Solution to Coordination Game
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Solution to Coordination Game
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.
Proof
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:
- $\left({\text{Mozart}, \text{Mozart} }\right)$
- $\left({\text{Mahler}, \text{Mahler} }\right)$
Thus there are two steady states:
Just because both players have a mutual interest in reaching the preferred Nash equilibrium $\left({\text{Mozart}, \text{Mozart} }\right)$, this does not rule out the steady state outcome $\left({\text{Mahler}, \text{Mahler} }\right)$.
Sources
- 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $2.3$: Examples: Example $16.1$