A game is in equilibrium when no player can increase his or her payoff by changing strategy, so long as the other players do not change their strategies. Prove that the simple liability game is in equilibrium when the injurer and the victim take efficient care

Asmall town wants to build some new recreational facilities. the proposed facilities include a swimming pool, recreation center, basketball court and baseball field. the town council wants to provide the facilities which will be used by the most people, but they face budget and land limitations. the town has $400,000 and 14 acres of land. the pool requires locker facilities which would be in the recreation center, so if the swimming pool is built the recreation center must also be built. also, the council has only enough flat land to build the basketball court or the baseball field. the daily usage and cost of the facilities (in $1,000) are shown below. which facilities should they build? facilityusagecost ($1,000)landswimming pool4001002recreation center5002003basketball court3001504baseball field2001005