4. Suppose we make a slight change to Borel's poker model so that X and Y (the "cards" for players I and II) are exponentially distributed, instead of uniformly distributed between 0 and 1. In other words, P(X >z) =e=* and P(Y > y) = e-v. Everything else about the model is the same. Assume the optimal strategies for players I and II have the same form, i.e., there is some threshold, B, so that %3D • Player I bets for sure if X > B, and bets with some probability q if X < B, and • Player II calls if Y > B, and folds if Y
4. Suppose we make a slight change to Borel's poker model so that X and Y (the "cards" for players I and II) are exponentially distributed, instead of uniformly distributed between 0 and 1. In other words, P(X >z) =e=* and P(Y > y) = e-v. Everything else about the model is the same. Assume the optimal strategies for players I and II have the same form, i.e., there is some threshold, B, so that %3D • Player I bets for sure if X > B, and bets with some probability q if X < B, and • Player II calls if Y > B, and folds if Y
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:4. Suppose we make a slight change to Borel's poker model so that X and Y
(the "cards" for players I and II) are exponentially distributed, instead of
uniformly distributed between 0 and 1. In other words, P(X > r) =e=*
and P(Y > y) = e-v. Everything else about the model is the same.
Assume the optimal strategies for players I and II have the same form,
i.e., there is some threshold, B, so that
%3!
• Player I bets for sure if X > B, and bets with some probability q if
X < B, and
• Player II calls if Y > 3, and folds if Y < 3,
Find 3 and q. Hint: use the indifference argument, just like we did for
the standard Borel model. You do not need to prove that the 3 and q you
derive are optimal.
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