// zero-sum properties // minimum expected time user 1 can guarantee to eventually send a packet <<usr1>>R{"time"}min=?[F s1=3] // minimum expected time users 1 and 2 can guarantee to eventually send their packets <<usr1,usr2>>R{"time"}min=?[F s1=3 & s2=3] // minimum expected time users 1, 2 and 3 can guarantee to eventually send their packets <<usr1,usr2,usr3>>R{"time"}min=?[F s1=3 & s2=3 & s3=3] // maximum probability user 1 can guarantee to send a packet <<usr1>>Pmax=?[F s1=3] // maximum probability users 1 and 2 can guarantee to send their packets <<usr1,usr2>>Pmax=?[F (s1=3 & s2=3)] // maximum probability users 1, 2 and 3 can guarantee to send their packets <<usr1,usr2,usr3>>Pmax=?[F (s1=3 & s2=3 & s3=3)] // maximum probability user 1 can guarantee to send a packet within a deadline <<usr1>>Pmax=?[F (s1=3 & t<=D)] // maximum probability users 1 and 2 can guarantee to send their packets within a deadline <<usr1,usr2>>Pmax=?[F (s1=3 & s2=3 & t<=D)] // maximum probability users 1, 2 and 3 can guarantee to send their packets within a deadline <<usr1,usr2,usr3>>Pmax=?[F (s1=3 & s2=3 & s3=3 & t<=D)] // nonzero-sum properties // expected time each user eventually sends a packet // players act individually <<usr1:usr2:usr3:usr4>>min=? (R{"time"}[F s1=3] + R{"time"}[F s2=3] + R{"time"}[F s3=3] + R{"time"}[F s4=3]) // expected time each user eventually sends a packet // players 3 and 4 form a coaltion <<usr1:usr2:usr3,usr4>>min=? (R{"time"}[F s1=3] + R{"time"}[F s2=3] + R{"time"}[F s3=3 & s4=3]) // expected time each user eventually sends a packet // players 1 and 2 and 3 and 4 form a coaltions <<usr1,usr2:usr3,usr4>>min=? (R{"time"}[F s1=3 & s2=3] + R{"time"}[F s3=3 & s4=3]) /// probability each user eventually sents a packet <<usr1:usr2:usr3:usr4>>max=? (P[F s1=3] + P[F s2=3] + P[F s3=3] + P[F s4=3]) // probability each user eventually sents a packet within a deadline <<usr1:usr2:usr3:usr4>>max=? (P[F (s1=3 & t<=D)] + P[F (s2=3 & t<=D)] + P[F (s3=3 & t<=D)] + P[F (s4=3 & t<=D)])