Prisoners Dilemma

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Seneca College *

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101

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Economics

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Apr 3, 2024

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Prisoners Dilemma/ Nash Equilibrium:  Game theory's foundational ideas, the Prisoner's Dilemma and Nash Equilibrium, have a profound impact on how decisions are made in competitive situations. Consider two companies which are competing in the same industry, like Walmart and Staples, both companies are successful and are known to a vast majority of people, however, both are competing to be better than each other. Normally the pricing of both organizations is price friendly and avoids getting into a price war with each other. Nevertheless, during the Black Friday sale, both of them know that this time, the sales will significantly increase compared to the usual, If both companies decide to keep the prices high, they could enjoy high revenue in this season . Therefore, both businesses must decide whether to maintain high prices in order to maximize profits or cut rates in order to draw in more clients. To beat the other competitor, each company will try to offer discounts and coupons to satisfy the needs of the customers, which will eventually end up in getting more attention from the potential customers. Both companies stand to gain greatly from maintaining their high prices. Every business, though, is compelled to cut rates in order to draw in more clients. If the two companies have different prices, the one with cheaper prices will draw in more clients and turn a larger profit. However, if both businesses cut their pricing, their earnings will also decline. The conflict that exists in competitive marketplaces between individual and collective reason is brought to light by the prisoner dilemma. In conclusion, the Black Friday pricing battle between Staples and Walmart provides a a practical illustration of the dynamics of competition in the retail sector. The choices these businesses took during this crucial time demonstrate the complex interaction between individual and group rationality in highly competitive markets, as illustrated by the Prisoner's Dilemma.  For the second example, consider two fast-food restaurants, let's suppose Pizza Pizza and Domino’s, both organizations are competing in the same market. And both of them have an option of either investing in quality assurance or not. Quality assurance could involve investing in superior ingredients, upholding hygienic standards, routinely educating employees, and putting in place harsh quality control procedures. If both Pizza Pizza and Domino’s choose to invest in quality assurance, both

restaurants pay the expense of the investment but also benefit from it as consumers recognize the superior food and both businesses' reputations grow. In the long run, this might result in a rise in client loyalty and possibly increased earnings. This is a win-win situation for both firms. However, if one restaurant chooses to invest in quality assurance while the other does not, the restaurant that invests will pay the price and may end up with a bigger market share if customers decide to eat at the higher-quality eatery instead of the other. It's a win-lose scenario for both restaurants. On the other hand, if neither of the restaurants invests in quality assurance, they both save money but run the danger of losing business because of possible problems with the quality of the cuisine. This can damage their brand and cause them to lose money. They are in a lose-lose scenario here. From a financial perspective, it could appear best for both establishments to avoid investing in quality control. On the other side, this results in a poor choice outcome overall. Even if both restaurants' investments in quality assurance will increase customer happiness and maybe boost revenues, the Nash equilibrium in this for both eateries is to not invest in quality assurance as it could be costly and the benefits might not be visible immediately. Shapley Value:  To illustrate the Shapley Value, let's look at an example. Consider a car manufacturing company where two managers, Karl and Mark, are working together on a project to increase a car manufacturing plant's productivity. Ten thousand dollars is the project's overall benefit (or profit). Based on each manager's contribution to the project, the Shapley Value can be utilized to divide this benefit equally between the two managers. Let’s say Karl is responsible for the optimization of the assembly line while Mark is responsible for improving the quality control of the whole production efficiency. Karl may optimize the assembly line process and earn $4000 if he works on this project alone. Similarly, Mark can enhance the quality control procedure and earn $3000 by working alone. Karl and Mark can nevertheless merge their knowledge to optimize both the assembly line and quality control procedures, generating a $10,000 overall profit, when they collaborate. In this Shapley value calculates how both the managers are contributing as their average marginal contribution to the overall benefits over all possible permutations of the partnership. In this case, there

are two possible combinations from both perspectives of Karl’s and Mark’s. In the permutation from Karl’s end, his marginal contribution is $4000, which is the revenue generated by him alone, in addition to this, the marginal contribution of Mark’s marginal contribution is $6000 (which is calculated by subtracting total revenue from the revenue generated by Karl on his own). The second permutation from Mark’s end, his total contribution is $3000 (which is revenue generated by Mark alone) and Karl’s marginal contribution is $7000 (which we calculated by subtracting total revenue from the one that Mark generated alone). The average of a manager's marginal contributions over all possible combinations is their Shapley Value. The Shapley Values for Mark and Karl are, thus, ($6000 + $3000)/2 = $4500 and ($4000 + $7000)/2 = $5500, respectively. As a result, the overall benefit is distributed fairly, taking into account the value that each management brought to the project. The Shapley Value distributes the advantage based on each manager's unique contributions, even though the overall value is higher when both managers collaborate.  The receptionist in a hotel is essential to maintaining both operational effectiveness and client happiness. For the second example, let's consider a situation in a hotel where two receptionists Alice and Bob, are working side by side to provide excellent customer service to their clients. The Shapley value considers the marginal contribution of each player when joining different coalitions. Their combined service has a 95 out of 100 customer satisfaction score, or overall benefit. Depending on how much Alice and Bob contributed to the service, the two can divide this benefit equally using the Shapley Value. Assume Alice is responsible for checking in the guests and attending to their needs throughout their stay, moreover, Bob is in charge of checking out guests and responding to any questions that arise after their visit, It takes both of these responsibilities to deliver top-notch customer service. If Alice is working alone, she can manage the check-in process and the requests that are made by customers in between their stay, which generates a customer satisfaction score of 60. Similarly, when Bob works alone, he can handle the check-out process and the after-stay inquiries, which generates a customer satisfaction score of 50. However, when both Alice and Bob work together, with their combined expertise, they can manage the complete guest experience, from check-in to check-out, producing a total customer

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satisfaction rating of 95% and answering any questions that may arise after the guest leaves. It takes both of these responsibilities to deliver top-notch customer service. The two permutations are from the side of Alice and Bob. Alice’s marginal contribution is 60 which she generated on her own, and Bob’s marginal contribution is 35 which is calculated by subtracting the total score from the one generated by Alice. The second permutation is from Bob’s side, his marginal contribution is 50 which he generated alone, and Alice’s marginal contribution is 45, the total score minus the score generated by Bob alone. The average of each receptionist's marginal contributions across all permutations is their Shapley Value. Consequently, Alice's Shapley Value is (60 + 45)/2 = 52.5, and Bob's is (35 + 50)/2 = 42.5. The value that every receptionist brings to the client experience, guarantees a fair allocation of the overall benefit. The Shapley Value distributes the benefit based on each receptionist's unique contributions, even though the overall value is higher when both receptionists collaborate. Name:- Adarsh R ID:- 129820239

Prisoners Dilemma

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