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Drivers Dilemma
This game has simplistic mechanics that anyone can learn and enjoy. It has deep strategic concepts that are perfectly suited for those who yearn for some intellectual challenge. The aspects of driver's dilemma make the game universally appealing and specifically for those who keen on gaming theory as well as those into strategic games.
In this game, there are two people, Mr. Blue and Mr. Red. These two are supposed to drive their cars at full speed straight ahead or to swerve at the last minute.
The following are possible results of the game.
Mr. Blue
Mr. Red
Goes Straight
Goes Straight
They Crash
Goes Straight
Swerves
Mr. Blue is happy he wins, Mr. Red is sad he loses
Swerves
Goes Straight
Mr. Blue is sad he loses, Mr. Red is happy he wins
Swerves
Swerves
They stare at each other shocked at what they've done
After knowing the general results, it is important to understand the game by reorganizing the possible results into a matrix.
See all 3 images
This is the payoff matrix. The rows represent the moves that Mr. Blue is most likely to make. The columns represent the...
Red is most likely to make. Each box represents the result from each combination of decisions. This matrix makes it easy to see the results of different combinations of moves by the two.
A quick example: If Mr. Blue swerves, then the result will be either of the top 2 boxes, depending on Mr. Red's move. On the other hand, if Mr. Blue goes straight, then most likely the result will be either of the bottom 2 boxes, also depending on Mr. Red's Move.
To make this easier to analyze, a replacement of illustrations with numbers is necessary.
In case they both swerve and stare at each other= 0 for both
In case they both go straight and crash = -5 for both
One swerving and one going straight = 1 for the winner (straight) and -1 for the loser (swerve)
0,0
-1, 1
1,-1
-5,-5
Simple Analysis:
The game is now organized into an easily readable payoff matrix.
Best Response:
The first analysis focuses on something called a best response. Here, essentially, taking blue as an example, Mr. Blue knows what Mr. Red will do. Then how does he react?
If Mr. Blue knows Mr. Red will swerve, the focus will be on the left column. Mr. Blue sees that if he swerves, he will…
references about the action profile.
Nash equilibrium is useful in analyzing the results of strategic interaction of the two decision makers. It gives a clue in predicting possible outcome when the two players make decisions at the same time. The underlying insight in the John Nash's concept is that one cannot predict the outcome of the choices of many decision makers if those decisions are analyzed in isolation. Instead, one must investigate each players the possible action while considering the other persons decision-making.
A Nash Equilibrium occurs when the players play a best response. In the above game, both players going straight is not a Nash Equilibrium. For this to happen one of the players would have to swerve. Nonetheless, both the players swerving is also not a Nash Equilibrium for this to happen, one of the players would have to go straight. A Nash Equilibrium occurs when one player swerves and one player goes straight. This is because none of the players is able to improve their outcome by changing their action as both the players are playing a best response.
The above game is not complex and the illustration outlines the basics of game theory. It is fun as well as lays a solid foundation for one to look at an example and technique of gaming.
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