Coward game
The coward game ( English chicken game ), game with the downfall , hazard or fear-hare game is a problem from game theory . This game is also known as brinkmanship in literature and can be seen as a variant of the falcon-dove game .
It's about the scenario of a test of courage : two sports cars drive towards each other at high speed. If you evade, you prove your fear and have lost the game. If neither player evades, both players have passed the test of courage, but do not derive any personal benefit from it because they lose their lives in the collision.
Play with doom as a simple two-player game with two strategies
The game with doom is modeled in game theory as a two-person game with two strategies each (evade, drive on). The payouts (in utility units) could look like the following bimatrix :
| Player 2 | |||
|---|---|---|---|
| Evade | Continue driving | ||
| Player 1 | Evade | 4/4 | 2/6 |
| Continue driving | 6/2 | 0/0 | |
The player who drives on in cold blood while the other player gets scared and evades has the greatest benefit of 6. The evasive did not pass the test of courage, but kept his life, which corresponds to a utility of 2. If both avoid, their benefit is 4, since they do not lose face in front of each other and survive.
The game has three Nash equilibria . Two in pure strategies (evade / continue and continue / evade) and one in mixed strategies (both players evade with a probability of 1/2). The Nash equilibrium in mixed strategies depends on the exact values in the payoff matrix. If the victory z. B. valued particularly high (use of 8 instead of 6), the Nash equilibrium is not at [(1/2; 1/2), (1/2; 1/2)], but at [(1 / 3; 2/3), (1/3; 2/3)].
Limits of the model
When the game of doom is played in reality, players have more than two options (strategies). So you are not just faced with the decision to continue driving or to evade, but you can z. B. evade at different times. Furthermore, a simultaneous evasion in the same direction can also lead to a collision. In addition, before the actual test of courage, they may have the opportunity to take actions that influence the behavior of the opponent, for example by trying to convince the opponent that they themselves will not evade under any circumstances.
This could be done through a credible self-commitment : If one of the players succeeds in changing the payouts in such a way that evasion leads to a lower benefit for him in any case than continuing (continuing as the dominant strategy), then his announcement is in any case continue driving, credible. His opponent can be sure that his (rational) teammate will make his announcement come true.
A little more specifically, one of the players could consider: “Only if I can convince the other that my car is, B. explodes as soon as I steer left or right, my threat is credible and the other can choose the best response to my strategy, which in this case would probably be an evasion. ”Another example would be: If one If the player throws the steering wheel out of the window while driving, he makes it clear to the other that he can no longer evade. Stanley Kubrick indicated by the doomsday device such a possibility for the nuclear strategy of a State in his film Dr. Strange or: How I Learned to Love the Bomb (from 1964) on. However, this world destruction machine was kept secret for too long and is therefore ineffective for this strategy.
If this possibility of credible self-commitment is explicitly built into a symmetrical, multi-level model, in which both players can influence the payouts accordingly before the actual race, there are again two (non-symmetrical) Nash equilibria:
- Player 1 binds himself credibly, does not evade, player 2 evades;
- Player 2 binds himself credibly, does not evade, player 1 evades.
So this complication of the model does not help to determine a clear solution to the game.
Irrational game
An irrational game can bring advantages in the game of cowards. For example, a player could get drunk before driving to show the opponent that they cannot act sensibly while driving. In irrational play, the opponent cannot predict how one will act. This strategy can also be used in politics ( Madman theory ).
literature
- Theodor W. May: Individual decision-making in sequential conflict games . Lang-Verlag, Frankfurt am Main 1983. ISBN 3-8204-5135-8
Individual evidence
- Jump up ↑ pigeons and falcons. (PDF; 123 kB) p. 4 , accessed on July 1, 2010 .
- ^ William Poundstone, Prisoner's Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb, Anchor / Random House, 1992, p. 212, "The Madman Theory"