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Game Theory, formulating a payoff matrix

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0

$begingroup$

Rowena and Colin play a hide-and-seek game. Rowena hides in one of 3 locations,
and then Colin searches them in some order. If he searches in order i, j, k then his search
cost is ci, ci + cj or ci + cj + ck, depending upon whether Rowena hides in i, j or k, respectively, and where c1, c2, c3 are all positive. Rowena (Colin) wishes to maximize (minimize) the expected search cost.
Formulate the payoff matrix for this game.

I don't know how to formulate the matrix - if Rowena is in position i and Colin searches there first, then the exppected pay off will be ci so the diagonal elements will have entries ci. But for the non-diagonal entries, the expected payoff depends on what colin chooses after his first wrong attempt...

Could someone provide an answer with an explanation?

game-theory

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asked Mar 18 at 20:05

MathematicianPMathematicianP

3416

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Hint: it would be a 3*6 matrix, 3 corresponding to Rowena's choice in hiding location , and the 6 corresponding Colin's choice in the order of search of locations ( eg. $krightarrow jrightarrow i$)
  $endgroup$
  – user3257842
  Mar 18 at 20:36
  
  
  

  
  
  
  

add a comment | 

0

$begingroup$

Rowena and Colin play a hide-and-seek game. Rowena hides in one of 3 locations,
and then Colin searches them in some order. If he searches in order i, j, k then his search
cost is ci, ci + cj or ci + cj + ck, depending upon whether Rowena hides in i, j or k, respectively, and where c1, c2, c3 are all positive. Rowena (Colin) wishes to maximize (minimize) the expected search cost.
Formulate the payoff matrix for this game.

I don't know how to formulate the matrix - if Rowena is in position i and Colin searches there first, then the exppected pay off will be ci so the diagonal elements will have entries ci. But for the non-diagonal entries, the expected payoff depends on what colin chooses after his first wrong attempt...

Could someone provide an answer with an explanation?

game-theory

share|cite|improve this question

asked Mar 18 at 20:05

MathematicianPMathematicianP

3416

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Hint: it would be a 3*6 matrix, 3 corresponding to Rowena's choice in hiding location , and the 6 corresponding Colin's choice in the order of search of locations ( eg. $krightarrow jrightarrow i$)
  $endgroup$
  – user3257842
  Mar 18 at 20:36
  
  
  

  
  
  
  

add a comment | 

$begingroup$

Rowena and Colin play a hide-and-seek game. Rowena hides in one of 3 locations,
and then Colin searches them in some order. If he searches in order i, j, k then his search
cost is ci, ci + cj or ci + cj + ck, depending upon whether Rowena hides in i, j or k, respectively, and where c1, c2, c3 are all positive. Rowena (Colin) wishes to maximize (minimize) the expected search cost.
Formulate the payoff matrix for this game.

I don't know how to formulate the matrix - if Rowena is in position i and Colin searches there first, then the exppected pay off will be ci so the diagonal elements will have entries ci. But for the non-diagonal entries, the expected payoff depends on what colin chooses after his first wrong attempt...

Could someone provide an answer with an explanation?

game-theory

share|cite|improve this question

asked Mar 18 at 20:05

MathematicianPMathematicianP

3416

$endgroup$

share|cite|improve this question

asked Mar 18 at 20:05

MathematicianPMathematicianP

3416

share|cite|improve this question

asked Mar 18 at 20:05

MathematicianPMathematicianP

3416

asked Mar 18 at 20:05

MathematicianPMathematicianP

3416

asked Mar 18 at 20:05

MathematicianPMathematicianP

3416