Suppose Antonio and Trinity are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that followsshows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Antonio chooses Up and Trinitychooses Down, Antonio will receive a payoff of 7 and Trinity will receive a payoff of 5.TrinityUpDownUp4,87,5AntonioDown3,25,6In this game, the only dominant strategy is forto chooseThe outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses,and Trinity choosesGrade It NowSave & ContinueContinue without saving@2F2#380QF3MacBook Air44F7DllF844F1074$405Λ&%5678* 0QWERTYU1ANSX90-OODFGHJKLonراHcommandC>BNMΛ--P[HΛcommandopti

Based on the payoff matrix you've provided: Explanation:In this game, the only dominant strategy is…

Answered: Suppose Antonio and Trinity are playing…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The options for the last 3 fill-in-the-blanks are "Up" or "Down." Thank you!
Consider the following game - one card is dealt to player 1 ( the sender) from a standard deck of playing cards. The card may either be red (heart or diamond) or black (spades or clubs). Player 1 observes her card, but player 2 (the receiver) does not - Player 1 decides to Play (P) or Not Play (N). If player 1 chooses not to play, then the game ends and the player receives -1 and player 2 receives 1. - If player 1 chooses to play, then player 2 observes this decision (but not the card) and chooses to Continue (C) or Quit (Q). If player 2 chooses Q, player 1 earns a payoff of 1 and player 2 a payoff of -1 regardless of player 1's card - If player 2 chooses continue, player 1 reveals her card. If the card is red, player 1 receives a payoff of 3 and player 2 a payoff of -3. If the card is black, player 1 receives a payoff of 2 and player 2 a payoff of -1 a. Draw the extensive form game b. Draw the Bayesian form game
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The US and Canada have overfished North Atlantic cod stocks nearly to the point of extinction. Both countries wish to preserve the cod industry (and hence the cod stocks), so the two countries sign an agreement to limit fish hauls. Each country has two possible strategies: comply with the agreement (limit fishing) or renege on the agreement (overfish). Each country’s payoffs for different strategy combinations are given in the matrix below. The numbers in the cells represent utilities, and the payoff ordering is (US, Canada). QUESTIONS: 1.If this is a one-shot game (i.e., it is played once), do the players have a dominant strategy? If so, what is it? Briefly explain your answer. 2.What is the equilibrium of this game? Is it Pareto-optimal? How do you know?
QUESTION 4 Suppose there are 2 players in a non- cooperative game theory situation. Player A can move Up or Down while Player B can choose Left or Right. The following matrix contains the payoffs that each player receives under 4 scenarios. The first number in each cell refers to the payoffs for Player A. Player A Up Down A. B. C. 10, 60 D. 20, 80 Player B Suppose Player A moves first and Player B moves second. There is one equilibrium, Up, Left Left There is one equilibrium: Down, Right. 50, 90 40, 50 There are two equilibria, (Down, Left) and (Up, Right) Right There is one equilibrium in this game, Up Right
“To be or not to be, that is the question.” Imagine that in answering this question Hamlet had the following data to consider. Hamlet must choose either “To Be” or “Not to Be.” If Hamlet chooses “To Be” then his enemy the King will make a decision to either “Kill” Hamlet or let him “Live.” If Hamlet is killed by the King his payoff in this game is 200 since he will have been killed by the King who is his uncle and who also killed Hamlet’s father, the King’s brother, who was the prior king. If the King decides to let Hamlet Live then Hamlet will be able to avenge his father’s death and his payoff will be +300. Hamlet also considers suicide an option but given the uncertainty of the afterlife if he chooses not to be then his payoff is +100 since his doesn’t what the afterlife holds for one who kills himself. Draw the complete game tree for this situation. Be sure to accurately label the tree and include the payoffs. Assume Hamlet will choose the course of action that offers the highest…
7
Keith and Blake play a simultaneous one-shot game. Keith chooses between Top and Bottom, whereas Blake chooses between left and right. Payoffs are given by (Keith's payoffs are listed first and Blake's payoffs second): Top+left: 3,-6. Top+right:0,-7 Bottom+left:4,0. Bottom+right:-2,6. In a mixed strategy equilibria, Keith will play Top with what probability? 1. 6/7 2. 1/4 3. 1/2 4. 1/7 5. 0 6. 3/4
Consider the 2-player, zero-sum game "Rock, Paper, Scissors". Each player chooses one of 3 strategies: rock, paper, or scissors. Then, both players reveal their choices. The outcome is determined as follows. If both players choose the same strategy, neither player wins or loses anything. Otherwise: • "paper covers rock": if one player chooses paper and the other chooses rock, the player who chose paper wins and is paid 1 by the other player. "scissors cut paper": if one player chooses scissors and the other chooses paper, the player who chose scissors wins and is paid 1 by the other player. "rock breaks scissors": if one player chooses rock and the other player chooses scissors, the player who chose rock wins and is paid 1 by the other player. We can write the payoff matrix for this game as follows: rock paper scissors rock 0 -1 1 paper 1 0 scissors -1 1 -1 0 2. Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper…
Consider the following 3-player static game with row player Batman (his choices are a and b), column player Catwoman (her choices are c and d), and matrix player Joker (his choices are left, middle and right). In the payoff triples the first entry is Batman's payoff, the second entry is Catwoman's payoff, and the third entry is Joker's payoff. left middle right d d d a 1,1,5 1,0,1 a 1,1,3 1,0,0 a 1,1,0 1,0,0 0,0,0 0,1,0 0,0,0 0,1,3 b 0,0,0 0,1,5 (a) Give a belief for Joker about his opponents' choice combinations that supports his choice of middle (i.e. such that middle is optimal for him). (b) Solve the game with iterated strict dominance. (c) Construct an epistemic model such that, for every choice found in (b) there exists a type such that: • the choice is optimal for the type, • and the type expresses common belief in rationality.
Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays up

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