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:

$\tuple {\text {Bach}, \text {Bach} }$

$\tuple {\text {Stravinsky}, \text {Stravinsky} }$

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): $\text I$ Strategic Games: Chapter $2$ Nash Equilibrium: $2.3$: Examples: Example $15.3$