Simulation Repository -

This site contains Game Theoretic Simulations, simulations for the social sciences and simulations. The repository contains a number of basic simulations for studying social phenomenon and is being developed for pedagogic and teaching purposes. The repository currently contains simulations like Sugarscape, two-person games for illuminating social phenomenon, Axelrod's cultural dissemination model, Zhang and Challet's Minority Game model, Grim's evolution of communication and Prejudice Reduction model. The Simulation Repository is an ongoing project and new simulations will be added to the repository in the future. \n\n''Acknowledgement:'' The repository and the aforementioned simulations were created by [[Muhammad Aurangzeb Ahmad|http://www.cs.rit.edu/~maa2454/research]]\n

Here are a some basic well known simulations to start with.\n!Conway's Game of Life\nConway's Game of Life is actually a celleular automata. The simulation consists of a two-dimensional grid of cells. Cells interact with their eight adjacent neighbours at every iteration. A cell can be 'dead' or 'alive' at any given iteration. For the k^^th^^ iteration the behavior of the cells at k+1^^th^^ iteration is described by the following rules.\n# A live cell with fewer than two neighbours dies.\n# A live cell with more than three neighbours dies.\n# A dead cell with exactly three neighbours becomes alive.\n# A live cell with two or three neighbours lives.\nThe Game of Life is supposed to illustrate that even complex patterns can be obtained from seemingly simple rules.\n\n''Parameters:'' The simulation will open in a new window. The simlation is setup on a 125 x 110 grid and will run for a million iterations.\n[img[Game Of Life|GameOfLife.gif]]\nClick on the follwoing link to run the simulation: ''[[Run Simulation|GameOfLife.html]]''\n''Simulation created by:'' [[Muhammad Aurangzeb Ahmad]]\n\n!Sugarscape\nSugarscape was developed by Joshua M. Epstein and Robert L. Axtell at the Brookings Institute in the early 1990s. The aim of their research was to study "How do social structures and group behaviors arise from the interaction of individuals?" The results of their work are delineated in the book ''Growing Artificial Societies''. The simualtion below is the basic version of the sugarscape simulation. It simulates the behavior of agents who need a resource called \s\ssugar\s\s to survive, hence the name Sugarscape. Agents have vision, a metabolism and other genetic attributes. The movement of the agents is governed by simple rules. Whenever an agent moves, it burns sugar at an amount equal to its metabolic rate. Agents die if and when they burn up all their sugar.\n\nThe colored moving cells represent the two "ethnic" groups in the simulation, the yellow circles represent sugar, the darker the color the greater is the amount of sugar present in the area.\n[img[Sugarscape|Sugarscape.jpg]]\nClick on the follwoing link to run the simulation: ''[[Run Simulation|Sugarscape.html]]''\n''Link:'' [[Official|http://www.brook.edu/press/books/artifsoc.htm]]''[[ Growing Artificial Societies|http://www.brook.edu/press/books/artifsoc.htm]]''[[ page at Brookings|http://www.brook.edu/press/books/artifsoc.htm]]\n\n''Simulation created by:'' [[Muhammad Aurangzeb Ahmad]]

''[[Ankur Teredesai|http://www.cs.rit.edu/~amt/cms]]''\nAssistant Professor\nDepartment of Computer Science\nRochester, NY 14623\nRochester Institute of Technology\n

''Axelrod's Model of Cultural Dissemination''\nAxelrod's[1] model of dissemination of culture is based on the idea that local convergence will lead to global polarization. Each "site" in teh following simulation can interact with its four immediate neighbors. Associated with each "site" are five traits. The greater the commonalities that the sites have with one another in terms of traits the greater the likelihood that their traits will become the same. The main idea behind Axelrod's model is that over teh course of many iterations different "sites" will come together to form cultures. Surprisingly the whole world does not always converge into a single cultural unit but sometimes results in more than one units in the final stage.\n[img[Cultural Dissemination|cultural.jpg]]\nClick on the follwoing link to run the simulation: ''[[Run Simulation|BasicCulture.html]]''\n\n''Reference:'' R. Axelrod, J. Conflict Res. 41, 203 (1997), reprinted in R. Axelrod, The complexity of cooperation, Princeton University Press, Princeton, 1997\n''Simulation created by:'' [[Muhammad Aurangzeb Ahmad]]

[[About the Repository]]\n[[Contact]]

A randomized tournament for two person games specifically the Iterated Prisoner's Dilemma and Stag Hunt.\n!The Iterated Prisoner's Dilemma\nThe Prisoner's Dilemma can be illustrated by considering the following situation as follows:\nSuppose Alice and Bob are caught trying to rob a bank. The prosecutor gives then the following choices:\n*If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. \n*If your accomplice confesses while you remain silent, they will go free while you do the time.\n*If you both confess I get two convictions, but I'll see to it that you both get early parole. \n*If you both remain silent, I'll have to settle for token sentences on firearms possession charges. \nThe above situation can be summerized as follows:\n* If one confesses then he/she DEFECTED from his/her partner.\n* If one remained silent then he/she COOPERATED with his/her partner.\nIf Alice and Bob have to play this game again and again then the situation is called the Iterated Prisoner's Dilemma\n\nThe most commonly used //pay-off// matrix for this game is as follows:\n||''@@color(#236666):Cooperate@@''|''@@color(#236666):Defect@@''|\n|''Cooperate''|3,@@color(#236666):3@@|0,@@color(#236666):5@@|\n|''Defect''|5,@@color(#236666):0@@|1,@@color(#236666):1@@|\n!Stag Hunt\nStag Hunt is a game which describes a conflict between safety and social cooperation. The game is also called "assurance game", "coordination game", and "trust dilemma." The game can be conceptualilzed as follows: Consider a situation in which two individuals go out on a hunt. They come accross a stag and a hare, now each has to individually choose to hunt the stag or hunt the hare. They have to make the choice without knowing the choice of the other. If an individual hunts a stag, he must have the cooperation of his partner to be successful. An individual can get a hare by herself but there is the additional risk that the other individual might do the same thing and they will not be able to hunt anything at all. It should be noted that the hare is worth less than a stag.\nThe most commonly used //pay-off// matrix for this game is as follows:\n||''@@color(#236666):Cooperate@@''|''@@color(#236666):Defect@@''|\n|''Cooperate''|4,@@color(#236666):4@@|0,@@color(#236666):3@@|\n|''Defect''|3,@@color(#236666):0@@|3,@@color(#236666):3@@|\n!The Tournament\nEach strategy in the tornament is represented as a binary string which describes how to react to the opponent's last move. The first entry in the string represents the default first move, while the second entry represents what to do if the other person cooperates in the last move and the next entry represents what to do if the other person defects. If the size (memory) of the strategy is greater then it represents how to reach based on //k > 1// moves.\n\n''Parameters:'' Total strategies represents the number of strategies that are in the tournament. Minor Iterations are the number of times each strategy play aganist each other before reseting their initial moves. Major iterations represent the number of times the strategies play one another times the number of minor iterations. The opponent strategies area shows the strategies and their opponent strategies. The results give the rankings for the strategies.\n[img[The Tournament|ipd.jpg]]\nClick on the follwoing link to run the simulation: ''[[Run Simulation|2PersonGame.html]]\n''Simulation created by:'' [[Muhammad Aurangzeb Ahmad]]

[[Basic Simulations]]\n[[IPD Stag Hunt]]\n[[Cultural Dissemination]]\n[[Minority Game]]\n[[Prejudice Reduction]]\n[[About the Repository]]\n[[Contact]]\n\n[[Site Setup]]

''Description:''\nThe minority game was developed by Yi- Cheng Zhang and Damien Challet from the University of Fribourg. The game is inspired by the El Farol bar problem. The Minority Game can be described as follows:\n<<<\nConsider an odd number of players such that each has to choose one of two choices (sides) independently for k iterations. The players who end up on the minority side win.\n<<<\n[img[Minority Game|minGame.jpg]]\nClick on the follwoing link to run the simulation: ''[[Run Simulation|gametheory/index.html]]''\n\nThe game can be used to represent problems and situations where it is advantageous to be in the minority //e.g.,// if a group of people come to know about the price of stocks for the near future then they will be able to reap the most benefits if they are in the minority //i.e.,// not many people come to know about it,\n\n''Reference:'' D. Challet and Y.-C. Zhang, [[Emergence of Cooperation and Organization in an Evolutionary Game|http://xxx.lanl.gov/abs/adap-org/9708006]], Physica A 246, 407 (1997) \n''Simulation created by:'' [[Muhammad Aurangzeb Ahmad]]\n

Muhammad Aurangzeb Ahmad recently graduated with honors from the Computer Science department at the [[Rochester Institute of Technology|http://www.rit.edu/]] double minoring in Philosophy and Mathematics. I was also part of the Data Mining Research Group at the Center for Advancing the Study of Cyber Infrastructure.\n\n''Contact:'' maa2454 [at] cs [dot] rit [dot] edu

This is a spatialized model for prejudice reduction which provides support to the contact hypothesis for prejudice reduction. Each cell is the grid is an agent that can interact with its neighbors at any given time. The following models are based on Grim et al's model of Prejudice Reduction. Each cell in the grid represents an agent and at every iteration the agents interact with their neighbors. The sum of their scores is then added for //k// iterations and then for the next set of iterations if an agent has a neighbor which has a score higher than its score then it adopts the strategy of that neighbor, if there are more than one agents which have the same highest scores then the agent adopts the strategy of one of the neighbors with the highest scorers at random. Hence the grid converge to a a situation where certain mixture of strategies become stable. In the following simulations the two grids can be thought of as superimposed on one another. The grid on the left represents the strategies used by the agents, while the grid on the right represents the respective ethnicities of the agents.\n\n''Strategies:'' There are nine strategies which are randomly assigned to the agents. The first eight strategies can be represented as three-tuples where the first entry represents the first move when the simulation starts, the second represents the move when the other agent cooperates and the third represents the move when the other agent defects. The nineth strategy is prejudiced Tit-for-Tat in which the agent plays Tit-for-Tat when it is playing with its own ethnic group but always defects when it is playing with an agent of another ethnic group. The graphs represent the percentage of each strategy which is present in the simulation.\n\n''Social Identification:'' For the last two simulations, in addition to ethncities and strategies, the added element of social identification is added //i.e.,// an agent is given an extra point if it interacts with another agent of its own ethnic group.\n\n!Segregated Grid\nIn this simulation the agents are segregated. The simulation converges to a mixture of Tit-for-Tat and prejudiced Tit-for-Tat.\n[img[Segregated Grid|seg.jpg]]\n''[[Prejudice Reduction Simulation: Segregated Grid|Segregated.html]]''\n!Integrated Grid\nIn this simulation the agents are segregated. The simulation converges to Tit-for-Tat at the end.\n[img[Integrated Grid|int.jpg]]\n''[[Prejudice Reduction Simulation: Integrated Grid|Integrated.html]]''\n!Segregated Grid with Social Identification\n''[[Prejudice Reduction Simulation: Segregated Grid w/ Ident Point|SocialIdentSeg.html]]''\n!Integrated Grid with Social Identification\n''[[Prejudice Reduction Simulation: Integrated Grid w/ Ident Point|SocialIdentInt.html]]\n\n''Simulation created by:'' [[Muhammad Aurangzeb Ahmad]]

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Simulation Repository