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A Probabilistic Analysis of Prisoner’s Dilemma with an Adaptive Population

A Probabilistic Analysis of Prisoner’s Dilemma with an Adaptive Population. Yao Chou, Craig Wilson Department of Electronic and Computer Engineering Brigham Young University. Organization. 1 Introduction. 2 The Theory. 3 E xperiment. 4 A nalysis And conclusion.

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A Probabilistic Analysis of Prisoner’s Dilemma with an Adaptive Population

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  1. A Probabilistic Analysis of Prisoner’s Dilemma with an Adaptive Population Yao Chou, Craig Wilson Department of Electronic and Computer Engineering Brigham Young University

  2. Organization 1 Introduction 2 The Theory 3 Experiment 4 Analysis And conclusion Prisoner dilemma story Definition Results 3 Case Studies Mathematic model Application Estimation processing Estimate the final distribution

  3. 1 Introduction • If A and B both betray the other, each of them serves 2 years in prison • If A betrays but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa) • If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge) Prisoner dilemma story Mathematic model

  4. 1 Introduction If both choose split the money will be evenly divided. If one chooses split and the other steal the one who choose steal gets all the money. However if both choose steal neither receives anything. Prisoner dilemma story Mathematic model

  5. 1 Introduction Goals: Create a formal mathematical model to analyze prisoner’s dilemma, with adaptable player strategies. Prisoner dilemma story Apply probabilistic analysis and estimation Mathematic model Determine whether a given distribution will converge

  6. 2 The Theory Definitions Estimation processing

  7. 2 The Theory Type A Definitions . Type B Estimation processing

  8. 2 The Theory The PDF Definitions Estimation processing

  9. 2 The Theory Definitions Estimation processing

  10. 3 Experiments ， Estimation code Simulation code

  11. 3 Experiments ， Estimation code Simulation code

  12. 3 Experiments ， We use the same original distribution µ=0.6 σ2=0.1 Gaussian distribution Case 1 100% A Case 2 100% B Case 3 A+B

  13. 4 Results and Conclusions ， Case 1 100% A Case 2 Case 3

  14. 4 Results and Conclusions ， Case 1 100% A Pr ≈ .999 Case 2 Case 3 Pr > 0

  15. 4 Results and Conclusions ， Case 1 Case 2 100% B Case 3

  16. 4 Results and Conclusions ， Case 1 Case 2 100% B Case 3

  17. 4 Results and Conclusions ， Case 1 Case 2 100% B Case 3

  18. 4 Results and Conclusions ， Case 1 Case 2 Case3 A 70%, B 30%

  19. 4 Results and Conclusions ， Case 1 Case 2 Case3 A 70%, B 30%

  20. 4 Results and Conclusions ， Case 1 Case 2 Case3 A 70%, B 30%

  21. 4 Results and Conclusions Successful building a mathematical model for prisoner’s dilemma Able calculate steady state expectations Conclusion More work needs to be done to calculate variance in the system. (This got really ugly) Found unexpected results with convergence.

  22. Thank you！

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