Definition:Coordination Game
Definition
The coordination game is an instance of a class of games whose mechanics are as follows:
There are two players: $\text A$lexis and $\text B$everley.
They wish to go out together to a musical concert to experience either the music of Mozart or Mahler.
Unaccountably, both $\text A$ and $\text B$ prefer Mozart. (It takes all sorts to make a world.)
The key points are:
- $\text A$lexis and $\text B$everley wish to coordinate their behaviour
but:
- they have common interests.
Payoff Table
The payoff table of the coordination game is as follows:
| $\text B$ | ||
| $\text A$ | $\begin {array} {r {{|}} c {{|}} } & \text {Mozart} & \text {Mahler} \\ \hline \text {Mozart} & 2, 2 & 0, 0 \\ \hline \text {Mahler} & 0, 0 & 1, 1 \\ \hline \end {array}$ |
Analysis
Solution
From the payoff table:
| $\text B$ | ||
| $\text A$ | $\begin {array} {r {{|}} c {{|}} } & \text {Mozart} & \text {Mahler} \\ \hline \text {Mozart} & 2, 2 & 0, 0 \\ \hline \text {Mahler} & 0, 0 & 1, 1 \\ \hline \end {array}$ |
There are two Nash equilibria:
- $\tuple {\text {Mozart}, \text {Mozart} }$
- $\tuple {\text {Mahler}, \text {Mahler} }$
Thus there are two steady states:
Just because both players have a mutual interest in reaching the preferred Nash equilibrium $\tuple {\text {Mozart}, \text {Mozart} }$, this does not rule out the steady state outcome $\tuple {\text {Mahler}, \text {Mahler} }$.
Sources
- 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $\text I$ Strategic Games: Chapter $2$ Nash Equilibrium: $2.3$: Examples: Example $16.1$