const int k1; const int k2; // both users maximise the expected reward before their battery becomes empty <<user1:user2>>{NE,SW}max=? (R{"r1"}[F e1=0] + R{"r2"}[F e2=0]) <<user1:user2>>{NE,FR}max=? (R{"r1"}[F e1=0] + R{"r2"}[F e2=0]) <<user1:user2>>{CE,SW}max=? (R{"r1"}[F e1=0] + R{"r2"}[F e2=0]) <<user1:user2>>{CE,FR}max=? (R{"r1"}[F e1=0] + R{"r2"}[F e2=0]) // both users maximise the expected reward for the first k steps <<user1:user2>>max=? (R{"r1"}[C<=k1] + R{"r2"}[C<=k2]) // user 1 maximises the expected reward before their battery becomes empty // while user 2 maximises the expected reward for the first k steps <<user1:user2>>max=? (R{"r1"}[F e1=0] + R{"r2"}[C<=k2]) // both users maximise the expected reward at the kth step <<user1:user2>>max=? (R{"r1"}[I=k1] + R{"r2"}[I=k2]) // both players maximise the probability their battery becomes empty // should be 1+1=2 <<user1:user2>>max=? (P[F e1=0] + P[F e2=0])