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Game Theory

Game Theory. Game 7 Repeated Games. Opponent “ Personalities ”. Tit-for-Tat Tit-for-Two-Tat Grim Trigger Strategy Random Equilibrium (Cheater). Opponent “ Personalities ”. Tit-for-tat Cheat  Cheat Collude  Collude Tit-for-two-tat Cheat twice  Cheat Collude  Collude

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Game Theory

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  1. Game Theory Game 7 Repeated Games

  2. Opponent “Personalities” • Tit-for-Tat • Tit-for-Two-Tat • Grim Trigger Strategy • Random • Equilibrium (Cheater)

  3. Opponent “Personalities” • Tit-for-tat • Cheat  Cheat Collude  Collude • Tit-for-two-tat • Cheat twice  Cheat Collude  Collude • Grim Trigger Strategy • Collude  Collude Cheat  Cheat forever • Random • Flip a coin: heads I cheat, tails I collude • Equilibrium (Cheater) • Cheat, cheat, and cheat some more

  4. Highest / Lowest Payoffs Against Each Strategy Strategy Payoff maximum minimum Tit-for-tat20+0.410+0.4 Tit-for-two-tat25+0.210+1.2 Grim trigger20+0.410+0.4 Random20(avg) 10 (avg) Equilibrium100 Total 95+1.040+2.0

  5. Highest / Lowest Payoffs Against Each Strategy Strategy Payoff maximum tit-for-tat Tit-for-tat20+0.420+0.4 Tit-for-two-tat25+0.220+1.2 Grim trigger20+0.420+0.4 Random20(avg) 15 (avg) Equilibrium10 10 Total 95+1.085+2.0

  6. Results (both sections) Random Tit-for-tat

  7. Grading on a Curve • Score between 0 and 100 • How close are you to one of these two benchmarks? • Random: 61 (low)  0 • Tit-for-tat: 87 (high)  100 • (Note: always defect earns 64  12)

  8. The Highest Scores … • Cameron 119 • Jeff 113 • Jordan 102

  9. And … • Cal 10 • Osman 5

  10. And … Earlier Section: • One student-1

  11. The Flip Side • How my evil opponents did against the class • Listed Best to Worst • Tit-for-Tat (FNPC) • Grim Trigger Strategy ( NPC) • Equilibrium (Cheater) ( C) • Tit-for-Two-Tat (FN ) • Random ( )

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