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Game Theory 2

Essay Instructions:

In an iterated prisoner’s dilemma game, one may decide to punish an opponent who has defected by responding with defection for a certain number of rounds, then reverting to cooperation. This strategy would result in the punished player losing, say, $x each round (starting next round) for n rounds. Show that the present value of the money lost is (δ – δ n+1 ) x (1 - δ), AND NOT (δ - δn + 1) x/ (1 - δ).

 

Hint: Call the present value of these loses T and parallel the work above.

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Game Theory
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Game Theory
Question 1: co-payments are basically fixed fees that an individual will pay whenever having a prescription filled, seeing a physician, or when one is admitted to the hospital. Every insurance plan will establish the flat fees up front. Insurance firms utilize these copayments partly to share expenses with people, thereby acting as an incentive for insurance companies to increase coverage. Co-payments cut a small portion of the costs, and they can save an insurance firm a significant amount of money. Deductible is the amount that an individual would pay towards specific medical expenses before his/her plan begins to pay a share of the costs. A deductible amount is computed every year so one has to meet a new deductible every year of the policy. As soon as one meets this deductible, he/she starts to enjoy health insurance benefits, and will then only have to pay monthly premiums as well as coinsurance if appropriate. A plan that has a high deductible would have a low monthly premium. If one is fairly healthy, it is best for him/her to pick a high deductible when purchasing a policy in order to lower one’s monthly premium costs. In this way, deductible serves the incentive function.
Question 2: high overtime pay may discourage productivity in the sense that if an employee knew that she is going to make substantial amount of money every hour after a particular point in the day, then this worker might be less productive so that she could make that money. As such, productivity of this worker during the day might reduce as she waits for the overtime and make a lot of money. If the firm provided incentives based upon the amount of work done by each employee, the results in terms of productivity would definitely be different.
Question 3: In the iterated prisoner’s dilemma, both the 2 players at the same time decide between defection for individual benefit, and cooperation for common benefit. This decision is usually repeated over several rounds. Both Player A and Player B take the previous actions of the opponent into consideration when deciding how to act in the succeeding iterations (Stevens, 2008).
If the players play the game precisely n times and they each understand this, defecting in each round is game theoretically optimal. In the game, to continuously defect is the only Nash equilibrium; constant defection is the only subgame-perfect equilibrium. The subgame-perfect equilibrium promises each of the players in IPD any average payoff between 3 and 2 as long as δ is sufficiently high. This equilibrium does not have to offer simil...
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