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
- Hawk-Dove 7.0/10
- The Prisoner's Dilemma 7.0/10
- Stag Hunt 6.1/10
Source: Standard coordination game of the game-theory literature, named and analysed in Luce and Raiffa, 'Games and Decisions' (1957). Statement written for AxiomIQ.