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- Design the payoffff matrix of a game with no Nash Equilibria. The game should have 2 players, 2 strategies for each player, and the payoffffs for each player should be either 0 or 1.PLAYER B LEFT RIGHT UP 5 FOR A, 30 FOR B 10 FOR A, 12 FOR B PLAYER A DOWN -2 FOR A, 10 FOR B 8 FOR A, 15 FOR B In the above game, the players are seeking to maximize the number they recieve. They choose at the same time. What is the Nash equillibrium? Player A will choose UP and player B will choose LEFT Player A will UP and player B will choose RIGHT Player A will choose DOWN and player B will choose LEFT Player A will choose DOWN and player B will choose RIGHT Player A will choose LEFT and player B will choose UP Player A will choose LEFT and player B will choose DOWN Player A will choose RIGHT and player B will choose UP Player A will choose RIGHT and player B will choose DOWNAnn and Stella want to watch a movie together this weekend. There are 8 movies playing in theatres on Saturday, and 11 movies playing in theatres on Sunday. Ann first chooses a day - either Saturday or Sunday. Then, knowing the day that Ann picked, Stella chooses one movie from those playing in theatres on that day. How many pure strategies does Stella have?
- Two hunters are on a stag hunt. They split up in the forest and each have two strategies: hunt for a stag (S), or give up the stag hunt and instead hunt for rabbit (R). If they both hunt for a stag, they will succeed and each earn a payoff of 9. If one hunts for stag and the other gives up and hunts for rabbit, the stag hunter receives 0 and the rabbit hunter 8. If both hunt for rabbit then each receives 7. Compute all Nash equilibria for this game, called 'The Stag Hunt', depicted below. Which of these equilibria do you think is most likely to be played? Why? S R S 9,9 8,0 R 0,8 7,7Solve 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?Game Theory Consider the entry game with incomplete information studied in class. An incumbent politician's cost of campaigning can be high or low and the entrant does not know this cost (but the incumbent does). In class, we found two pure-strategy Bayesian Nash Equilibria in this game. Assume that the probability that the cost of campaigning is high is a parameter p, 0 < p < 1. Show that when p is large enough, there is only one pure-strategy Bayesian Nash Equilibrium. What is it? What is the intuition? How large does p have to be? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
- Consider the following sequential-move game: This game involves three players, each making sequential decisions. The game proceeds as follows: • Player 1 initiates the game by choosing between two actions: Left and Right. • Depending on Player 1's choice, Player 2 then decides, choosing between two actions, left (I) and right (`r`). • Finally, Player 3 makes the last move in the sequence, choosing between actions `a` and `b`. The payoffs are determined by the sequence of choices made by all three players. Each payoff is represented by the triplet (x,y,z), where x, y, and z denote the payoffs for Player 1, Player 2, and Player 3, respectively. For example, if Player 1 chooses 'Left', Player 2 chooses 'I', and Player 3 chooses `a` the resulting payoff would be (3,1,2). This indicates that Player 1 receives a payoff of $3, Player 2 receives a payoff of $1, and Player 3 receives a payoff of $2 for this particular sequence of actions. Left Player 2 Player 1 Right Player 2 Player 3 Player 3…4. You have probably had the experience of trying to avoid encountering someone, whom we will call Rocky. In this instance, Rocky is trying to find you. It is Saturday night and you are choosing which of two possible parties to attend. You like Party 1 better and, if Rocky goes to the other party, you get a payoff 20 at Party 1. If Rocky attends Party 1, however, you are going to be uncomfortable and get a payoff of 5. Similarly, Party 2 gives you a payoff of 15, unless Rocky attends, in which case the payoff is 0. Rocky likes Party 2 better, but he is likes you. He values Party 2 at 10, Party 1 at 5, and your presence at either party that he attends is worth an additional payoff of 10. You and Rocky both know each others strategy space (which party to attend) and payoffs functions.There are three players who must each choose an “effort” level from 1 to 7, that is, Si = {1, 2, 3, ..., 7}. The payoff for each player i is ui(si, s−i) = 10 max{s1, s2, s3} − si. How many pure- strategy Nash equilibria are there? Select one: a.2 b.4 c.none of the other answers d.3 e.1
- For various values of X(for player1 and player 2), find all Nash equilibria of the following game with von Neumann-Morgenstern preferences:Evaluate this statement All Nash equilibra are dominant strategy equilibria but not all dominant strategy equilibria are Nash EquilibriaThe bimatrix represents a simultaneous move game between Rowena and Colin. Rowena's payoff is the left number in each cell. ROWENA Up Down 0.25Left +0.75Right 0.65Left +0.35Right Find Colin's mixed strategy that makes Rowena indifferent between a pure strategy of playing Up and a pure strategy of playing Down. 0.5Left +0.5Right Left 1,16 2,20 0.45Left +0.55Right COLIN Right 4,6 3,40
