Show that there does not exist a pure-strategy perfect Bayesian equilibrium in the following extensive-form game. What is the mi strategy perfect Bayesian equilibrium? R Player 1 M Player 2 3
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- Derive all of the rationalizable strategies for the game shown.Nash equilibrium refers to the optimal outcome of a game where there is no incentive for the players to deviate from their initial strategy. An individual (or player) can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. Given this premise, can there be a no Nash equilibrium?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 game
- If a game has a mixed strategy Nash equilibrium then which of the following statements is true? There is at least two pure strategy Nash equilibrium. There are at least two rationalizable strategies. Players prefer any pure strategy Nash equilibrium to the mixed strategy Nash equilibrium. Players always prefer to mix when the other player mixes. None of the above.Which of the following statements about a Nash equilibrium is not correct? A. Each player plays a best response to opponents' Nash strategies. B. No player has a profitable unilateral deviation. C. For each finite noncoopertiave game there always exists a pure strategy Nash equilibrium. D. A game has at least two players. Which one of the following statements is incorrect? A. For dynamic games with complete information, not all subgame perfect Nash equilibrium points can be found by backward induction. B. A finite dynamic game with complete information may also have a normal form representation. C. A finite static game with complete information may not have a pure strategy Nash equilibrium. D. A finite static game with complete information cannot have an extensive form representation. Which one of the following statements is correct? A. A supergame cannot have any subgame perfect Nash equilibrium. B. A supergame can only have finite number of subgame perfect Nash…Find all Nash equilibria for the two-player game (image attached). Provide necessary computation.
- 4. Correlated EquilibriaConstruct an example (not one from class or the reading) of a Normal form game with a correlated equilibrium that is not a Nash equilibrium.Within a voluntary contribution game, the Nash equilibrium level of contribution is zero, but in experiments, it is often possible to sustain positive levels of contribution for a long period. How might we best explain this? A) Participants are altruistic, and so value the payoff which other participants receive, benefiting (indirectly) from making a contribution. B) Participants believe that if they make a contribution, then other participants will be more likely to make a contribution. C) Participants in experiments believe that they have to make contributions in order to receive any payoff from their participation. D) Participants have experience of working in situations in which cooperation can be sustained for mutual benefit and so have internalised a social norm of cooperationIf a player does not have a dominant strategy, can the game still have a Nash equilibrium? No. At least one player must have a dominant strategy for the outcome to be a Nash equilibrium. Yes. There is no need for a dominant strategy to exist in order to have a Nash equilibrium. The outcome is a Nash equilibrium because each player has made his or her optimal choice based on the optimal choice of the other player. No. If there is no dominant strategy, there is no predictable outcome and therefore no Nash equilibrium. Yes. A Nash equilibrium is possible only if neither player has a dominant strategy. If a dominant strategy exists, it is no longer a Nash equilibrium.
- E3 Bayesian Game]. Consider a Bayesian game described by a following payoff matrix. Please solve (show your solution). 1. Enumerate all pure strategies for each player. 2. Suppose that player 1 observes his type ?1 = 3. How does player 1 think of the probability of ?2? 3. Find a (pure strategy) Bayesian Nash equilibrium.Real Options & Game Theory Is the following statement true or false (explain your answer): In any strategic-form game, if a player has a dominant strategy, then all of the other strategies of that player are dominated.q60c- Is the Nash equilibrium the best outcome for this problem? Explain
