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(Sequential truel) Each of persons A, B, and C has a gun contain- ing a single bullet. Each person, as long as she is alive, may shoot at any surviving person. First A can shoot, then B (if still alive), then C (if still alive). (As in the previous exercise, you may interpret the players as political candidates. In this exercise, each candidate has a budget sufficient to launch a negative campaign to discredit exactly one of its rivals.) Denote by pi the probability that player i hits her intended target; assume that 0 pi 1. Assume that each player wishes to maximize her probability of survival; among outcomes in which her survival probability is the same, she wants the danger posed by any other survivors to be as small as possible. (The last assumption is intended to capture the idea that there is some chance that further rounds of shooting may occur, though the possibility of such rounds is not incorporated explicitly into the game.) Model this situation as an extensive game with perfect information and chance moves. (Draw a diagram. Note that the subgames following histories in which A misses her intended target are the same.) Find the subgame perfect equilibria of the game. (Consider only cases in which pA, pB, and pC are all different.) Explain the logic behind A's equi- librium action. Show that "weakness is strength" for C: she is better off if pC pB than if pC > pB.
Now consider the variant in which each player, on her turn, has the additional option of shooting into the air. Find the subgame perfect equilibria of this game when pA pB. Explain the logic behind A's equilibrium action.
Is the income elasticity of demand for real cash balances significantly different from one?
Find the set of pure strategy symmetric Nash equilibria of the game, and the set of pure evolutionarily stable strategies. What happens if each player has n actions, corresponding to demands of 1, 2, . . . , n units of payo? (and δ 1/n)?
If the game was played twice, would playing in the first period be a subgame perfect equilibrium first-period outcome? Explain why or why not.
case study1game theorytimemagazine and newsweek are twocompetingnews magazines.suppose thateach
A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16 ball bearings is 29.5 g. with a standard deviation o..
What is her payoff if she deviates to a lower or higher effort level? Is any action profile in which not all the players' effort levels are the same a Nash equilibrium?
A firm incurs production costs C(q) = F + mq, and transportation costs T(q) = aq + ????2, where q is the output of each of its plants. What is the optimal plant size, and how does it vary with the parameters F, m, a and b?
Show that army 2 can increase its subgame perfect equilibrium payoff (and reduce army 1's payoff) by burning the bridge to its mainland, eliminating its option to retreat if attacked.
Suppose that the MBA education industry is constant cost and is in long run equilibrium. Demand raise, but due to strict accreditation standards, new companies are not allowed to enter the market.
Express the following in the Σ notation and What is the value of b - Find the P( X ≤ 2 ); prob( X ≤ 3 ); prob( 2 ≤ x ≤ 3).
Demand for airline tickets fluctuates throughout the year, which affects the price of an airline ticket. Suggest the type of game that may be most appropriate for a specific airline to play to address the differences in demand and elasticity and the ..
Suppose that a pair of 14-sided dice are rolled (the sides are numbered 1-14 and yes, these do actually exist).
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