Question

Rose is a police officer who must decide whether to search for known robber and wanted suspect, Colin, or patrol the streets on traffic duty. Colin must decide between staying out of sight and continue prowling the streets and committing crimes. Rose’s payoff for patrolling the streets on traffic duty is 10 (utility) units, while her payoff for looking for Colin depends on whether she catches him. If Colin prowls the streets when Rose is looking for him, then she will certainly catch him and she will obtain a payoff of 25 (utility) units. (The significant increase in payoff units comes from the benefit of getting Crimin’ Colin off of the streets and the fame that results from being the officer responsible for the take down.) If Colin is caught by Rose, then will result in a payoff of -20 units for Colin. If Colin prowls the streets while Rose is on traffic duty, then she will not catch him and he has his run of the town, obtaining a payoff of 20 units. If Colin is hiding while Rose is looking for him, then she will not catch him and her payoff will be 0 units. If Colin stays hidden, then his payoff is 0 units.

Answer 1

From the above information available, we can draw the game in the matrix form or the normal form as follows :

The Payoffs are in the form of (ROSE, COLIN)

COLIN
ROSE		HIDE	PROWL
SEARCH	(0, 0)	(25, -20)
PATROL	(10, 0)	(10, 20)

Player 1 is Rose - police officer. Rose has two strategies in the game to choose from that are Patrolling or Searching for Colin .

Player 2 is Colin - the criminal. Colin has two strategies in the game which are as follows, Hide or prowl in the streets committing crime.

• When Rose patrols on her traffic duty, her payoff is 10.
• If Colin is prowling the streets when Rose is searching for Colin, then Rose will certainly catch him and obtain 25 units of utility.
• If Colin is caught by Rose then his payoff is -20 units. And Colin will certainly get caught when Rose is searching and Colin is prowling.
• If Colin is prowling while Rose is on patrol, Colin will not get caught and will have the payoff of 20 units.
• If Colin is hiding when Rose is searching for him, Colin will not get caught and Rose will have the payoff of 0 units.
• And if Colin keeps on hiding, his payoff is 0 units.

The best response strategy for Rose is catching Colin and keep on searching for him. But, thus option will be the worst response for Colin.

And for Colin, Prowling and not getting caught is the best response for him as he gets the highest utility under this strategy.

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