Coordination Game

A coordination game is one in which both players strictly prefer to coordinate on the same outcome rather than miscoordinate, but may disagree about which coordination outcome they prefer. The lecture covers two flavours: Battle of the Sexes (two pure NE, each player prefers a different one) and the simple coordination game where one equilibrium Pareto-dominates the other but the other is "safer" (risk-dominant).

When to use

Recognise a coordination game whenever the matrix has multiple pure-strategy Nash Equilibria on the diagonal and the off-diagonal cells are strictly worse for both players. The exam-relevant subtlety: when one diagonal cell carries a catastrophic downside for off-equilibrium play (e.g. payoff $-100$), the Pareto-dominant equilibrium may not be the risk-dominant one — comment on both. A mixed-strategy NE also exists; solve by making each player make the other indifferent.