Game Theory, formulating a payoff matrix The Next CEO of Stack OverflowFinding best response function with probabilities (BR) given a normal-matrix representation of the gameGame theory problem: Poker with bluffingNash Equilibrium for the prisoners dilemma when using mixed strategiesAir Strike GameThe Goblin GameQuestion about Game theory, matrix games.I need help understanding a question regarding a game played by two players.Best strategy for a gambling situationProbability of survival using optimal strategyMultiplayer cooperative game with imperfect information
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Game Theory, formulating a payoff matrix
The Next CEO of Stack OverflowFinding best response function with probabilities (BR) given a normal-matrix representation of the gameGame theory problem: Poker with bluffingNash Equilibrium for the prisoners dilemma when using mixed strategiesAir Strike GameThe Goblin GameQuestion about Game theory, matrix games.I need help understanding a question regarding a game played by two players.Best strategy for a gambling situationProbability of survival using optimal strategyMultiplayer cooperative game with imperfect information
$begingroup$
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
asked Mar 18 at 20:05
MathematicianPMathematicianP
3416
$endgroup$
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
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
asked Mar 18 at 20:05
MathematicianPMathematicianP
3416
$endgroup$
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
game-theory
asked Mar 18 at 20:05
MathematicianPMathematicianP
3416
asked Mar 18 at 20:05
MathematicianPMathematicianP
3416
asked Mar 18 at 20:05
MathematicianPMathematicianP
3416
asked Mar 18 at 20:05
MathematicianPMathematicianP
3416
asked Mar 18 at 20:05
MathematicianPMathematicianP
3416
3416
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 |
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
1
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
$begingroup$
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
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$begingroup$
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