In trying to solve for the Cournot - Nash equilibrium, given (",") = R₁ (2) = 60-2 60-2 and (v) = R₂₁ = solve for y, . Answer: 45-1 2 C In trying to solve for the Cournot-Nash equilibrium, given (y) R₁(y)=60-y and = (y) R₂(y)= 45-y solve for y 2 Answer:
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- In trying to solve for the Cournot-Nash equilibrium, given (y;) = R₁(y) = 30-y 60-y == and (y2) = R₂(y) = solve for yConsider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.Solve the Subgame Perfect Nash Equilibria for the following games A and B in the image below. 1. The Nash Equilibria for (a) are/is: 2. The Nash Equilibria for (b) are/is 3. Is there Subgame Perfect Nash Equilibria for A? 4. Is there Subgame Perfect Nash Equilibria for B?
- Problem #4: Bayesian Nash Equilibrium Consider the following game, which has two states of nature shown in the two game tables below: "Harmful" (p = 1/3) "Helpful" (1-p = 2/3) Player 2 X Y 3, 2 Player 2 Y 2, 3 3, 2 1,0 0,1 A 0,1 3,2 A Player 1 Player 1 В 0,1 B a) Assume that Player 1 knows what the true state of nature is when playing this game, but Player 2 does not. Find all of the game's Bayesian Nash equilibria. (Hint: It may help to arrange the game tables appropriately.) b) Now, assume that Player 2 knows the true state of nature, but Player 1 does not. Find all of the game's Bayesian Nash equilibria.why is a nash equilibrium stableSuppose 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 0,0
- Consider the following game: PLAYER 2 Left Middle Right Up 0,0 2,5 5.4 PLAYER 1 Middle 1,2 7,3 4,3 Down 5,5 3, 1 2, 1 Which of the following statements is true? There are two Nash equilibria, and they are both Pareto efficient. There is a unique Nash equilibrium. There are two Nash equilibria, and they are both Pareto inefficient. There are two Nash equilibria, but only one is Pareto efficient. None of these.What is Nash equilibriumExplain the difference between a Bayesian-Nash Equilibrium and a Nash Equilibrium.
- Which of the following DOES NOT accurately describe a Nash equilibrium? O It is the set of strategies which provides the players with the highest possible combined payoffs. All of these choices accurately describe a Nash equilibrium. O It is a set of strategies such that no player can receive a higher payoff by changing only their own strategy. It is a set of strategies such that no player, after seeing what the other players' strategies were, regrets their choice of strategy. It is a set of strategies such that every player, after seeing what the other players' strategies were, is satisfied (if not actually happy) with their choice of strategy.What is the distinctive characteristic of the Nash equilibrium?Suppose you are interested in applying equilibrium theory to the following game, where 61 = {E,F}. Show that there is Bayesian Nash equilibrium in which player 2 plays a sub-optimal action. Player 2 1,1 GF Player 1 R -1,0 NF 0,0 Nature A 1,0 GE 1- p R -1, –1 NE 0,0