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**LDD Detection theory**

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**Question 1: Explain how a person can choose freely, but his or her choices are caused by past events.**

**Answer:** Free will choices are made by personal beliefs and attitudes. The connection with previous event s are not taken by people

**Question 2: Draw the causal tree for Newcomb's Problem when Eve cannot perfectly detect Adam's causal history.**

**Answer:** Eve → Ignore Events of Adam

The causal tree explains the reason for Eve's failure to find Adam's causal history and the possible alternatives to the problems. The possible cause as presented in the above diagram is theexistence of many variables in the history which makes it complicated and difficult

**Question 3: Derive the expected payoff formulas conditional on taking money from the black box only, or from both boxes. Then use them to solve for another formula that equals the smallest value of M (denoted Mmin) required in order for Adam's average benefit from opening only the black box instead of both boxes by at least some positive multiple S of the guaranteed money L in the clear box.**

**What is the resulting formula for Mmin. Finally, assume (L, δ) = (400, 3), (r, w) = (.58, .43) and use this formula to calculate Mmin this case.**

**Answer:** (M min) = (L .δ) (r + w) = (400 × 3) × (0.58 + 0.43) = 1200 x 1 = 1200

From both box = 1200/0.4 = 1500

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**Question 4: Suppose a CD player tries to detect whether its partner is CD player instead of a DD player, by looking for external signals that are at least as typical for DD players than for CD players. Draw a diagram to explain how two boundaries bi, and bH are optimally determined. Show on the diagram where it is optimal to respond C versus D. Also explain what happens to the boundaries when detection becomes more cautious by raising the minimum likelihood ratio.**

**Answer:** Maximum likelihood ratio = P(bi) + P( bH) = r/w

The boundary of bi is less than bH for CD players than DD players

**Question 5: What is the meaning of the LDD detection strategy?**

**Answer:** LDD detection theory is a mechanism used in detecting signals from a CD or DD. It involves the identification of the detection principles that are used in the analysis of the players change over a period

**Question 6: What is the main problem with the green-beard strategy? Explain how the LDD strategy overcomes this problem.**

**Answer:** Problem is lack of proper prediction events. LDD observes the pattern of events of DD and CD players to overcome the problem

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Question 7: Assume a population contains either CD or DD players, where each player is randomly matched with a partner taken from the whole population. Also assume the fear and greed payoff differences are equal. What are the expected payoff formulas for CD players [denoted E(CD I E" ) ] and for DD players [ E(DDIE") ] ] depending on the fraction of CD players in the population, denoted exp.

**Answer:** Expected payoff = Pi€ xP(CD) + P (DD)

**Question 8: Use the expected payoff formulas of Part B to algebraically derive an inequality for the signal reliability ratio r/w that determines when the CD players will outperform the DD players.**

**Answer:** Expected pay off of CD players = P(1-0.4) = 0.6

Expected pay off DD = 0.4

**Question 9: Use this inequality with Part A, to explain how CD players can always outperform DD players starting from any positive initial fraction of CD players.**

**Answer:** CD players can predict using LDD strategy and have many positive traits than DD players

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**Question 10: Use the inequality from Question 3; to obtain an inequality required for *cr) = 1 to remain stable against DD invaders. Also draw the ROC diagram for visually representing this stability inequality.**

**Answer:**

**Question 11: Use a diagram similar to that shown in Part A to derive a prediction of what will happen to the CD players' equilibrium probability of cooperating; if the cooperation payoff difference increases relative to the fear and greed payoff differences.**

**Answer: **

Question 12: Again use a diagram similar to Part A to derive a prediction of what will happen to the CD players' equilibrium probability of cooperating; if they use cell phones rather than talking face-to-face.

**Answer:**

**Question 13: What kind of factors could further enhance or degrade the effectiveness of face-to-face communication, and if so, how would this affect the probability of cooperating ?**

**Answer:** To enhance the face to face communication, players should be taken for recreation to create good relationship and provided with equal pay and respect for the service. This will increase the cooperation among the team. Factors that reduce face to face communication are tit for tat, revenge and badmouthing attitudes that affect the cooperating.

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