Battle of the Sexes
A couple prefers being together but disagrees on the venue. Payoffs: both at Opera (2, 1), both at Football (1, 2), apart (0, 0). Besides the two pure equilibria, there is a mixed Nash equilibrium. With what probability does each player attend their own preferred venue in it? Express as a fraction.
Related problems & prerequisites
Worth solving first
- Weak-Link Effort Game 3.0/10
Source: Standard coordination game of the game-theory literature, named and analysed in Luce and Raiffa, 'Games and Decisions' (1957). Statement written for AxiomIQ.