Game Theory Analysis on Chicken
Link: https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/chicken.html
This article looks at the game of chicken using game theory analysis. Chicken is the situation where two cars are driving at one another with great enough speed such that braking is not a viable option, the only options are to either swerve off, or keep driving straight. If one person swerves and the other does not, then the one who swerves is the proverbial “chicken”. The article creates a symmetric payoff matrix for drivers A and B of 2,2 for swerve-swerve, 3,1 for drive straight-swerve, and 0,0 for drive straight-drive straight. Using mixed strategy analysis, we can predict probability p that A drives straight and q that B drives straight. It is apparent right away that p=q because of the symmetry of the payoff matrix and after balancing payoffs, we find that p = ½. This means that to optimize payoffs, both drivers should randomly mix between swerving half the time and not swerving half the time.
Upon first inspection this outcome seems to make sense as this game closely resembles the Dove-Hawk game gone over in class where dis-cooperation is always the best strategy. However, if we look at the resulting p and q from our analysis, this would suggest that 25% of the time both cars swerve, 50% of the time one car swerves becoming the “chicken” and the other car doesn’t. The remaining 25% of the time, neither car swerves and the cars hit each other and for the purpose of this discussion, we will say both drives die. Now it becomes apparent that there is some error in our analysis if statistically speaking, it would only take 4 games for both our players to be dead. To remedy this, we can propose a change to the payoff matrix where swerve-swerve becomes 1,1, drive straight-swerve becomes 10,0, and drive straight-drive straight becomes -100,-100 to reflect the severity of this outcome. Notice that the preference of choices is still the same, but the weights behind them are now different. Redoing our mixed strategy analysis, we find that p=q = .917. This means that 84.17% of the time both cars will swerve, 15.23% of the time one car will swerve and become “chicken”, and only 0.6% of the time, both cars will drive straight and die which is much more reasonable. This highlights the importance of making sure that one has an accurate payoff matrix before doing any analysis on it.