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PD N-Person with Strategies

by Tan Yongzhi (Submitted: 11/14/2012)

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## WHAT IS IT?

This model aims to study the effects of cooperating and competing within a society
- Competitors gain more individually
- Cooperators help the society to gain more collectively

Based on the Prisoner’s Dilemma or Game Theory, the Prisoner's Dilemma is usually defined between two players and within Game theory which assumes that players act rationally. Realistic investigations of collective behaviour, however, require a multi-person model of the game that serves as a mathematical formulation of what is going on within a human society.

Various aspects of multi-person Prisoner's Dilemma have been investigated, but till today there is still no consensus about its real meaning.

The multi-person Prisoner's Dilemma considers a situation when each of N participants has a choice between two actions: cooperating with each other for the "common good" or defecting (following their selfish short-term interests). As a result of their choice, each participant receives a reward or punishment (payoff) that is dependent on its choice as well as everybody else's.

## HOW IT WORKS

Each patch will either cooperate (blue) or compete (red) at the start of the model

Each patch will receive a score based on its own choice and the choice its immediate (8) neighbours have chosen

In the next round, each patch will be assigned a strategy and behave accordingly based on the previous round

Payoff
- Cooperators get 1 point for every agent who chooses to cooperate within its surrounding multiplied by a factor of 0.8
- Competitors get the score of cooperators plus an additional 4 points.

Strategies
- Always Cooperate
- Always Compete
- Tit-for-Tat
- Unforgiving

Strategies are assigned to each agent based on their choice of action and the respective score it received from it. Agents who do well while cooperating will continue to cooperate, while agents who do poorly while cooperating will change their strategy, and agents who do fairly average while cooperating will employ a tit-for-tat strategy. Similarly, agents who do well while competing will continue to compete, while agents who do poorly while competing will change their strategy, and agents who do fairly average will employ the tit-for-tat strategy.

## HOW TO USE IT

Buttons
- Setup: setup the world to begin the simulation
- Go: have the patches select a strategy and act accordingly

Slider
- Initial Cooperation: determine the initial percentage of cooperators in the world

Plots
- Number of Agents: indicates the number of agents who cooperated or competed throughout the simulation
- Average Score per round: indicates the average score an agent would get from either cooperating or competing in a round
- Strategies Employed per round: indicates the number of agents using each strategy

## THINGS TO NOTICE

Notice the strategies used during the simulation and compare it to the end result. How has the use of each strategy changed over time.

Are the payoff curves the same for all agents? How do they differ?

How is the total payoff to all agents related to the number of cooperators?

Notice when do agents who compete score highest and when do they score similar to those who cooperate.

## THINGS TO TRY

Try sliding the initial-cooperation slider to configure the starting number of cooperators. How does it affect the score of the agents. How does it affect the strategies employed by agents?

## EXTENDING THE MODEL

Derive and use a proper formula instead of using logic to assign strategies to the agents.

Incorporate space into the model and allow patches to move about and interact with different patches. This allows patches to form coalitions and also the ability to choose to participate in a round of interaction or not. Doing so enables the user to increase the number of strategies available to choose from as well.

Extend the model so that each agent interacts with everyone else instead of simply interacting with its immediate neighbours. As the sample increases, how does this affect the result?

## RELATED MODELS

PD N-Person Iterated

PD Basic Evolutionary

## CREDITS AND REFERENCES

ccl.northwestern.edu

psychology.ucdavis.edu

http://www-cs-faculty.stanford.edu/~eroberts/courses/soco/projects/1998-99/game-theory/npd.html

Miklos N. Szilagyi. An Investigation of N-person Prisoners' Dilemmas. Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona, 85721. http://www.complex-systems.com/pdf/14-2-3.pdf

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