a probabilistic analysis of prisoner’s dilemma with an adaptive population
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
A Probabilistic Analysis of Prisoner’s Dilemma with an Adaptive Population
Yao Chou, Craig Wilson Department of Electronic and Computer Engineering Brigham Young University
Organization1
Introduction 2
The Theory3
Experiment4
AnalysisAnd
conclusionPrisoner dilemma story
Mathematic model
Definition
Estimation processing
3 Case Studies
Estimate the final distribution
Application
Results
1 Introduction
Prisoner dilemma story
Mathematic model
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)
1 Introduction
Prisoner dilemma story
Mathematic model
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.
1 Introduction
Prisoner dilemma story
Mathematic model
Goals:
Create a formal mathematical model to analyze prisoner’s dilemma, with adaptable player strategies.
Apply probabilistic analysis and estimation
Determine whether a given distribution will converge
2 The Theory
Definitions
Estimation processing
2 The Theory
Definitions
Estimation processing
.
Type A
Type B
2 The Theory
Definitions
Estimation processing
The PDF
2 The Theory
Definitions
Estimation processing
3 Experiments
Estimation code
，
Simulation code
3 Experiments
Estimation code
，
Simulation code
3 Experiments
Case 1100% A
Case 2100% B
Case 3 A+B
，
We use the same original distribution µ=0.6 σ2=0.1 Gaussian distribution
4 Results and Conclusions
Case 2
Case 3
，
Case 1 100% A
4 Results and Conclusions
Case 2
Case 3
，
Case 1 100% A
Pr ≈ .999
Pr > 0
4 Results and Conclusions
Case 3
，
Case 1
Case 2 100% B
4 Results and Conclusions
Case 1
Case 3
，
Case 2 100% B
4 Results and Conclusions
Case 1
Case 3
，
Case 2 100% B
4 Results and Conclusions
Case 1
Case 2
，
Case3A 70%,B 30%
4 Results and Conclusions
Case 1
Case 2
，
Case3A 70%,B 30%
4 Results and Conclusions
Case 1
，
Case 2
Case3A 70%,B 30%
4 Results and Conclusions
Successful building a mathematical model for prisoner’s dilemma
Able calculate steady state expectations
More work needs to be done to calculate variance in the system. (This got really ugly)
Found unexpected results with convergence.
Conclusion
Thank you！