Game Theory 2
answer each question per page. 3 questions = 3 pages. there are three different questions that covers three different topics. There is not direct connection . It just answer question separate like question 1, question 2, and question 3. please see lectures 3, 4 and 5 in PDF attached 1. A small time crook is being interrogated by a policeman. The crook committed a petty crime, but everyone knows that gathering sufficient evidence to prove it will be time consuming for the police. The policeman tells the crook that if she doesn’t confess, he’s going to spend all of his time making sure that she gets the harshest sentence possible. The crook, in light of the threat, confesses. Analyze these game strategies. Verify that this scenario represents a Nash equilibrium, provided that the policeman would actually follow through with his threat. Now verify that the sub game-perfect equilibrium is for the crook not to confess and for the policeman to go back on his threat. That is, explain why the policeman’s threat is actually not credible. 2. Prisoner’s dilemma situations arise frequently in life. Begin your answer to this question by providing a full explanation of what the prisoner’s dilemma is. In your life, it is likely that you have played such games and in some cases, you found a way to cooperate with the other player. In other cases, both of you betrayed each other. Consider examples of each situation and ask yourself: What made the difference? When were your strategies effective, and when not? 3. You and a friend are selected as contestants on game show. You each must pick a whole number from 1 to 7. You will pick an odd number, and your friend will pick an even number. If the numbers you pick are consecutive, such as 5 and 6, then you each win $1,000. If both you and your friend understand weakly dominated strategies, you’re guaranteed to win the money. How? If you and your friend both understand IEDS for weakly-dominated strategies, you can win the money every time, even if the numbers are selected from 1 to 100, with you choosing odd and your friend choosing even. How?
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Question 1
Nash equilibrium in game theory is understood as a solution concept of a non-cooperative game that involves at least 2 players where each player is presumed to know the equilibrium strategies of the other player. In Nash equilibrium, no player has anything to gain by only altering their own strategy (Shubik, 2012). The scenario represents Nash equilibrium. Both players have chosen a strategy and none of them can benefit by altering strategies whilst the other player keeps hers/his unchanged. In this scenario, the policeman has used the strategy of telling the crook that if the crook does not confess, then the policeman would spend all his time to ensure that the crook gets the harshest sentence possible. Understanding this strategy, the crook then confesses. In this case, the crook cannot benefit by changing her strategy while the other player – the policeman – keeps his strategy unchanged. As such, the current strategy of choices plus the corresponding payoffs in this scenario represent Nash equilibrium. In other words, the policeman is making the best decision that he can, taking into consideration the crook’s decision, and the crook is making the best decision that she can, keeping in mind the policeman’s decision. A sub-game perfect Nash equilibrium is basically an equilibrium in which the strategies of players represent Nash equilibrium in all sub-games of the original game (Shubik, 2012). The threat of the policeman is not actually credible. If the crook does not confess, the policeman would go back to his threat. Knowing this, the crook prefers not to confess, and thus, the threat by the policeman is actually not credible. This constitutes the sub game-perfect equilibrium.
Question 2
Prisoner’s dilemma refers to a paradox in decision analysis where 2 people acting their own best interest follow a course of action which does not lead to the perfect result. In essence, the archetypal prisoner’s dilemma is set up in such a manner that the two individuals decide to protect themselves at the expense of the other party. Due to pursuing an entirely logical thought process in order to help oneself, each participant finds herself in a worse state than if they had worked together with one another in the process of decision-making (Shubik, 2012). In other words, prisoner’s dilemma is a situation in which trust and cooperation wins whereas blind pursuit of self-interest loses. In life, I have played such games. In one vivid situation, I went to purchase a used car: a 2002 Opel Astra. In this business transaction, the car dealer, who ...