Coordination Games and the Stag Hunt

In the classic stag hunt, two hunters can each either cooperate to hunt a stag, which feeds both of them well but only works if both commit, or each individually hunt a hare, a smaller but guaranteed payoff that doesn't require the other person to show up. If both hunt stag, both do best. If one hunts stag and the other defects to hare, the stag-hunter gets nothing — the stag escapes without a full team. Both hunting hare is a safe, mediocre outcome that requires no trust in the other player at all.

The game has two stable ("Nash") equilibria: both hunt stag, or both hunt hare. Stag-stag is better for both, but hare-hare is safer, since it doesn't depend on trusting the other player's choice — this is what makes it a coordination game with a risk-dominant equilibrium that isn't the best one. Unlike a prisoner's dilemma, cooperation isn't individually tempting to betray for gain; the problem is purely one of trust and expectation, not incentive to cheat.

This pattern shows up directly in liquidity provision: a market where many participants quoting tight, large size benefits everyone (low costs, easy execution — the "stag"), but if a trader isn't confident others will also show up with size, showing up alone with a large quote is risky, so many retreat to smaller, safer quotes (the "hare") — even though collectively everyone would be better off coordinating on the bigger, riskier commitment.