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Example62_Prisoners_Dilemma.mp

+/* The Prisoner's Dilemma 
+Michael Collins
+August 10, 2020.
+https://en.wikipedia.org/wiki/Prisoner%27s_dilemma
+https://plato.stanford.edu/entries/prisoner-dilemma/#Symm2t2PDOrdiPayo
+
+In this case, the classic model is the output in the traces
+of the model with the payouts as documented in 
+"Game Theory and Strategy" by Philip D. Straffin
+Mathematical Association of America 1993
+isbn: 0-88385-637-9
+Chapter 12, page 73.
+
+Different in this MP model is how the payouts
+are computed.  Most models just assume the final
+amount of payouts for the matrix game. 
+
+Here the payout for Alice, and Bob respectively,
+is computed from 
+"Alice's view of the payoff for each possible event independently of Bob's view"
+
+This is represented by the columns in the tables below. 
+A simple arithmetic derivation from those columns is computed to have the 
+trace generation output each matrix element of the game as 
+a separate trace in the MP output. 
+
+Future work is to include other obvious matrices readily constructed 
+from this to be generated as part of the trace generation.
+
+This would represent something like a class of matrix games 
+to be constructed by the schema, one of which would be 
+the classic two person prisoners dilemma
+
+Notice that this code is almost exactly like
+MP native Example 23 -- number attributes. 
+That example is about a buyer purchasing different products
+from different stores.  
+
+A related version of the prisoners dilemma to shopping is
+documented at the Wikipedia article cited above. "The donation game."
+
+This model is only meant to be run at scope 1.  
+
+From Alice's viewpoint: (in this case the selfish view point). 
+the payoff for Alice when she confesses         = 1.
+the payoff for Alice when Bob does not confess  = 2. 
+in all other circumstances the payoff for Alice = 0.
+
+From Bob's viewpoint:   (in this case the selfish view point)
+the payoff for Bob when he confesses            = 1.
+the payoff for Bob when Alice does not confess  = 2.
+in all other circumstances the payoff for Bob   = 0.
+
+To map it to classic values to show negative payoffs -- that is a sort of normalizing. 
+The total payoff is computed from the assignments above and then subtracting 2. 
+
+*/
+
+
+/*—————————————————————————————
+ 	 		  Actors
+———————————————————————————————*/
+SCHEMA Prisoners_Dilemma
+
+ATTRIBUTES { number utility1, utility2, payout_alice, payout_bob ;};
+
+
+do_not_confess_alice: BUILD{ utility1:=  0 ; utility2:= 2 ;};
+confess_alice:        BUILD{ utility1:=  1 ; utility2:= 0 ;};
+do_not_confess_bob  : BUILD{ utility1:=  2 ; utility2:= 0 ;};
+confess_bob:          BUILD{ utility1:=  0 ; utility2:= 1 ;};
+
+
+ROOT Alice: ( do_not_confess_alice | confess_alice );
+
+ROOT Bob:   ( do_not_confess_bob   | confess_bob   );
+
+payout_alice:= SUM{ $act:( do_not_confess_alice | confess_alice | do_not_confess_bob | confess_bob ) APPLY $act.utility1  } - 2 ;
+payout_bob  := SUM{ $act:( do_not_confess_alice | confess_alice | do_not_confess_bob | confess_bob ) APPLY $act.utility2  } - 2 ;
+
+
+/*—————————————————————————————
+ 		        Interactions
+———————————————————————————————*/
+SAY( "Payout Alice = " payout_alice);
+SAY( "Payout Bob   = " payout_bob  );
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