Consider the following game played between a boss (B) and an employee (E). The bossoffers a wage, w 2 0, and after observing the wage offer the employee decides how mucheffort, e 2 0, to exert. The payoff function of the boss is up (w, e) = 2ve – w and the payofffunction of employee is ug (w, e) = w -+ awe. What are the subgame perfect equilibriumchoices of wage and effort as a function of a?O a. w=a and e=a2O b. w=a and e=a?O C. w=a? and e=Dad. w=a/2 and e=a

UE=w-e22+awea) ∂u∂e⇒-2e2+aw=0 ⇒-e+aw = 0therefore, eBR=aw or, w = eBRa

Consider the following game played between a boss (B) and an employee (E). The boss offers a wage, w 2 0, and after observing the wage offer the employee decides how much effort, e > 0, to exert. The payoff function of the boss is ug (w, e) = 2ve - w and the payoff function of employee is ug (w, e) = w-+ awe. What are the subgame perfect equilibrium choices of wage and effort as a function of a? Oa. w3a and e=a2 Ob. w=a and e=a? C. W=a? and e=a d. w=a 1/2 and e=a

Consider the following game played between a boss (B) and an employee (E). The boss offers a wage, w 2 0, and after observing the wage offer the employee decides how much effort, e > 0, to exert. The payoff function of the boss is ug (w, e) = 2ve - w and the payoff function of employee is ug (w, e) = w-+ awe. What are the subgame perfect equilibrium choices of wage and effort as a function of a? Oa. w3a and e=a2 Ob. w=a and e=a? C. W=a? and e=a d. w=a 1/2 and e=a

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Explain whether the statement is true or false and explain why? Statement 1: If a game has a Pareto efficient outcome, there exists a Nash equilibrium that leads to this outcome. Statement 2: If someone has linear indifference curves between contingent commodity bundles, then she must be risk averse and the risk premium is positive. Statement 3: Suppose we have a game with three pure strategies. In a (fully) mixed strategy Nash equilibrium, a player is indifferent between her three pure strategies
The action set of player 1 is {1,2, 3, 4, 5} (not considering the $ sign). When both players are rational, the theoretical SPNE is (5, 1). Now answer the following problems. What is the dollar equivalent of utility of happiness to ensure player 2 to accept the 2$ offer of player 1? Just write the number, no need to put the $ sign. 5| 5 What is the dollar equivalent of utility of happiness to ensure player 2 to accept the 4$ offer of player 1? Just write the number, no need to put the $ sign. 100 100
Player 2 Middle Left P1: $45 P1: $70 Up P2: $45 P2: $50 Player 1 P1: $50 P1: $60 Middle P2: $50 P2: $60 P1: $60 P1: $50 Down P2: $60 P2: $70 In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) (up, left) (up, middle) (up, right) (middle, left) (middle, middle) (middle, right) (down, left) (down, middle) (down, right) No equilibrium Right P1: $45 P2: $60 P1: $50 P2: $70 P1: $60 P2: $60
Use the following payoff matrix for a one-shot game to answer the accompanying questions. A 5,5 0, -200 B -200, 0 20, 20 Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication. Which of these outcomes would you consider most likely? Explain. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter, and what outcome do you think would occur as a result?
(4) Resource Allocation. Consider a combinatorial auction with three items {a,b,c} and three players (I, II, III. The valuations each player has for each subset of a b с ab bс ас abc I 1 2 1 6 4 11 II 3 5 3 3 5 III| 4 5 0 7 5 7 the items is shown below. What is the allocation produced under the VCG (Vickrey-Clarke-Groves) mechanism and what are the VCG payments of the players?
Suppose Edison and Hilary are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that Edison chooses Right and Hilary chooses Right, Edison will receive a payoff of 3 and Hilary will receive a payoff of 7. Hilary Left Right Left 4, 6 6, 8 Edison Right 7, 5 3, 7 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Edison chooses and Hilary chooses
A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z>Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. What do Ch and Cw equal if Yh = Yw (but this quantity is not equal to zero)? Please do fast ASAP fast
Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.
Cooperative Games - Game Theory
- Individuals 1 and 2 are forming a company. The value of their relationship depends on the effort that each expends. Suppose that individual i's utility from the relationship is x² + x; − xixj, where x¿ is individual i 's effort and x ; is the effort of the other person (i = 1, 2). Assume x1, x2 ≥ 0. Which statement is true? There is a Nash equilibrium in which each player chooses effort level k > 0. This equilibrium is Pareto efficient. There is no mixed-strategy Nash equilibrium. There is a unique Nash equilibrium in which each player chooses no effort x¿ = x; = 0. The set of Nash equilibria in this game is finite. There is a Nash equilibrium in which xi = 0 and x ; = 1| =
Consider a game in which, simultaneously, player 1 selects a number x € [2, 8] and player 2 selects a number y E [2, 8]. The payoffs are given by: и, (х, у) — 2ху — х? из(х, у) — 4ху — у?. Calculate the rationalizable strategy profiles for this game.
Consider a normal form game in which player 1 has three strategies, A1, B1, C1 and player 2 has three strategies, A2, B2, C2. Suppose that A1 is a best response to B2, B1 is a best response to A2, A2 is a best response to B1, and B2 is a best response to A1. Do we know with certainty whether A1 is rationalizable or not?