rock paper scissors гock 0. -3 1 1 раper scissors -1 -1 0. (a) Show that xT= ( ) and yT= ( ) together are not a Nash equilibrium %3D %3D 3' 3 for this modified 3 3 game.
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- NASH EQUILIBRIUM Consider the following game in strategic form. bị b2 a1 10,2 4,20 a2 6,28 9,14 аз 8,6 12,4 1-T-0 1-T The Equilibrium Existence Theorem guarantees that this game possesses at least one Nash equilibrium of the form (T*, o*,T*). Which values of a* are part of such an equilibrium? (Mark all values for which an associated equilibrium exists.) Select one or more: O 0.00 O 0.60 O 0.30 O 1.00 O 0.75 O 0.10 O 0.80 O 0.25ROWENA 2 Answer 1: 2 Answer 2: 2 Answer 3: 1 Earth Water Wind Answer 4: Fire of the Nash equilibrium, (Rowena's 1 Colin's 3 3 North 1.3 This simultaneous game has two Nash equilibria. The Nash equilibrium, (Rowena's 2 , Colin's 1,2 3,2 2,0 COLIN South 3,1 1,2 2,1 3,0 East 0,2 2,3 1,1 West 1.1 1,1 0,3 2,2 ) has a greater joint payoff than thatparameter z= 1 In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs tothe two players?
- Suppose you are interested in applying equilibrium theory to the following game, where 01 Nash equilibrium in which player 2 plays a sub-optimal action. {E, F}. Show that there is Bayesian Player 2 A • 1,1 GF Player 1 R • -1,0 NF 0,0 Nature A • 1,0 GE 1-p R -1, –1 NE 0,0L 0 4 15.1 X₂ A M R 0 1 4 0 2 B L 4 0 с X3 M R 0 1 3 FIGURE 15.5 Exercise 15.1. Equilibrium Selection: Consider the extensive-form game in Figure 15.5. a. Find all the Bayesian Nash equilibria of this game. b. Which of the Bayesian Nash equilibria are also perfect Bayesian equi- libria? Why?Tucker and Eddie are playing the following game. Tucker can choose A or B and Eddie can choose C or D. The first payoff is for Tucker, the second for Eddie. Eddie Tucker C D A 3, 2 4, 3 B 4, 5 3, 4 Identify the Nash equilibrium(s) in this game. What rational game theoretic advice would you offer Tucker and Eddie on how to play this game? If Tucker and Eddie follow your advice, what payoff should each expect? Show your work.
- In game theory, what is a subgame? What is a subgame-perfect Nash equilibrium? If possible, could you please provide an example? Thank you!Which of the following is FALSE for the Bayesian Nash equilibrium of a Bayesian game? A. Every Bayesian game in which there are finitely many players and finitely many actions and types for each player, there exists a Bayesian Nash equilibrium B. Every Bayesian game has multiple Bayesian Nash equilibria C. Bayesian Nash equilibrium of a Bayesian game is the Nash equilibrium of its associated ex-ante normal form gameConsider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?
- 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?rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.why is a nash equilibrium stable