A Probabilistic Analysis of Prisoners Dilemma with an Adaptive Population Yao Chou, Craig Wilson...

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！