##DESCRIPTION

## Game Theory, basic Nash Equilibria

##ENDDESCRIPTION

##KEYWORDS('Game Theory, Nash Equilibria')

## DBsubject('Game Theory')

## DBchapter('Simultaneous Move Games')

## DBsection('Nash Equilibria')

## Date('6/25/2014')

## Author('Adam Graham-Squire')

## Institution('High Point University')

## TitleText1('Games Of Strategy')

## EditionText1('2')

## AuthorText1('Dixit, Skeath')

## Chapter('4')

## Problem1('2a')

########################################################################

DOCUMENT(); # This should be the first executable line in the problem.

loadMacros(

"PGstandard.pl",

"PGunion.pl",

"MathObjects.pl",

"PGcourse.pl",

"PGML.pl",

"PGessaymacros.pl"

);

TEXT(beginproblem);

##############################

#

# Setup

#

Context("Numeric");

$a = non_zero_random(1,2,1);

$b = non_zero_random(3,4,1);

$c = non_zero_random(5,6,1);

$d = non_zero_random(7,10,1);

##############################

#

# Main text

#

BEGIN_TEXT

Find all Nash equilibria in pure strategies for the zero-sum game given below.

$PAR

$BCENTER

\{ begintable(3) \}

\{ row( "", "Left", "Right" ) \}

\{ row( "Up", "$a, -$a", "$d, -$d" ) \}

\{ row( "Down", "$b, -$b", "$c, -$c" ) \}

\{ endtable() \}

$ECENTER

END_TEXT

BEGIN_PGML

If both players play their optimal strategy, the Row player will have a payout of [________]{"[$b]"}.

Explain your reasoning for your answer above.

[@ ANS(essay_cmp()); ans_box(5,40) @]*

END_PGML

##############################

ENDDOCUMENT();