Solution to Bach or Stravinsky?

Solution to Bach or Stravinsky?

There are two players: $\text A$lexis and $\text B$everley.

They wish to go out together to a musical concert, but $\text A$ prefers Bach and $\text B$ prefers Stravinsky.

The key points are:

$\text A$lexis and $\text B$everley wish to coordinate their behaviour

but:

they have conflicting interests.

Proof

From the payoff table:

		$\text B$
$\text A$		$\begin{array} {r {{|}} c {{|}} } & \text{Bach} & \text{Stravinsky} \\ \hline \text{Bach} & 2, 1 & 0, 0 \\ \hline \text{Stravinsky} & 0, 0 & 1, 2 \\ \hline \end{array}$

There are two Nash equilibria:

$\left({\text{Bach}, \text{Bach} }\right)$

$\left({\text{Stravinsky}, \text{Stravinsky} }\right)$

Thus there are two steady states:

one in which both players always choose Bach

one in which both players always choose Stravinsky.

Either, but not both, experience their preferred music.

Sources

• 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $2.3$: Examples: Example $15.3$