Terms Beginning With 'p'

Prisoner’s Dilemma

  • October 28, 2020
  • Team Kalkine

What is meant by Prisoner’s Dilemma?

Prisoners Dilemma is a game theory experiment that deals with the players’ decision making skills based on variable outcomes presented to them. There are two players in the game and neither of them is aware about the decision taken by the other. This is a crucial aspect of the game as the independent decision making of both the players alters the outcomes for both.

This example highlights the trade-off faced by individuals between being competitive and being cooperative. If the players cooperate then the outcomes are relatively better for both, however if they do not, then one of them might be better off while the other would be worse off.

Game Theory, branch of applied mathematics, is defined as the competitive and strategic interaction between 2 more or players in an economic/philosophical situation, playing according to set norms.

How does the game work?

The game starts with two prisoners: Prisoner A and Prisoner B. Both are suspected of committing a crime, to which they have not admitted yet. Each of them wants the lowest possible prison sentence and does not know whether the other prisoner would confess or not. However, all possible outcomes are presented to them, upon which they must make their decisions.

There are four possible outcomes:

  1. Neither A nor B confesses: If neither of the prisoners confess to the crime, then they would both face one year of jail time (as they have been caught with weapons).
  2. Both A and B confess: Both would face 5 years or jail time if they both confess independently.
  3. A confesses and B does not confess: If only A confesses then he would not face any jail time, however B would face 20 years in jail.
  4. B confesses and A does not confess: Like in case 3, if only B confesses then he would not face any jail time, however A would be sentenced to 20 years in jail.

What do the different outcomes mean for the players?

The unique aspect of any game theory analysis, including Prisoner’s Dilemma game, is that the knowledge about the future outcomes might alter the current decision-making of the players. However, this knowledge about the future outcomes is partial as it depends not just on the player himself, but also on his accomplice.

Here the best possible outcome for either one is to go free, however, this is only possible at the cost of leaving behind the other to serve 20 years in jail. The worst possible outcome for either one of them, individually, is when the other confesses alone. Both these extreme outcomes for an individual player are limited to the win-lose cases. 

If the cooperative cases are examined, then the punishment lies somewhere in the middle for both. Among the cooperative cases, if neither of them confesses then they are better off than when they both confess.

What is the solution to this game theory experiment?

Both A and B know that if the other confesses, then the best strategy would be to confess as well. Also, if either one of them thinks the other has not confessed then the best strategy would again be to confess, as that acts in the personal interest of the last decision maker.

Thus, it can be argued that the safer outcome for both would be to confess, irrespective of what the other does.

The absolute strategy of staying quiet for either of the players can only be beneficial when both are sure that the other will stay quiet as well. Therefore, to stay on the safe side both can go by the rationale that admitting to the crime would serve their collective best interest.

Here, it is important to understand the concept of Nash equilibrium, developed by American mathematician, John Nash. This represents a state where neither player has an incentive to change the decision, considering that other does not change the decision too.

To find out the Nash Equilibrium, the first step would be to find out the dominant strategy for an individual player. Dominant Strategy refers to that strategy which has a greater payoff for the player.

For instance, if player A confesses, then the prison time faced by him depending on whether B confesses or not are 5 years and 0 years, respectively. While if A does not confess then the sentence faced by him based on whether B confesses or not is 20 years and 1 year, respectively. It can be clearly seen that A faces lesser prison time when he confesses (5+0) compared to when he lies (20+1). Thus, the dominant strategy for A is to confess.

Given this strategy by A, B now must make his decision. Now B has two options, if he confesses then he would have to serve 5 years of jail time. And if he lies then he would have to serve 20 years of jail time. Thus, the better option for him also is to confess.

Now, taking the reverse course of action, we would consider the actions of A, given B’s dominant strategy. This would follow the same process as was seen in the previous case.

Thus, both A and B can reach the Nash Equilibrium when they confess.

How is Prisoner’s Dilemma solved in real-life?

The scenario of a trade war, or a price war between the producers of homogenous goods or threats by a country of releasing weapons onto another nation are some of the real-life examples of the prisoner’s dilemma game. However, the Nash equilibrium strategy is not pareto optimal. This is so because either of them can become better off if he deflects from this strategy.

For instance, both A and B know that it is possible to reach a relatively better outcome by not confessing at all. However, this would only be beneficial to both when they co-operate. Thus, it is difficult to estimate whether co-operation would be achieved or not. Therefore, effectively, it might seem better to play safe rather than going for the pareto optimal strategy.

Nash Equilibrium strategy might not be the most efficient way to solve Prisoner’s Dilemma. A possible solution to tackle this is to iterate the Prisoner’s Dilemma game. This means repeatedly playing the game. 

Consider the case of finite iterations, each player knows that there will be an end to the game, where they can deflect from the Nash Equilibrium outcome. However, in the case of infinite iterations, a backwards induction could help solve the case. Both players know that there is going to be another stage to the game, thus they feel it is better to stay safe and confess. As a result, repeated iterations fetch the same strategy of confess-confess. Therefore, these iterations will only work when they are done an infinite number of times.

 What is Game Theory? Game theory is a mathematical statistical analysis of how individuals react to different circumstances presented to them. Each situation comes with a set of payoffs and the individuals must decide which move to play based on these expected playoffs. Since these payoffs are known to the players depending on different moves by all the participants, the entire course of action depends on the strategy chosen by the players. This strategy might be incentivising for one and harmful for the other or can be beneficial to both. Thus, the players must decide whether to collaborate, or to work for their own profits. The concept of game theory has various applications in real life. A game theory set up can help alter an individual’s strategy based on his assumptions about the opponent’s move. Thus, it helps determine a sustainable outcome in a situation where two individuals find themselves at conflict. However, not all game theory set ups can be solved productively as they involve trade-offs between what the players desire.  What are the different terms used in game theory analysis? PLAYERS: There are two players in most game theory experiments, and each player is affected by the strategy played by both the players. PAYOFFS: Payoffs refer to the outcomes for each player of the game based on different strategies. A payoff matrix depicts the different situations and the associated outcomes by both the players in a diagram form. STRATEGY: It refers to the course of action adopted by the players depending on the payoff matrix known by them. It can be for personal profit or in collaboration with each other. INFORMATION SET: The players are aware about the possible strategies and the payoffs attached to them. This information forms the information set which is used by the players to choose their moves. What is Nash Equilibrium? Nash equilibrium refers to that outcome in the game in which both players have achieved the best possible solution through a collaboration. This is the state from which neither of the players would want to deviate. This outcome may not always be optimal for both. In certain instances, it might be possible to make one player better off by making the other worse off. What is Pareto Optimality? Pareto Optimality refers to that stage in which both players have reached their best potential. This state considers the individual’s best outcome rather than the collaborative best outcome. Thus, it is that state from which it is not possible to make one player better off without making the other worse off. The outcome for both the players is at its best. A Nash equilibrium may not always be pareto optimal. This means that the outcome which is the collaborative best between both players may not be pareto optimal. Thus, it is possible to deflect from that outcome and make both players reach their personal best. What are the different types of strategies used by the players? The strategies in the game can be of two types: Pure Strategy: This is the strategy which is fully defined for a player and can be thought of as ‘occurring with full probability’. Mixed Strategy: This involves assigning probabilities to pure strategies. This allows players to randomly choose a pure strategy. Thus, pure strategy can be termed as a mixed strategy occurring with probability equal to 1. How is the concept of game theory applied? Prisoner’s Dilemma: The most common application of Game Theory can be seen in the example of Prisoner’s Dilemma. This game involves two prisoners who are not aware about each other’s decisions in the game. Both have been suspected of committing a crime and are held for questioning. The prisoners face different years of jail sentence based on the strategy they choose. The payoff matrix is as follows:   Here the Nash Equilibrium is achieved when both A and B confess. Thus, (5,5) is the collaborative best that both the players can perform. However, this is not the pareto optimal solution. The pareto optimal outcome is (1,1) as both players want to serve as less jail time as possible. Thus, it is not possible for one to be better off without making the other worse off if neither one of them confesses.   Battle of the Sexes: Battle of the sexes is a game where a girl and a boy want to go on an outing together, however the girl prefers going to see an opera while the boy prefers going to a football match. However, going to these places separately does not earn them any payoffs, while going together gives higher payoff to only one of them and not both.   The payoff matrix is as follows: There are two possible Nash equilibria in this game. One is achieved when both go to Opera and the other when they both go to watch the Football match. Is the concept of game theory accurate? The limitation of game theory is that it is based on certain assumptions. It assumes that the players would always act in favour of their personal interests. However, it is possible to witness real life scenarios where people are more collaborative as well as altruistic. It is also possible that in a real life set up, stability is achieved at an outcome which is not a Nash Equilibrium. Depending on the varied social set ups as well as personal preferences, game theory may not always justify real life situation.

Golden parachute refers to an agreement between an employee and an employer under which the employer promises large financial benefits to the employee when he is terminated due to a merger or an acquisition of the company. It can be understood as a compensation offered to certain employees when they are terminated before their contract ends. A Golden parachute clause can discourage companies from a merger or from getting acquired due to the large financial sum involved. This clause is usually included in the agreement of the top executives in a business. The purpose of offering a golden parachute is to ensure that the employee is not disadvantaged or forced out of the company. Companies may offer golden parachute benefits in the form of cash, a special bonus or stock options. Golden handshake is also a clause much like the golden parachute with the only difference of inclusion of severance packages offered upon retirement too. Why was the golden parachute clause introduced? The golden parachute clause was introduced to protect the shareholders and other higher-level executives in case of a merger or a takeover. The term was first used in 1961 and in the 1970s firms began introducing the golden parachute clause in their employment contracts. Over time the intent with which the golden parachute clause was included in an employee’s contract started to change, with newer modifications making it too lenient at times. In current times, the clause has come to be interpreted as a lot more than what it originally was supposed to represent. During the 1980s, the golden parachute became a standard norm followed by various companies. Even small firms adopted a golden parachute clause to protect their employees. Companies would include monetary as well as other benefits for their employees in case the company undergoes a merger, takeover or anything alike. At the same time, companies have expanded the golden parachute and have introduced more leniency to it, causing some to believe it serves as a free pass for top level employees to leave office with a truck load of money and other benefits. How are golden parachutes beneficial? Golden parachutes can be beneficial for both employee and employer, in the following ways: Employee: The biggest advantage of a golden parachute clause for an employee would be the purpose behind the clause, i.e., the protection of said employee in case of a merger or acquisition. It acts as a security for the employee and is an insurance for the long term, making the position more lucrative for applicants. A job with a golden parachute clause is guaranteed to attract more applicants and would be highly valued compared to a job without the clause.   The other advantage for employees is avoiding inadvertent takeovers by big firms. Big companies might be tempted to acquire a well performing firm and its top-level employees. In the presence of a golden parachute clause, companies would give a second thought before they acquire a firm due to the costs involved, thus, protecting the employees from structural changes to the firm.   A golden parachute also offers clarity to an executive when faced with the dilemma of whether to get into a merger or not. When an employee has guaranteed financial benefits post the merger and has the option of retaining his job in case the merger does not happen, then he would act in the best interest of the company. An employee that has nothing to lose either way would act according to what is best for the company. Employer: An employer may benefit from a golden parachute as well. In the case of employee termination post a merger or acquisition, employers might be faced with the accusation of unfair treatment of their employees. A golden parachute allows employers to maintain cordial relations with the fired employees as well as it avoids legal proceedings by the latter. Thus, an employer could include a golden parachute clause to protect himself as well. What are the issues associated with the golden parachute clause? Golden parachutes may sometimes be too expensive for companies and thus, might not be feasible for small firms. Moreover, the clause is only included in the contracts of few selected employees and is not made available for the entire employee base. Another critique of the golden parachute is the leeway provided under current modifications of the golden parachute contracts offered by companies. Some contracts may allow employees to walk away with a large sum of money rather than act in the best interest of the company.  They might also shirk from their work and underperform as they would earn a guaranteed sum of money once they are terminated. In addition to these issues, golden parachutes might not discourage mergers as is expected out of such a contract. Many opponents of the policy argue that the cost associated to a golden parachute may be too miniscule compared to the overall cost attached to the merger. Thus, the cost of a golden parachute might not be enough to discourage a merger, which would make them highly ineffective. 

What is Comparative Advantage? The international trade theory of Comparative Advantage indicates the competence of a nation to produce a good or service at a lower opportunity cost compared to other trading agents. The comparative advantage looks at a relative cost of production rather than the overall monetary cost for the product.  The concept of comparative advantage majorly arises because a trading partner on the back of its competence in factors of production such as infrastructure, location, climate, labour skills, etc. holds an edge over the others during a trade. It shows the overall gains from the international transaction compared to an autarkic situation by identifying the opportunity cost.  Significantly, the choice between trading a good or producing the same has remained as a critical question for the economies. The doubt enquiring which trading agent should produce the product and which should export often assumes a centre stage for macroeconomic decisions. The simple answer to the dilemma would be that an economy which can produce a particular product at the lowest cost should involve in production. At the same time, other nations can import the product.  The concept of Absolute advantage is very much the same, which asserts that economies should involve in the trade of goods which they can produce at the lowest cost. However, what if out of the two nations, one holds an absolute advantage over both the products? Although Absolute Advantage theory in such case would discourage bilateral trade, the concept of comparative advantage indicates that how both economies mutually profit in such situations from trade.  Understanding Opportunity Cost  The economies possess a finite amount of resources, which can be employed to produce goods and services. The choice to create a particular good is accompanied by the sacrifice of options to make other goods and services using the same resources. The next best possible alternative which is foregone when opting for a production of a particular product or service is called Opportunity Cost for that product or service.  Production possibility frontier is used to understand the concept of Opportunity cost. The graph indicates the possible combinations of Good X and Good Y that can be produced in an economy at a given time.  Image Source: ©Kalkine Group If an economy wants to increase the production of Product Y from Y1 to Y2, then it is required to reduce the production of Product X from X1 to X2. Thus, the Opportunity Cost for ΔY is ΔX.  Role of Opportunity Cost in Comparative Advantage The decision to produce a particular product and import the other is made by taking into consideration the opportunity cost. The product in which the Opportunity cost of a product is comparatively higher is generally forfeited.  Understanding How Opportunity Cost is Beneficial to Both Trading Economies Let us look at the case where two economies, say Germany and France are considering the trade of two products, A and B.  The table below indicates the number of products that are produced per resource input (here labour hours).  Image Source: ©Kalkine Group Looking at the production efficiency of Spain and Germany for both the products, it is clear that Germany holds an absolute advantage for both. In contrast, Spain is at Absolute Disadvantage in either case.  Thus, for mutually beneficial trade, as indicated by David Ricardo’s theory, the commodity in which Spain has a lower comparative disadvantage is ascertained. It is done by the concept of Opportunity cost.  Spain’s opportunity cost for Product A is 2/1 that is 2 while its Opportunity cost for Product B is ½, that is 0.5. Since the opportunity cost for Product B is lower for Spain, it will manufacture product B.  Similarly, for Germany, the Opportunity cost for Product A is 3/6, that is 0.5 while Opportunity cost for Product B is 6/3, that is 2. Thus, Germany would manufacture Product A.  The trade occurs between two countries, with Spain exporting 6 units of Product B to Germany in exchange of 6 units of Product A.  How Germany gets Benefitted from Trade The resource invested by Germany to produce 6 units of Product A (6A) would have only produced 3 units of Product B. However, through the trade of 6As, Germany can get 6Bs. Thus, Germany is benefitting by 3 units of Product B.  How Spain Gets Benefitted from Trade Spain is importing 6 units of Product A. Labour hours that would have been required to produce those many units of product A would produce 12 units of Product B. It is importing 6As in exchange for 6Bs. Meanwhile, the remaining 6Bs remains is the benefit for Spain. Thus, Spain can denote its resources to produce B.  Comparative advantage theory of David Ricardo The earlier Theory by Adam Smith postulated that a beneficial bilateral trade is only possible when each of the two countries involved in a trade deal possesses an absolute advantage in one of the commodities. However, David Ricardo asserted that valuable trade between two economies is possible even if one of the countries is at an absolute advantage for both the entities.   David Ricardo’s theory implies that despite a nation not able to produce either of the two commodities more efficiently than the second nation would benefit from international trade.  The opportunity cost of products for nations is compared to make production and trade decisions. In the case of comparative advantage, the economy produces that product where it has a lower opportunity cost than its trading partner.  Limitations of the Comparative Advantage Theory The Comparative Advantage Theory is based on a specific set of consideration while it does address varying real-world scenarios, which altogether limits the scope of the theory. These include: Assumption of a Simple Model The Comparative Advantage Theory postulated by David Ricardo considers a simple model involving a trade of two products between two countries. However, the actual system is much more complex as a range of products and services are produced. Furthermore, the globalised trade scenario involves a web involving exchange of services and products across different nations.  Considering Trade in an Ideal Market Situation An ideal market situation is assumed in theory for Comparative Advantage. Thus, the market is supposed to be perfectly competitive without the presence of any market imperfectness. Today’s international trade scenario involves nations striving to promote their domestic producers to ensure trade surplus. However, in theory, no such barrier to entry is considered.  Transportation and other Expenditures during Trade The cost consideration for the product does not take into account supporting costs such as transportation and other related expenditures that are involved in the shipment of a product. Thus, the whole picture of profits attained is not visible through the comparative advantage theory. 

What is a sunk cost? A sunk cost is a cost that has already been incurred by a business or an individual and cannot be recovered by any means. They should not be considered while making an investment decision or while doing any projections. Since a sunk cost cannot be changed or recovered, businesses do not include them in their financial analysis. However, they continue to be an unavoidable aspect and affect businesses in one way or the other. Sunk costs are the costs which cannot be retrieved in any way, not even through a resale of the item on which the cost has been incurred. They may not be improved upon in the future and only exist in the financial history of the company. What are some examples of sunk costs? Advertising Expenditure: When a company invests in the marketing of a new product, it is a sunk cost. It cannot be retrieved by any means, irrespective of whether the business is able to prosper consequently. Therefore, it should not influence the future business decisions of the firm. Employee Training: When a company invests in training their employees for a new project or on a new software, then the company does so with the intent of gaining future profits from that investment. However, consider the adverse scenario when the new process for which employees are being trained gets terminated. Now the cost of training the employees is a sunk cost as it cannot be retrieved in the form of higher revenue through a new project. Research and Development: Companies invest in research and development of their processes. Suppose for instance, a mobile manufacturing company invests in the production of a better-quality camera for their smartphones. They hire professionals and purchase new equipment to achieve the same. However, if the company is unable to manufacture the new camera, their costs are sunk. Therefore, the salary paid to the professionals and the costs incurred by the firm while purchasing new machines are all sunk costs in this example. Hiring Employees: Every company must train employees before hiring them. The cost incurred in hiring process can also become a sunk cost. If the employee quits the job or is not able to continue working in the company, then the cost becomes a sunk cost. Therefore, sunk costs are bound to happen, especially in new businesses. They cannot be eliminated; however, they can be avoided in the future based on a company’s past experiences. However, even if sunk costs have been influenced by a past decision, a firm’s future decisions should not be influenced by them. What is the sunk cost fallacy? Sunk cost fallacy is a concept slightly different from the economic concept of sunk costs. Sunk cost fallacy states that businesses might be compelled to go ahead with a decision only because of the sunk costs associated with that decision. This can hurt the business in the long run, as sunk costs should not be used to make future decisions. As explained, sunk costs are the costs in businesses that cannot be retrieved, while a fallacy is a mistaken belief. Thus, investors and businesses are mistakenly under the false impression that going ahead the sunk cost decision would help the company earn back the money they invested. This fallacy occurs because people perceive the sunk cost as an investment that has already been made. Thus, they decide to go ahead with it, instead of wasting the amount spent on it. This may not always be beneficial because the sunk cost decision might not be the best decision for the investor to go forward with. For instance, consider the example of a car manufacturing business that has promised to launch a cheaper variant of one of their existing models after 2 years. However, for some reason, even after two years, the company was not able to develop a cheaper variant. However, the business decides to go ahead with the same decision and announces another date for the launch of the variant. The logical decision here would be to let the sunk costs go and not let them influence future course of action for the company. If the company realises that a cheaper variant is not achievable in the stipulated time, then investing a little more in it would add to the losses. What is the sunk cost dilemma? Sunk cost dilemma refers to the dilemma faced by a business or an individual before falling prey to the sunk cost fallacy. Continuing from the above example of the car manufacturing company, the sunk cost dilemma occurs after two years when the new variant has not yet been developed. Deciding between terminating the project and adding more investment to it is a crucial decision. The sunk cost theory suggests that, in the above example, the project should be terminated, instead of the company investing more time and money into it. How are sunk costs resolved? Businesses should not focus on eliminating sunk costs, rather they should focus on mitigating their effects. Every successful business has many underlying sunk costs that are foregone in building it. Therefore, it is important to not let sunk costs deter the flow of business. However, it is important to note that businesses may find it easier to avoid falling for the sunk cost fallacy. By feeding previous information into sophisticated models, businesses might be able to decide their plan of action when faced with the sunk cost dilemma.

We use cookies to ensure that we give you the best experience on our website. If you continue to use this site we will assume that you are happy with it. OK