Hi Everyone,
I will continue my game theory series with the chicken game. Chicken game is one of three famous games discussed in game theory. The other two games are battle of the sexes and prisoner’s dilemma. I have a post on prisoner’s dilemma that can be accessed in a link at the end of this post. The next blog in this series will be battle of the sexes.
Chicken game is a very competitive game. In order to win requires at least one player to back down. The worst scenario occurs when neither player backs down. The chicken game is often described in the context of two drivers driving directly at each other. The driver that swerves to avoid crashing, loses. If neither driver swerves, the cars will crash. This could seriously injure or kill both drivers. The crash is the worst of the four possible outcomes of the game. The other three possible outcomes are:
The chicken game can be analysed using the normal form game (normal form game is explained in the introduction to game theory post, the link to this post can be found at the end of this post). The normal game is presented in the table below.
Note: In the matrix above, the first number is for the row player (Driver 1) and the second number is for the column player (Driver 2)
Both drivers not swerving is the worst outcome. This has been shown in the game as a payoff of -100 for both drivers. Both drivers swerving is not a great outcome for either driver but nobody gets injured and neither driver loses. This has been shown in the game as a payoff of 0 for both drivers. One driver swerving while the other does not, results in victory for the driver not swerving and some slight embarrassment for the driver that did. This has been shown in the game as a payoff of 20 to the winning driver (driver that did not swerve) and -5 for the losing driver (driver that swerved).
The chicken game does not have a dominant strategy for either player (dominant strategy is also explained in the introduction to game theory post). Therefore, different outcomes will be reached each time the game is played. All four outcomes are possible for the chicken game. This is what is called a mixed equilibrium in game theory. The payoffs of the game can be used to determine the probability of each of the four possible outcomes. I will cover mixed equilibrium in a lot more detail in another post.
There are several strategies that can be applied to enhance a driver’s chances of winning a chicken game. The most effective strategies involve convincing the other driver that you are never going to swerve. This can be achieved by obtaining a reputation for not swerving. If the other driver knows that you have not swerved in previous chicken games they are more likely to swerve in fear of the head-on collision. Making a convincing commitment on the spot could pressure the other driver into swerving. On way to do that is to remove the steering wheel from the car. The other driver will know swerving is no longer an option and therefore must swerve to avoid the head-on collision.
The hypothetical example of the car version of chicken game is quite extreme. This is necessary to get the basic concept across. In reality, chicken game is quite common. Workers strikes are a very typically application of the chicken game.
Workers might be unhappy because of unsatisfactory working conditions, lack of pay increases or even pay cuts. They are most likely to collectively negotiate with management. The workers must decide if they want to accept what management is offering. Management must decide if they want to meet the demands of the workers. These decisions can be analysed using the normal form game as shown below.
The matrix shows that if an agreement is reached (don’t demand, accept), the workers can benefit a little and there is a small cost to the company of meeting these demands. The matrix shows if workers demand more than what management offers and management agree (demand, accept), the workers benefit more and there is a larger cost to the company. The matrix shows if management do not accept any of the workers’ demands and the workers do not pursue any further (don’t demand, don’t accept), workers do not benefit and there are no extra costs to the company. The matrix shows if management do not agree to the workers terms and the workers wish to pursue their demands further by striking (demand, don’t accept).
Let’s assume an agreement has not been reached between workers and management of the company. Therefore, the workers rally together and refuse to work. While they are not working, they are not getting paid. While they are not working, the company that employs them is not earning revenue.
While the workers are on strike both the workers and company are losing out. This is like the case of not swerving. The longer the strike progresses, the larger the cost to both parties. It can be expected that eventually one party will concede or an agreement of some sorts will be made. Let’s continue the chicken game after the strike has commenced. These decisions can be analysed using the normal form game as shown below.
The new matrix includes the costs of the strike incurred, so far, to both parties. As with the previous matrix there are four possible outcomes. The four outcomes are as followers:
In this scenario, I have reduced the company’s cost of continuing the strike. It is fairly common that companies are able to find alternative sources of revenue, or other employees that are not part of a workers union, or some of the striking workers come to an agreement independent of the remaining striking workers. Striking workers are more likely to find that financial pressure increases as the strike progresses. The cost of them striking increases as bills and other financial obligations cannot be met. In many countries, strikes do not have a particularly high success rate. Companies and government are generally more powerful and able to weather strikes better than the workers Source.
Chicken games are quite often not just one-off events. Obtaining a track record in playing the chicken game can be used to influence future games. Let’s use our example of the workers strike. If the workers can outlast the company or government, they will be better positioned for future strike action. If worker strike action fails, management are less likely to take future strikes seriously. Absorbing a large cost in order to win one game of chicken could lead to less costly victories in the future.
Chicken game is one of the more important games to understand in game theory. A wrong approach to a chicken game could be very costly in both the short-run and long-run. It is important to be aware of your strength and endurance as well as the strength and endurance of the other players. A long drawn out game of chicken hurts all involved. This is especially true for the loser of the game. However, in the long-run, if the game of chicken is expected to be repeated, a long drawn out game that results in a win, even though very costly, could be worthwhile.
I hope you enjoyed this post. I will be covering the game ‘battle of the sexes’ in another post. I also will be looking at the real life application of game theory. This will also include investigating how game theory can be applied to the Steemit bots.
For more information on game theory, you can access my introduction post using the link below:
You can also access my post on prisoner’s dilemma using the link below:
