Games sequential moves-game played b/w pitcher and batter, Game Theory

Problem: Consider a (simplified) game played between a pitcher (who chooses between throwing a fastball or a curve) and a batter (who chooses which pitch to expect). The batter has an advantage if he guesses the pitch that is actually thrown. This is a constant-sum game, where the payoff is measured by the probability that the batter will get a base hit (a high probability of a hit is good for the batter and bad for the pitcher).


If a pitcher throws a fastball, and the batter guesses fastball, the probability of a hit is 0.300.
If the pitcher throws a fastball, and the batter guesses curve, the probability of a hit is 0.200.
If the pitcher throws a curve, and the batter guesses curve, the probability of a hit is 0.350.
If the pitcher throws a curve, and the batter guesses fastball, the probability of a hit is 0.150.


(a) Suppose that the pitcher is “tipping” his pitches (tipping means that the pitcher is holding the ball, positioning his body, or doing something else in a way that reveals to the opposing team which pitch he is going to throw). For our purposes, this means that the pitcher-batter game is now a sequential game in which the pitcher announces his pitch choice before the batter has to choose his strategy.


(b) Suppose that the pitcher knows he is tipping his pitches but can’t stop himself from doing so. Thus, the pitcher and batter are playing the game you just drew. Find the rollback equilibrium of this game.


(c) Now change the timing of the game, so that the batter has to reveal his action (perhaps by altering his batting stance) before the pitcher chooses which pitch to throw. find the rollback equilibrium.


Solution:

 (b) Pitcher throws a fastball; batter guesses fastball.

(c) Batter guesses curve; pitcher throws a fastball


Posted Date: 9/27/2012 3:23:43 AM | Location : United States







Related Discussions:- Games sequential moves-game played b/w pitcher and batter, Assignment Help, Ask Question on Games sequential moves-game played b/w pitcher and batter, Get Answer, Expert's Help, Games sequential moves-game played b/w pitcher and batter Discussions

Write discussion on Games sequential moves-game played b/w pitcher and batter
Your posts are moderated
Related Questions
Paired Prisoners' Dilemma Students can be paired off and instructed to play several ver-sions of a particular game with a prisoners' dilemma structure.Provide each pair with a


Game 1 Color Coordination (with Delay) This game should be played twice, once without the delay tactic and once with it, to show the difference between out- comes in the s

A payoff offerd as a bequest for someone partaking in some activity that doesn't directly provide her with profit. Often, such incentives are given to beat the ethical hazard drawb

Living from 1845 to 1926, Edgeworth's contributions to Economics still influence trendy game theorists. His Mathematical Psychics printed in 1881, demonstrated the notion of compet

Twentieth century mathematician who expanded on earlier fastened purpose theorems. a hard and fast purpose theorem defines the conditions on a perform, f(x), beneath that there exi

A sequential game is one among imperfect data if a player doesn't grasp precisely what actions different players took up to that time. Technically, there exists a minimum of one da

A trigger strategy sometimes applied to repeated prisoner's dilemmas during which a player begins by cooperating within the initial amount, and continues to cooperate till one defe

Assuming that there are only 2 airline companies in the world, Delta and US Airways, what is the ((Nash) Equilibrium) or price that each company in the following matrix will charge

A uniform worth auction may be a multiunit auction during which each winning bidder pays identical worth, which can or might not be equal to the participants' bids. Alternatively,