a) Consider a set of monetary outcomes X ={x1, ... , xK} where the outcomes are arrangedin increasing order x, << XK. Let p and q be simple lotteries. We say that lottery p•..first-order stochastically dominates lottery q, if the following holds:KKE p(x;) > E qcx,)j=ij=iwith at least one of the inequalities being strict. Explain the intuition of first-order stochas-tic dominance. Show that, for expected utility preferences with vNM utility u that is strictlyincreasing in money, if p first-order stochastically dominates q then p > q.

a) Consider a set of monetary outcomes X {x1, ... , Xg} where the outcomes are arranged in increasing order x, < .… < xK. Let p and q be simple lotteries. We say that lottery p first-order stochastically dominates lottery q, if the following holds: K K E P(x,) > E q(x,) for all i = 1, ... K, j=i j=i

a) Consider a set of monetary outcomes X {x1, ... , Xg} where the outcomes are arranged in increasing order x, < .… < xK. Let p and q be simple lotteries. We say that lottery p first-order stochastically dominates lottery q, if the following holds: K K E P(x,) > E q(x,) for all i = 1, ... K, j=i j=i

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

Consider the game in the image attached below, which is infinitely repeated at t = 1, 2, ... Both players discount the future at rate: delta E (0, 1). The stage game is in the image attached. "Grim Trigger" strategies: Describe the "Grim Trigger" strategy profile of this game. Draw the finite automata representation of this strategy profile. Find the lowest value of delta for this strategy profile to form a subgame perfect equilibrium.
1. Consider a sequential continuum game with two players, in which Player 1 first chooses a continuous variable £₁, and then Player 2 selects £2, with payoff functions ₁ and 7₂. Find the best response for P2, as the function î2 = BR₂(x1), for each given #₂: (a) (b) (c) T₂(x1, x₂) ) = (1400 — x1 — x2)x2 − 13x² T₂(x1, x₂) T₂(X1, X2₂) = : 100x2 + 3x1x2 − 14x1 – 30x1x² = 15x2 x² + x² +1
a) Consider a set of monetary outcomes X = {x1,... , Xk} where the outcomes are arranged in increasing order x, g(x;) for all i = 1,... K, j=i j=i with at least one of the inequalities being strict. Explain the intuition of first-order stochas- tic dominance. Show that, for expected utility preferences with vNM utility u that is strictly increasing in money, if p first-order stochastically dominates q then p > q.
Exercise 1.8. Consider the following "third-price" auction. There are n≥ 3 bidders. A single object is auctioned and Player / values the object $v,, with V, > 0. The bids are simultaneous and secret. The utility of Player / is: 0 if she does not win and (v-p) if she wins and pays $p. Every non-negative number is an admissible bid. Let b, denote the bid of Player i. The winner is the highest bidder. In case of ties the bidder with the lowest index among those who submitted the highest bid wins (e.g. if the highest bid is $120 and it is submitted by players 6, 12 and 15, then the winner is Player 6). The losers don't get anything and don't pay anything. The winner gets the object and pays the third highest bid, which is defined as follows. Let be the winner and fix a Player j such that b₁ = max({b,,...,b,}\ {b}) [if GAME THEORY - Giacomo Bonanno 39 max({b,...,b}\{b;}) contains more than one element, then we pick one of them]. Then the third price is defined as max({b₁,...,b}\{b,,b;}).…
a) Consider a set of monetary outcomes X = {x1,...,Xk} where the outcomes are arranged in increasing order x, E q(x,) for all i = 1, ... K, j=i j=i with at least one of the inequalities being strict. Explain the intuition of first-order stochas- tic dominance. Show that, for expected utility preferences with vNM utility u that is strictly increasing in money, if p first-order stochastically dominates q then p > q.
Let A be an m x n matrix representing the payoff of n securities in m states of the world. If the market is complete, which of the following statements are true? Provide counter examples in case not. (a) A is of full rank (b) A is invertible (c) The prices of n securities are free of arbitrage
Repeated Game Consider the game below, which is infinitely repeated at t = 1,2, .... Both players discount the future at rate d E (0, 1). The stage game is C C 5,5 0,6 D 6,0 1,1 1. The following three questions are about "Grim Trigger" strategies. (a) Describe the "Grim Trigger" strategy profile of this game. (b) Draw the finite automata representation of this strategy profile. (c) Find the lowest value of 8 for this strategy profile to form a subgame perfect equilibrium. 2. Suppose that the players play (C,C) in period t = 1, 3, 5, ... and plays (D,D) in period t = 2,4, 6, ... Compute the discounted payoff of each player. 3. Find a subgame perfect equilibrium such that, on the equilibrium path, (D,D) is played at periods t = 1, 3, 5, ..., and (C,C) is played at periods t = 2, 4, 6, ... Write down the finite automata representation for the strategy profile you proposed. Find the lowest value of d for the profile to form a subgame perfect equilibrium.
Why do sellers generally prefer a Vickrey auction to a regular sealed bid if sellers don’t receive the highest bid in the Vickrey auction? Sellers only have to sell their item if the bid is the highest-price bid. The second-highest bid in a Vickrey auction is generally higher than the highest bid in a regular sealed-bid auction. The second-highest bid is about the same in both auctions. Sellers prefer the final price is not revealed to all bidders. Sellers would never prefer Vickrey auctions.
Consider the version of the Beauty Contest game from the class, in which the players are trying to guess the average guess minus one. More precisely, the utilities now are: ui (si; sj ) = -|si-(-1)| where sj/#l forj belong tI (a) Which strategies are strictly dominated in this game, and by which alternative strategies? And so, what is the set of strategies BR11 (b) What is the set BR21 ? What is the set BRni for any n > 0?
Consider the following model about the auctions. We have two buyers each obtain a private signal about the value of good being auctioned. The signal can be either high (H) or low (L) with equal probability. If both obtain signal H, the good is worth 1; otherwise, it is worth 0.a. What is the expected value of the good1 to a buyer who sees signal L and to a buyer who sees signal H?b. Suppose buyers bid their expected value computed in part (a). Show that they earn negative profit conditional on observing signal H.
Consider the following payoff matrix B R U 7, 7 4,17 A 17,4 6,6 Players A and B repeatedly play this game with an infinite horizon. Future payoffs are discounted with 1/(1+r), where r is the long-term interest rate. Determine the interval of r for which the Carrot-and-Stick strategy does form a Nash-equilibrium when the opponent can discover any deviation immediately. Remember the following relation TA+Lt-1 (14+t) TB TB = TA + O r>0.1 O r0.2 Or-1 O r1
Is the set of SPE of any extensive form game with perfect information is identical to the set of Nash Equilibria of the induced normal form game? If yes, provide a proof. If no, provide an explanation by illustrating a game. [Maximum word limit for this question is 80 words.]