Game theory – Notes from competetive strategy

I have just completed the first week of the course Competetive Strategy by Tobias Kretschmer on Coursera. If you are interested in game theory and competitive strategy, then i highly recommend the course (the first test deadline is the 22th of July). The course is free and the video lectures are of excellent quality and easy to follow. It isn’t necessary to read anything, since the video lectures cover all the theory needed to take the tests.

When I take these classes, I like to take notes. In another online class I found some note on a blog, which was very useful. Therefore I would like to share my notes too for other fellow Competitive Strategy users.

Week 1

Simultaneous games

Games consist of the following parts:

• Players
• Actions
• Rules
• Payoffs

In game theory a strategy is defined as: A player‘s plan of actions in a game, given any possible circumstances.

A dominant strategy is one that always does better than any other strategy. This has the outcome, that if a dominant strategy exist, then a rational player will always follow this strategy. If a dominant strategy exist for your rival, you know what your rival will do.

A dominated strategy is one that never does better than another strategy. With the assumption of rationality, you can rely on your rival never following a dominated strategy.

In the elimination process you remove all the dominated strategies, since they will not be followed by a rational player.

A Nash equilibrium is a combination of strategies where no player would want to deviate from their strategy.

A Nash equilibrium is not the same as a dominant strategy. A dominant strategy looks as one company in isolation, while a Nash equilibrium exist because of combined strategies.

A Nash equilibrium can contain dominant strategies, but not dominated strategies.

A Nash equilibrium does not have to contain dominant strategies.

A game does not have to contain a Nash equilibrium and can contain mere than one.

The prisoners dilemma is a concept describing the situation where all players would be better of, but where joint payoffs are not optimized, since players act in their own self interest.

Sequential games

In sequential games we can not use a matrix, but we can use a game tree instead.

Sequential games have a time element. The first decision starts the game.

Backward induction is used to solve a sequential game. This means elimination of actions at the final node and from there work forwards.

It can be important to make commitments, so rival firms believe your threats. Many threads are not credible.

Differences in simultaneous and sequential games

Week 2

Reasons for cooperation

Competetion is not always in the companies best interest. The prisoners dilemma is an example of this.

There are two mechanisms to achieve cooperation between profit maximizing firms:

1. Repeated games
2. Commitment

Repeated games

The game does not happen only once, but is repeated. One player can threaten another player (If you does not behave cooperatively in this game, we will retaliate in the next game).

These kind of threats can enforce cooperation in some situations (Depends on the type of repeated games).

There are two types of repeated games:

1. Finite repetition
2. Infinite repetition

Finite repetition

Infinite repetition

Commitment

Cooperative commitment can be done in different ways:

• Reputation building
• Self-binding commitment
• Most favored customer clause

Week 3

Complements