(a) Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Player B Player A $5 $10 $5 (b) Is there a pure strategy? Why or why not? ---Select--- ✓. Since the maximum of the row minimums is ---Select--- (c) Determine the optimal strategies and the value of this game. probability Player A selects $5 probability Player A selects $10 probability Player B selects $5 probability Player B selects $10 = = $10 = = Does the game favor one player over the other? and the minimum of the column maximums is

(a) Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Player B Player A $5 $10 $5 (b) Is there a pure strategy? Why or why not? ---Select--- ✓. Since the maximum of the row minimums is ---Select--- (c) Determine the optimal strategies and the value of this game. probability Player A selects $5 probability Player A selects $10 probability Player B selects $5 probability Player B selects $10 = = $10 = = Does the game favor one player over the other? and the minimum of the column maximums is

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

4
In a gambling game, Player A and Player B both have a $5 and a $10 bill. Each player selects one of the bills without the other player knowing
the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match,
Player B wins Player A's bill.
(a) Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A.
Player B
Player A
$5
$10
$5
(b) Is there a pure strategy? Why or why not?
---Select--- . Since the maximum of the row minimums is
--Select---
(c) Determine the optimal strategies and the value of this game.
probability Player A selects $5
probability Player A selects $10
probability Player B selects $5
probability Player B selects $10
=
=
$10
=
=
Does the game favor one player over the other?
Yes
O No
and the minimum of the column maximums is
(d) Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to
improve Player A's winnings?
If Player B begins playing each bill 50% of the time, Player A should instead select $5 with probability
probability
Comment on why it is important to follow an optimal game theory strategy.
Following the optimal strategy ---Select--- other players from taking advantage of the strategy you're playing, since they cannot improve
their expected payout by not playing the optimal strategy.
and select $10 with

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