// Futures market investor (McIver and Morgan 2007)
// gxn/dxp

//stpg
smg

// Player info
player investor [invest], [noinvest], [cashin], [done] endplayer
player env [bar], [nobar], [month] endplayer

// Scheduler use to synchronise system transitions
module sched

	m : [0..2];

	// At the start of the month, investor makes decision
	[noinvest] (m=0) -> (m'=1); 
	[invest] (m=0) -> (m'=1);
	// Then, decision is made whether to bar or not
	[bar] m=1 -> (m'=2);
	[nobar] m=1 -> (m'=2);
	// Then, market changes
	[month] m=2 -> (m'=0);
	// Once investor has cashed in shares nothing changes
	[cashin] m=0 -> (m'=0);
	[done] m=0 -> (m'=0);

endmodule

// Investor
module investor
	
	// State: 0 = no reservation, 1 = made reservation, 2 = finished
	i : [0..2];

	// Decide whether to do nothing or make reservation
	// (if currently not reserving or was barred last time)
	[noinvest] (i=0 | i=1 & b=1) -> (i'=0);
	[invest] (i=0 | i=1 & b=1) -> (i'=1);
	// Cash in shares (if not barred)
	[cashin] i=1 & b=0 -> (i'=2);
	// Finished
	[done] (i=2) -> true;

endmodule

// Bar on the investor
module barred
	
	// State: 0 = not barred, 1 = barred
	// (initially cannot bar)
	b : [0..1] init 1;

	// Bar or not bar (cannot if do so last month)
	[nobar] true -> (b'=0);
	[bar] b=0 -> (b'=1);

endmodule

// Value of the shares
const vmax;
const vinit;
module value
	
	v : [0..vmax] init vinit;

	[month] true -> p/10 : (v'=min(v+1,c,vmax)) + (1-p/10) : (v'=min(max(v-1,0),c));

	// Note that, because the shares and the cap are updated simultaneously,
	// v can exceed c temporarily (but by at most 1).
	// We leave this as-is for compatibility with the original model

endmodule

// Probability of shares going up/down
const int pmax = 10;
module probability
	
	// Probability is p/pmax and initially the probability is approx 1/2
	p : [0..pmax] init floor(pmax/2);

	[month] (v<5) -> 2/3 : (p'=min(p+1,pmax)) + 1/3 : (p'=max(p-1,0));
	[month] (v=5) -> 1/2 : (p'=min(p+1,pmax)) + 1/2 : (p'=max(p-1,0));
	[month] (v>5) -> 1/3 : (p'=min(p+1,pmax)) + 2/3 : (p'=max(p-1,0));

endmodule

// Cap on the value of the shares
const int cmax = vmax;
module cap
	
	c : [0..cmax] init cmax;

	[month] true -> 1/2 : (c'=max(c-1,0)) + 1/2 : (c'=c); // probability 1/2 the cap decreases

endmodule

// Labels
label "finished" = i=2;

// Reward: one-off collection of shares value at the end
rewards "profit"

	// Use state rewards:
	//i=1 & b=0 & m=0 : v;
	
	// Could also use transition rewards
	 [cashin] i=1 : v;
	
endrewards

rewards "penalties"

	[invest] true: 1;
	[noinvest] true: 1;

endrewards