// CSG model of medium access control 
// extends model of 
// Brenguier, R.: PRALINE: A tool for computing Nash equilibria in concurrent games. 
// In: Proc. CAV’13. LNCS, vol. 8044, pp. 890–895. Springer (2013)
// with probability of failure with one or both players transmit

csg 

player p1 mac1 endplayer
player p2 mac2 endplayer

const int emax; // energy bound
const double q1; // probability single user successfully transmits
const double q2; // probability two users successfully transmit

module channel // used to compute joint probability distribution for transmission failure

	c : bool init false; // is there a collision?

	[t1,w2] true -> q1 : (c'=false) + (1-q1) : (c'=true); // only user 1 transmits
	[w1,t2] true -> q1 : (c'=false) + (1-q1) : (c'=true); // only user 2 transmits
	[t1,t2] true -> q2 : (c'=false) + (1-q2) : (c'=true); // both users transmit
	
endmodule

module mac1 // user 1
	
	s1 : [0..1] init 0; // has player 1 sent?
	e1 : [0..emax] init emax; // energy level of player 1
	
	[w1] true -> (s1'=0); // wait
	[t1] e1>0 -> (s1'=c'?0:1) & (e1'=e1-1); // transmit
	
endmodule

// construct second user with renaming
module mac2 = mac1 [ s1=s2, e1=e2, w1=w2, t1=t2 ] endmodule

// reward structure for player 1
rewards "r1"
	s1=1 : 1;
endrewards

// reward structure for player 2
rewards "r2"
	s2=1 : 1;
endrewards