This game is based on the Hangman's Paradox. Suppose that a judge, Player 1, sen- tences...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
This game is based on the Hangman's Paradox. Suppose that a judge, Player 1, sen- tences a prisoner, Player 2, to be hanged in one the next 7 days (T is an integer). Moreover, the judge tells the prisoner that the day of hanging will be a surprise. Formally, there are T possible periods in the game. In any of the first T - 1 periods of the game, Player 1 chooses whether to hang (H) or not (N), and Player 2 simulta- neously chooses (i.e. guesses) whether he will be hanged (h) or not (n). If Player 1 chooses H in any of the first T - 1 periods, the game ends at the end of that period. Otherwise, the game proceeds to the next period. [Note: at the end of each period, players' actions in that period become publicly observable.] In the 7th period, Player 1 has only one action available: H (player 2 still has his two actions). Note that there is a terminal node only after a period in which Player 1 chooses H. Payoffs at any terminal node are (-1, 1) if player 2 chose h in that period (hence, he was not surprised) and (1, -1) if player 2 chose n in that period (hence, he was surprised). (a) Argue that there are proper subgames in this game (a subgame is a proper sub- game if it is not the game itself). (10 pts) (b) Suppose T = 2. Is there a Nash equilibrium that is not subgame perfect? (10 pts) (c) Suppose T = 3. Is there a Nash equilibrium that is not subgame perfect? (10 pts) Notice that in the game as described so far, neither player's terminal utility is affected by 2's guess in any period that 1 chooses N. We incorporate this factor by now modifying payoffs so that at each terminal node, we augment a disutility to player 2 and an extra utility to player 1 of > 0 for every period in which 2 played h but 1 played N during the path taken to that terminal node. This game is based on the Hangman's Paradox. Suppose that a judge, Player 1, sen- tences a prisoner, Player 2, to be hanged in one the next 7 days (T is an integer). Moreover, the judge tells the prisoner that the day of hanging will be a surprise. Formally, there are T possible periods in the game. In any of the first T - 1 periods of the game, Player 1 chooses whether to hang (H) or not (N), and Player 2 simulta- neously chooses (i.e. guesses) whether he will be hanged (h) or not (n). If Player 1 chooses H in any of the first T - 1 periods, the game ends at the end of that period. Otherwise, the game proceeds to the next period. [Note: at the end of each period, players' actions in that period become publicly observable.] In the 7th period, Player 1 has only one action available: H (player 2 still has his two actions). Note that there is a terminal node only after a period in which Player 1 chooses H. Payoffs at any terminal node are (-1, 1) if player 2 chose h in that period (hence, he was not surprised) and (1, -1) if player 2 chose n in that period (hence, he was surprised). (a) Argue that there are proper subgames in this game (a subgame is a proper sub- game if it is not the game itself). (10 pts) (b) Suppose T = 2. Is there a Nash equilibrium that is not subgame perfect? (10 pts) (c) Suppose T = 3. Is there a Nash equilibrium that is not subgame perfect? (10 pts) Notice that in the game as described so far, neither player's terminal utility is affected by 2's guess in any period that 1 chooses N. We incorporate this factor by now modifying payoffs so that at each terminal node, we augment a disutility to player 2 and an extra utility to player 1 of > 0 for every period in which 2 played h but 1 played N during the path taken to that terminal node.
Expert Answer:
Answer rating: 100% (QA)
Answers a There are proper subgames in this game because at each period before the final period T Pl... View the full answer
Related Book For
Posted Date:
Students also viewed these economics questions
-
Dickens, Kristen, is enrolled as a doctoral student in the Counselor Education at the University of New Orleans. She is a registered counselor intern in the state of Louisiana and works at a...
-
The formal study of probability began with questions regarding gambling and games of chance. The conventional analysis of gambling is based on the expected values of these games which is always...
-
The conjugate base of diethyl malonate can serve as a nucleophile to attack a wide range of electrophiles. Identify the product that is formed when the conjugate base of diethyl malonate reacts with...
-
What are the basic kinds of reports produced by an MIS?
-
In center lathe, cutting tool is fed in ____ directions with reference to the lathe axis.
-
According to one estimate, more than half of the jobs created in India since 1991 have been in the informal sector. a. What is the informal sector? Why might businesses choose to operate in the...
-
Paper Company acquired 80 percent of Scissor Company's outstanding common stock for $296,000 on January 1, 20X8, when the book value of Scissor's net assets was equal to $370,000. Problem 3-37...
-
11.A simple LR circuit is connected to a battery at t = 0. The time instant at which rate of energy storage in inductor is half of power delivered by battery 2L (1) In 2 (3) In 2 (2) In (4) (4) In 3
-
In application, sensitivity analysis is a useful and practical way to Group of answer choices determine the feasible region. find an extreme corner point. consider mathematical shortcomings. consider...
-
A person going eastwards with a velocity of 3 km per hour, finds that the wind appears to blow directly from the north. He doubles his speed and the wind seems to come from north-east. Find the...
-
1. Chad has an income of I = $100, which he dedicates to purchasing soda and pizza. The price of soda is $1 per can, while that of pizza is $2 per slice. 1.1 Find the equation of his budget...
-
The hypothetical city of Hurstville is trying to decide how many city beautification projects should be approved each year. These projects involve planting gardens, commissioning murals, and building...
-
Use the estimated labor time requirement to schedule production of Job 114, including the start and end dates. Assume the plant will already be operating at full capacity every day while completing...
-
Royal Shipping has a 3-year,7%semi-annual coupon bond with a $1000 par value. The bond currently has a yield to maturity of 6.5%.What is the percentage change in the current value of the bond if the...
-
The City of Grinders Switch maintains its books in a manner that facilitates the preparation of fund accounting statements and uses worksheet adjustments to prepare government-wide statements. 1....
-
Nurses arent just angry because of pay. Were angry for a lot of reasons. Were angry because of years of brutal cuts to health and social care in the name of austerity. Cuts cost lives patients and...
-
Provide a draft/outline of legal research involving an indigenous Canadian woman charged with assault causing bodily harm under (Sec 267b) of the Criminal Code, where the crown wants a 12-month jail...
-
George Johnson earns $5 per hour in his job as a truffle sniffer. After allowing time for all of the activities necessary for bodily upkeep, George has 80 hours per week to allocate between leisure...
-
Horst and Nigel live in different countries. Possibly they have different preferences, and certainly they face different prices. They each consume only two goods, x and y. Horst has to pay 14 marks...
-
Karl Kapitalist is willing to produce p/2 20 chairs at every price, p > 40. At prices below 40, he will produce nothing. If the price of chairs is $100, Karl will produce ______. At this price, how...
-
A firm is looking to locate its production facilities in one of two countries. The wage rate in Country 1 is 10 and the cost of capital is also 10 . The wage rate in Country 2 is \(20 \%\) higher,...
-
While processes differ somewhat among the three main manufacturers of cricket balls in international matches, all top-quality cricket balls are handcrafted to exacting specifications and standards....
-
Governments may use, and have used, wage subsidies to reduce unemployment in times of economic recession. For example, from January to August 2009, Mexico provided wage subsidies to certain firms in...
Study smarter with the SolutionInn App