B have two strategies, i.e., either to outsource their marketing budget or not. In the following table, it can be observed that companies A and B are not aware of each other’s strategies. Both the companies operate on the assumption that the other company will choose the best strategy for itself, hence both the companies will choose the strategy that benefits themselves.
This example can also be used to represent the sequential move games. Suppose company A makes the first move and decides either to outsource its marketing strategies or not (as shown in the image below). It can be seen in the image below that the first strategy was decided by company A, and the decision of company B is based on the decision of company A. However, the outcome of the game is dependent upon the strategy of company B. In this example, the second player (company Y) has the knowledge of the strategy of the first player (company X).
5. Constant Sum, Zero-sum and Non-Zero-Sum Games
In the constant sum game, even if the players have received different outcomes, the sum of all the outcomes will always remain constant. In the zero-sum game, the net of all the player’s outcomes is zero. In a zero-sum game, the available resources can not be affected by the strategies of the different players. Also, the important feature of this game is that the gains and losses are proportional, i.e., the loss of one player is equal to the gains of the other player. On contrary to this, in the non-zero games, the net of all the outcomes of the players is not zero. The non-zero-sum games can be converted to zero-sum games if we add an extra player (dummy player). The dummy player’s losses are proportional to the net earnings of the other players. The main examples of zero-sum games are gambling and chess, in these games clearly if one player losses the other player wins, i.e., the loss of one player is the gain of the other player. Also, ‘matching coin’ is a most used type of zero-sum game. It consists of two players, says player A and player B. In this game, each player simultaneously puts the coins on the table, and the payoff is dependent upon whether the coins match or not. If both the coins show head or tails, then player A will win the game and gets the coin of player B. If the coins do not match, player B will win the game and he/she will keep the coin of player A.
Examples of Game Theory Strategies
Game theory is used to analyse the number of games. Let us understand the analyses of some games through the following examples,
1. Prisoner’s Dilemma
The prisoner’s dilemma is one of the most popular examples of game theory. Let us suppose two people say Prisoner-A and Prisoner-B are arrested for committing a crime, however, the prosecutor still needs a shred of proper evidence to decide their conviction. To get the confession from the prisoners they question the two in the different rooms. Both the prisoners are separated and there are not any means of communication between them. The officials proposed some deals to both the prisoners. According to the deals, if both the prisoners confess the crime, each of the prisoners will receive a prison sentence of five years. If prisoner-A confesses the crime, but prisoner B denies it, then Prisoner A will receive a three years prison sentence, and prisoner B will be freed. If prisoner B confesses, but prisoner A denies, then prisoner B will get the three years prison sentence, and prisoner A will be freed from the prison sentence. If both the prisoners do not confess, they both will receive two years of prison confession. Now, from all of the given deals, the most favourable one is that neither of the prisoners confesses as they are receiving the lesser punishment (two years of imprisonment) in this case only. However, the problem is that the prisoners do not know the strategies each other, they are not certain whether the other prisoner will confess or not. According to the Nash equilibrium, the prisoners are more likely to choose the deal that is best for their own but is worst for both of them collectively, i.e., the expression ‘tit for tat’ is considered the best solution as per the game theory. The concept of tit-for-tat was presented by an American mathematical psychologist, Anatol Rapoport, who stated that the players are likely to not cooperate if provoked, while they are likely to cooperate if unprovoked.
The deadlock is a social dilemma similar to the example of the prisoner’s dilemma in which the players either cooperate with each other or do not cooperate (defect). In a deadlock, if organization X and organization Y both cooperate, then both the organization will receive the payoff of 1, and if they both do not cooperate, they will receive the payoff of 2. If organization X cooperates and organization Y defects, the organization will get the payoff of zero, while organization Y will get the payoff of 3. Unlike prisoner’s dilemma, in case of deadlock, if both the organizations do not cooperate is also an effective strategy. Let us understand the deadlock through an example. Suppose the two powerful nations are trying to settle for an agreement that manufacturing nuclear weapons should be prohibited. In this case, cooperation means that both nations stick to the agreement and do not manufacture nuclear weapons, while the defections imply that either one or both the nations secretly break the agreement and manufacture the nuclear weapons. Unfortunately, in this case, the dominant outcome for either of the nation would be secretly breaking the agreement and manufacturing nuclear weapons because it will give that nation a benefit over the other nation in case the war occurs. The other effective option is that if both the nation do not cooperate and keep on manufacturing nuclear weapons. The following image represents the example of a deadlock between organization X and organization Y.
3. Cournot Competition
This game is named after its inventor Augustin Cournot, a French mathematician who presented this model in 1838. Its concept is similar to the prisoner’s dilemma. The Cournot model is utilized in explaining the duopoly, i.e., the competition between the two main organizations in a market. For example, suppose the company X and Y both manufacture similar products and they can manufacture the product in large and small quantities. If both the companies corporate with each other and decide to manufacture the product in lower quantity, then the limited supply of that product in the market will result in a rise in the price of that product, hence both the companies will get the benefit. However, if both the companies revoke and decide to defeat each other and produce the product of higher quality, it will result in a low price of that product and both the companies will face the drawbacks. Also, if one company cooperates and produces the product in lower quantity while the other company do not, i.e., produce the product in high quantity, then the former company will suffer the loss, while the latter will earn the maximum profit. The payoff matrix of company X and company Y is shown in the image-A below (profits are represented in millions of dollars).
4. Dictator Game
In this game, player X has to decide the division of the payoff with the player Y, who has zero contribution to the decision of player X. According to the results revealed by different experiments, it was found that in this scenario, 50 per cent of people keep all the payoff to themselves, 45 per cent of people give a small share of the payoff to the other, while only 5 per cent of people split the payoff equally. The dictator game is almost similar to the ultimatum game; in the ultimatum game, a certain amount of cash is given to player X, part of which he/she has to give to the player Y, who has to either accept or reject the given amount. If player Y rejects the amount offered, then both the players will get nothing.
5. Coordination Game
In coordination games, the players get the maximum benefits if they choose the same strategy. For example, suppose the two giant tech companies are in the dilemma of whether to introduce new technology in the computers that would make them earn huge or advance the old technology that would make them earn only a few. The problem is if only one company decides to introduce the new technology in computers the customers would find it difficult to adapt to the new technology and prefers to buy the systems with the technology that the customers are familiar to use, hence as a result the company will face losses. On the other hand, if both the companies decide to introduce the new technology, the customers will be left with no other option than to buy the computers with the new technology. Hence, in this case, both the companies will earn more and gets a profit.
6. The Centipede Game
In the centipede game, the two players get the alternative turns to get the larger share of the money stash, which is increasing slowly. It is a sequential game as players do not make the move simultaneously, in fact, they make the moves one after the other, hence they are aware of the strategy of the player who made the move before them. The game ends the moment when the players get the stash, where one player gets the larger portion and the other gets the smaller portion. For example, suppose player X starts the game and has to either ‘take’ or ‘pass’ the stash, which amounts to two dollars. If player X takes the stash, then both player X and player Y will get one dollar each, but if player X pass the stash, now, player Y has to decide whether to pass or take the stash. If player Y takes this stash, he will get the three dollars (previous 2 dollars + 1 dollar), while player X will get the zero dollars. However, if player Y passes, player A gets the chance to decide. In case both the players always choose to pass the stash, they both will receive the payoff of 100 dollars at the last. The catch here is that the players will get the maximum payoff if both the players keep on passing until the last of the game. But, as predicted by the Nash equilibrium, if any of the players disrupt the game and choose to ‘take the stash’ the players are likely to get the lowest payoff of one dollar. However, some experimental studies have revealed that this type of rational behaviour, which is anticipated by the game theory, is rarely observed in real life.
7. Volunteer’s Dilemma
In the case of the volunteer’s dilemma, someone has to take the responsibility for the benefit of a large number of people. According to the game theory, the worst outcome would be, if nobody dares to volunteer. For example, suppose some junior members of the recruitment agency assigned by the government to hire the people for various state-level vacancies are frauds and are responsible for the malfunctioning the recruitment drives. The higher authorities are unaware of this malfunctioning. Some other members who know about this fraud are hesitant to tell the higher authorities about this fraud as they are scared to lose their job or be called whistleblowers by the members involved in the fraud. But, if nobody dares to volunteer the fraud will result in a large disruption in the state.
Real-Life Game Theory Examples
Every person uses game theory in his/her everyday life whether consciously or unconsciously. Our everyday decisions of doing a particular task first and the other tasks later are based on the concept of the game theory. Let us discuss some real-life examples where the concepts of game theory are being utilized.
1. Pricing Decision
Game theory helps in determining the strategies of the consumer and the retailer price. Retailers attract the market by luring them with attractive sales on particular goods or services to increase their sales. You must be aware of that off-season sale, when the vendors offer the product at an amazing price, well this is one of the strategies of the game theory. The two main players in this game of pricing decisions are the retailers and the consumers. The customers want the goods at the best prices, and the retailer makes use of the best pricing tactic.
2. Collective Bargaining
One of the best examples of game theory is negotiation or collective bargaining. For example, in case of a strike by the employees to raise their wages, the union and management negotiate with the protestors and prefer to increase the wages because as per the game theory this seems to be the best possible solution to handle the situation as this ensures the benefits of both the workers and the management. Other applications include negotiations with the suppliers and negotiation for compensation or incentives by the workers to the management or the supplier.
3. New Product Decision
The understanding of Game theory helps businesses to decide whether they should launch a new product or not. Game theory helps them in understanding the moves of the competitor that may launch a similar product, and also the strategies they may apply in defence. The game theory can provide a rough analysis of the success and the failure of the new launch, hence businessmen could take the best decision with the help of game theory.
4. In Negotiating Salary
Asking for raise in salary is a complex task, it gets even more complex if more than one person is involved in the negotiation. The game theory helps in better negotiation with the manager. One should be aware of the kind of services he/she provides and the worth of those services in the company. One can not simply go and ask for a raise just because he/she wants a higher salary. According to the game theory, you must be well known about the person with whom you are making the salary negotiations and be prepared for the potential responses and the counter-arguments. If you know how to effectively respond to the person with whom you are negotiating about the salary, then chances are high that you will get the raise, considering you have the skill and values that add worth to the organization.
5. While Buying Car
Game theory can help you to buy the car at a much cheaper price than the amount it will cost you otherwise. The first step of car buying is looking for the dealers near your area that sells the car you want. Now, rather than simply visiting the dealers and bargaining with the salesperson, the better step is to call each dealer and mention to them that you are looking for a particular car and you will buy it from the dealer that will give the best offer. The dealer may deny negotiating about the price on the mobile, but you should respond confidently that you are only available for the negotiations over the phone and will consider buying if the offer is good. The dealer will then try to give the best offer to seal the deal. Hence, by using the strategies of the game theory you can buy the car at much lower prices.
6. Real Estate
You may have never noticed before, but the game theory finds its applications in real estate. Most of the real estate negotiations are already understood by the agents which makes it easier for sealing a deal. But, the situation is entirely different in the multi offers deals. You will only have the three options if the bid you have submitted is announced as a multi-offer situation by the real estate agent. These three options are
- Keeping the original offer
- Withdrawing the current offer
- raises the offer price
To win the bid the person have to overbid the other bidder. If the game theory is followed, the person should bid the number he/she has calculated to win the bid according to his/her budget, rather than increasing the price in bidding over the budget. In this case, even if you lose the bid, you still had made an effective decision because bidding at a price that is not in your budget is an incorrect decision that may cause a burden on you.
7. Rise and Fall of Bitcoin
Sometimes the decisions of the people in doing a certain task are not only based on their own perspective but it is influenced by the decisions of the majority of the population. Stock trading and crypto trading are prominent examples of decisions dependent upon other people and utilization of game theory. Suppose you want to buy a bitcoin. What would be your first step? Of course, you will look at the chart of the recent fluctuation to decide whether to buy the bitcoin or not. You see that a large number of people are buying the bitcoin and they are gaining profit and you also buy the bitcoin. Now, suppose a well known financial expert posts a tweet that questions the stability of the bitcoin. Like another majority of people, you also think of selling the bitcoin as an expert has criticized it, and the value of the bitcoin gets lower. Hence, in this case, the game theory results in the rise and fall of bitcoin.
8. During Auction
Before putting any of your assets in the auction, deciding the type of auction that would be suitable for better gain is an important step. There are a number of different methods in which an auction can be conducted; the ‘second prize auction’ recommended by Canadian-American economics professor William Vickery is one of the best ways of conducting an auction. In this method, the members bid for the asset by offering the highest amount, however, the person who bid the highest amount is not required to give the highest bid price, instead, he/she has to pay the second-highest bid price. This strategy makes the participants bid for the higher amount as they will think that they are saving money as they have to pay the second-highest bid price and not the highest bid price.