Supporting Information: Analytical derivations for the multi-player doping game
نویسندگان
چکیده
3 Nash-equilibria in the three-player case 5 3.1 Pure strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.1 Case 1: everyone cheats (DDD) . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Case 2: two players cheat, one player plays fair (DDF) . . . . . . . . . . 6 3.1.3 Case 3: one player cheats, two play fair (DFF) . . . . . . . . . . . . . . . 7 3.1.4 Case 4: everyone plays fair (FFF) . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Mixed strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2.1 Case 5: everyone plays a mixed strategy (mmm) . . . . . . . . . . . . . . 8 3.2.2 Case 6: one player cheats with certainty, others play a mixed strategy (Dmm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2.3 Case 7: one player plays fair with certainty, others play a mixed strategy (Fmm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.4 Case 8: two players cheat with certainty, one plays a mixed strategy (DDm) 10 3.2.5 Case 9: two players play fair with certainty, one plays a mixed strategy (FFm) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2.6 Case 10: one player plays fair, one player cheats, the third is mixed (DFm) 10 3.3 Summary of the three-player case . . . . . . . . . . . . . . . . . . . . . . . . . . 11
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