Consider the following game: Table 1: A symmetric two-player coordination game Player 2 S1 S2 0, 1, 1, 0, S1 1 Player 1 82 1 1. Suppose that the initial weights for each player on the strategies of the opponent (s1, S2) are identical and given by wo = wi = (1, V2). Show that under fictitious play, the sequence of play oscillates between (s1, S1) and (s2, S2)

Consider the following game: Table 1: A symmetric two-player coordination game Player 2 S1 S2 0, 1, 1, 0, S1 1 Player 1 82 1 1. Suppose that the initial weights for each player on the strategies of the opponent (s1, S2) are identical and given by wo = wi = (1, V2). Show that under fictitious play, the sequence of play oscillates between (s1, S1) and (s2, S2)

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

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
Consider a bankruptcy game with two risk neutral players where V =$800,000, C1= $300,000 and C2=$800,000. a) What is the Nash bargaining solution?
Consider that there is one auctioneer who would like to sell one commodity and there are 2 individuals, 1 and 2. The auctioneer will apply the following tie-breaking rule: If there are multiple bidders who announce the highest bid, then select the bidder with the smallest index will be picked up as the winner. (For instance, let b(i) = b(j) . Then, i is the winner if and only if i < j.) Let each individual i's private value of the commodity, v(i), is given as: v(1) = $1600; v(2) = $2100. Considering a first-price auction, specify the set of Nash equilibria in this game.
1
Consider the following two-player game with three options for each player. (Payouts are listed for the row player first, then the column player.) player Y layery 3,3 A 1,5 4,4 6,2 K 8,1 3,7 5,2 0,6 1,1 Find a mixed Nash equilibrium for this game. Solution suggestion: Use two variables per player. If p and are the probabilities of selecting the first two strategies, then 1-p-q is the probability of selecting the third strategy. You will need to solve a system of equations.
Table 3. This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A. Profit for Firm B). Firm A Q=5 Q=6 Firm B Q=5 (24, 24) (30, 10) Q=6 (10,30) (19, 19) Refer to Table 3. The dominant strategy For Firm A is to produce Select one: O a. 5 units and the dominant strategy for Firm B is to produce 5 units. b. 5 units and the dominant strategy for Firm B is to produce 6 units. c. 6 units and the dominant strategy for Firm B is to produce 5 units. d. 6 units and the dominant strategy for Firm B is to produce 6 units.
a) Clearly indicate the eliminated dominated strategies. Apply the EIE algorithm, and determine the solution set of the game in normal form. b) Assuming that each player would not choose strategies that are strictly dominated, determine the Nash equilibria of the reduced game J2 (3,1) (4, 2) (2, 0) (0, 4) (1, 5) (3,0) (1, 3) (2, 2) a J1 (4, 1) (2, 5) (2,6) (5, 2)
QUESTION 1 We have two auto manufacturers, Tudor (initial monopolist) and Fordor (potential entrant). Tudor might try to use its price in the first stage of the game as a signal of its cost. Fordor's initial belief is that the probability of facing a low-cost Tudor is 40% and this matches the probability with which Tudor has the lower cost. The entry game between automakers is illustrated in the following game tree (The first number at each terminal node is Tudor's payoff): NATURE Tudor's cost low (Prob. 0.4) TUDOR Tudor's cost high (Prob. 0.6) TUDOR FORDOR Price low TUDOR FORDOR Price low Price high FORDOR In Bluff (LL) Out In Out In Out 100+69, 11-40 Honest (LH) 100+ 100,0 0+3,45-40 25+25,0 Converting the sequential game to a bimatrix form, fill in the blanks. 0+25,0 25+3,45-40 FORDOR Regardless (II) Conditional (OI)
In the normal form game below, the payoff matrix depends on the parameter a. 1 1 2 ABC a 0,2 6,4 -2,4 b 0, -24 -2a, 2a 8, 2 C 4,0 0,4 0, 14 Find the values of a, for which at least one pure strategy Nash equilibrium exists. Compute the value of a for which the expected payoff is the same for both players when the mixed strategy profile (01,02) = ((1/3,2/3,0), (0,1/4,3/4)) is played. Find the best response of player 1 (as a function of the parameter a) to player's 2 mixed strategy o2 = (1/2,1/2,0). Assuming a = 0 eliminate iteratively all dominated strategies and find a mixed strategy Nash equilibrium in this game.
Player 2 A B C А 2, 2 6,1 1,1 Player 1 B 1,6 5,5 1,1 1,1 1,1 4,4 Consider the simultaneous move game represented in normal form by this payoff matrix. Suppose that the game is repeated for two periods. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. (B, B) is played in the first period, (C, C) is played in the second period. (A, A) is played in both periods. (C, C) is played in both periods.
None
Consider the following game: p 2,10 0,5 5,2 0,5 5,10 Which of the following is FALSE for the SPE of this game? a. If p in [0.6, 1], then playing x is an equilibrim strategy for player 1 b. If p in [0, 0.6], then playing y is an equilibrim strategy for player 1 C. For all possible p values in [0,1], playing x is an equilibrium strategy for player 1 y y R Nature 1 2 1-p y R X 2,10