4. The Folk Theorem For each of the following games, find the static Nash Equilibria and either sketch or describe the set of socially feasible and individually rational payoffs. L R 8, 6 | 2, 9 5, 0 3, 1 D W E N 7, 7 4, 0 S 0, 4 | 0, 0
Q: U9. Consider a revised version of the game from Exercise S9: PROFESSOR PLUM Revolver Knife Wrench…
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Q: Find all Nash equilibria of the following two-player game. Provide necessary computation. L M R -2,1…
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A: The correct answer is given in the second step.
Q: 2. Find all mixed-strategy Nash equilibria (including pure-strategy Nas equilibria) for the game…
A: * SOLUTION :-
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Q: 4. Consider a first-price, sealed-bid auction in which the bidders' valuations are independently and…
A: * ANSWER :- *(4)
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A: rationalization of strategies is maximizing of payoff.
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- Does each individual in a prisoners dilemma benefit more from cooperation or from pursuing self-interest? Explain briefly.5 Consider a first-price sealed-bid auction in which bidders valuations are independently and identically distributed according to the Uniform distribution on the interval [0, 1]. Explain what the rules of the First Price Sealed bid auction are. Set it up as a Bayesian game. Compute a symmetric Bayesian Nash equilibrium for the two bidder case.Consider the location game we covered in Lecture 3. Now assume there arethree players (vendors). As we assumed in the lecture, consumers in each area choosethe closest vendor and if there are multiple closest vendors then these vendors receiveequal share of consumers in the area. Notice Si = {1, 2, 3, ...., 9} for i = 1, 2, 3. Here aresome examples of payoffs: u1(1, 1, 1) = 3, u1(1, 1, 9) = u2(1, 1, 9) = 2.25, u3(1, 1, 9) =4.5, u1(1, 5, 9) = u3(1, 5, 9) = 2.5 and u2(1, 5, 9) = 4. (a) Is s′1 = 1 strictly dominated by s′′1 = 2 for player 1?(b) Is s′1 = 1 weakly dominated by s′′1 = 2 for player 1?(c) Can you find a Nash equilibrium in pure strategies?
- on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?Consider the following coordination game: Player 2P1 Comedy Show Concert Comedy Show 11,5 0,0 Concert 0,0 2,2 a. Find the Nash equilibrium(s) for this game.b. Now assume Player 1 and Player 2 have distributional preferences. Specifically, both people greatly care about the utility of the other person. In fact, they place equal weight on their outcome and the other person’soutcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarianpreferences.c. Now consider the case where Player1 and Player2 do not like each other. Specifically, any positive outcome for the other person is viewed as anegative outcome for the individual, ρ = σ = -1. Find the Nashequilibrium(s) with these envious preferences.
- Prove that in the variation on the centipede game given in figure 14.5(b) the unique sequential equilibrium described is, in fact, the unique Nash equilibrium. (Hint: Take some presumed Nash equilibrium and suppose information set 2n+ 1 [for player 2] is the first unreached information set. Derive an immediate contradiction. Then suppose that node (2n) t is the first unreached information set and derive a contradiction that is one degree removed from immediate.)1) What are the Nash equilibria? Which one is unreasonable/non-credible threat? 2) What are the subgame perfect Nash equilibria? Does SPNE concept eliminate the unreasonable Nash equilibrium?Consider a modified Traveler’s Dilemma. In terms of strategy options that the players have and the dollars they earn, it is like the standard Traveler’s Dilemma, but the players do not have endless appetite for money. Up to 100 dollars, each dollar feels like a dollar. But any moneybeyond 100 is psychologically like 100 dollars. Assuming that players are maximizers of ‘psychological’ dollars instead of real dollars, describe all the Nash equilibria of this modified Traveler’s Dilemma.
- 1. Identify the Nash Equilibria and Subgame Perfect Nash Equilibria in pure strategy of this game. 2. Using beliefs (p, 1−p) at P2's decision nodes in their information set, show that one of the NE is not sequentially rational.For the operating systems game, let us now assume the intrinsic superiorityof Mac is not as great and that network effects are stronger for Windows.These modifications are reflected in different payoffs. Now, the payoff fromadopting Windows is 50 X w and from adopting Mac is 15 + 5 X m;n consumers are simultaneously deciding between Windows and Mac.a. Find all Nash equilibria.b. With these new payoffs, let us now suppose that a third option exists,which is to not buy either operating system; it has a payoff of 1,000.Consumers simultaneously decide among Windows, Mac, and nooperating system. Find all Nash equilibria.1 True or False : Every finite extensive - form game of imperfect information admits at least one pure - strategy Nash equilibrium . Justify if true or give a counter - example if not