Chicken (game)
When Feiglingsspiel (English Game Chicken ), play with the demise, Hazard or coward is it a problem from game theory. This game is also known under the name of brinkmanship in the literature and can be used as an expression of the hawk - dove game to be seen.
It's about the scenario of a test of courage: Two sports car driving at high speed towards each other. Who escapes, thus demonstrating his fear and has lost the game. Deviates from none, both players have indeed passed the test of courage, however, draw from it no personal benefit, because they lose their lives in the clash.
Game with the demise as a simple two-person game with two strategies
The game with the downfall is in game theory as a two-player game with two strategies ( dodge, continue ) models. The payoffs ( in units of utility ) might look like the following payoff matrix:
The greatest benefit of 6 has the player who continue to drive in cold blood, while his teammate gets scared and escapes. The Evasive has not passed the test of courage, but keep his life, representing a benefit of 2. If the two, so their utility 4 because they do not lose face each other and survive.
The game has three Nash equilibria. Two in pure strategies ( dodge / continue and continue / dodge ) and one in mixed strategies ( both players soft with a probability of 1/2 off). The Nash equilibrium in mixed strategies depends on the exact values in the payoff matrix. If the victory, for example, particularly high- rated ( Use 8 instead of 6 ), the Nash equilibrium is not with [( 1/2, 1 /2), (1/2, 1 /2) ], but for [( 1/3, 2 /3) (1/3, 2 /3) ].
Limitations of the model
If the game is played with the downfall in the real world, players have more than just two options ( strategies). So they do not just go down or evade before the decision, but they can avoid, for example, at different times. Furthermore, can cause a simultaneous Dodge in the same direction and to a collision. They also may have the ability to run before the actual test of courage actions that affect the behavior of the opponent, for example by trying to convince the enemy believe that they themselves will not dodge.
This could be done through a credible self- binding: If it is possible one of the players to change the payoffs so that for him to dodge in any case leads to a lower benefit than continue ( continue as a dominant strategy ), then the announcement that in any case continue on, credible. His opponent can be sure that his ( rational ) players will make his announcement true.
More concretely, one of the players could think this way: "Only if I can convince the other of them that my car, for example, exploded as soon as I steer left or right, my threat is credible and the other may be the best response (best response. ) choose my strategy, then what probably would be a Dodge in this case " another example would be: If one of the players before the ride empties a bottle of vodka, the sunglasses and then touches the steering wheel throwing out the window while driving, makes he the other, well it clear that he can no longer avoid. Stanley Kubrick indicated by the doomsday device such a possibility for the nuclear strategy of a state in his film Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb ( 1964 ) on. However, these doomsday device was too long kept secret and thus ineffective for this strategy.
If this possibility of credible self-commitment is explicitly incorporated into a balanced, multi-stage model, in which both players can influence the payouts accordingly before the actual race, but there are again two ( non-symmetric ) Nash equilibria:
This complication of the model therefore does not help to determine a unique solution of the game.
Irrational Games
An irrational game can bring advantages in Feiglingsspiel. An example of this is the above-mentioned self- Get drunk before driving, showing the enemy that they could not act rationally while driving. For irrational game can not predict how you will deal with the game opponents. This strategy can be pursued in the policy ( Madman theory ).