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:

one in which both players always choose Mozart
one in which both players always choose Mahler.


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