Q1) Player B secretly writes down one of the numbers (1,2,.9} and Player A tries to guess what it is with a cost of $1. If he guesses correctly, Player B pays him S10 and $8 for the odd and even numbers, respectively. If he doesn't guess correctly, he has no gain. Determine the optimal strategies of both players and the value of the game.
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- Determine the optimum strategies and the value of the game with the followingpayoff matrix of player A where A1, A2 are the strategies for player A and B1, B2 are for player B.B1 B2A1 5 1A2 3 4Nn3 Suppose an incumbent monopoly firm currently earns a profit of $50,000 per period. A potential entrant could enter and make a profit of $15,000 per period while also lowering the incumbent’s profit to $20,000 per period. The monopoly firm could seek to engage in predatory pricing, which would lead to both firms earning a loss of $5,000 per period. (a) Is there a Nash Equilibrium in this game? If so, what is it? (b) Discuss how this game might play out in the real world?Mohamed and Kate each pick an integer number between 1 and 3 (inclusive). They make their choices sequentially.Mohamed is the first player and Kate the second player. If they pick the same number each receives a payoff equal to the number they named. If they pick a different number, they get nothing. What is the SPE of the game? a. Mohamed chooses 3 and Kate is indifferent between 1, 2 and 3. b. Mohamed chooses 3 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2, and 3 if Mohamed chooses 3. c. Mohamed chooses 1 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2 and 3 if Mohamed chooses 3. d. Mohamed chooses 3 and Kate chooses 3.
- 4.25 The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): State of Nature Low Demand Medium Demand High Demand Decision Alternative s1 s2 s3 Manufacture, d1 -20 40 100 Purchase, d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. Use a decision tree to recommend a decision.Recommended decision: Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.EVPI: $5.Each of Player 1 and Player 2 chooses an integer from the set {1, 2, ..., K}. If they choose the same integer, P1 gets +1 and P2 gets -1; if they choose different integers, P1 gets -1 and P2 gets +1. (a) Show that it is a NE for each player to choose every integer in {1, 2, ..., K} with equal probability, K1 . (b) Show that there are no NE besides the one you found in (a).Amy must decide whether or not to make an investment that costs 1. The investment pays a return of 5, but is risky to Amy because Bill must be given charge of the asset if it is to be productive. If Amy invests, then Bill must decide whether to keep the entire return for himself, or to split the return, giving 3 to Amy and keeping 2 for himself. (Amy pays the cost 1 even if Bill does not pay her back.) If Amy does not invest, then both players get 0. This is called a trust game because Amy wants to invest only if she trusts Bill to pay her back. (a) Model this as an extensive-form game (b) What is the strategic-form corresponding to your extensive-form? (c) Find all of the Nash equilibria. Which are the subgame-perfect?
- 1. Draw tree of the game clearly, handwritten is preferable.You and a rival are engaged in a game in which there are three possible outcomes: you win, your rival wins (you lose), or the two of you tie. You get a payoff of 50 if you win, a payoff of 20 if you tie, and a payoff of 0 if you lose. What is your expected payoff in each of the following situations? (a) There is a 50% chance that the game ends in a tie, but only a 10% chance that you win. (There is thus a 40% chance that you lose.) (b) There is a 50–50 chance that you win or lose. There are no ties. (c) There is an 80% chance that you lose, a 10% chance that you win, and a 10% chance that you tie.What is the secure strategy for player B in the game presented in Table
- What is the payoff for both players in the SPNE of this game?-(2,5)-(3,4)- (2,2)- (5,1)- (1,7)In the coin game, two players begin with 13 coins. Players take turns to remove coins. At each turn each player is allowed to remove one, two, or three coins. The winner is the last player to remove coin(s). Suppose there are 9 coins remaining and it is your turn to remove coin(s). Your best strategy is to remove how many coins? a. 0 b. 1 c. 2 d. 3Q17. What the information sets in the above game denote? Player 2 does not observe the action of player 1, so he does not know in which decision node he/she is playing at. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and b, or one between c and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played one between a and c, or one between b and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and d, or one between b and c.