Weak-Link Effort Game
Two partners each simultaneously choose an integer effort level from 1 to 8. If partner i chooses a_i, then partner i's payoff is 10·min(a_1, a_2) − a_i². How many pure-strategy Nash equilibria (ordered pairs (a_1, a_2)) does this game have?
Related problems
Source: Weak-link (minimum-effort) coordination game, as in Van Huyck, Battalio and Beil (1990); payoff function original to AxiomIQ.