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COMP3160 ARTIFICIAL INTELLIGENCE Assignment
创建日期：2024-04-18 14:36:02
标签： COMP3160
ARTIFICIAL INTELLIGENCE Assignment

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COMP3160 ARTIFICIAL INTELLIGENCE Assignment 

 (Weight: 20%) Evolutionary Algorithms for Adversarial Game Playing Draft Submission Due: 11:55pm, Oct 29, 2021 (Friday, Week 12) Final Submission Due: 11:55pm, Nov 05, 2021 (Friday, Week 13) The goal of this assignment is to appreciate the efficacy of Evolutionary Algorithms, specif- ically Genetic Algorithm (GA), in the context of game theory. You will be using the DEAP package for Genetic Algorithm in order to evolve strategies for repeatedly playing variants of The Tragedy of the Commons (TC). Basically, there is a group of farmers (herdsman) in a village, and there is a community grazing area (“Commons”). If the farmers limit the number of cows that each of them is allowed to graze in the Commons, everyone prospers. If a few farmers flout the convention, they benefit at some cost to others. But if too many farmers flout the convention, then everyone suffers due to over-grazing. This game is quite pertinent to the sustainability issue. It is interesting in this context to read the obituary, Eli- nor Ostrom: An uncommon woman for the commons, that Kenneth J Arrow and colleagues wrote for an unusual political scientist who received Nobel Prize in economics. The Tragedy of the Commons is originally described by Hardin1 as follows: As a rationale being, each herdsman seeks to maximize his gain. Explicitly or implic- itly, more or less consciously, he asks, “what is the utility to me of adding one more animal to my herd?” This utility has a negative and a positive component. 1. The positive component is a function of the increment of one animal. Since the herdsman receives all the proceeds from the sale of the additional animal, the positive utility is nearly +1. 2. The negative component is a function of the additional overgrazing created by one more animal. Since, however, the effects of overgrazing are shared by all [. . . ], the negative utility for any particular decision-making herdsman is only a fraction of 1. Adding together the component particular utilities, the rational herdsman concludes that the only sensible course for him to pursue is to add another animal to his herd. And another; and another... But this is the conclusion reached by each and every rational herdsman sharing a commons. Therein is the tragedy. Each man is locked into a system that compels him to increase his herd without limit – in a world that is limited. Ruin is the destination towards which all men rush, each pursuing his own best interest in a society that believes in the freedom of the commons. Freedom in a commons brings ruin to all. We will look at two very simplistic models of this imagined scenario. Both of them are two-player games. In the first model (TC1), we assume a small grazing common land that can comfortably support two cows altogether, and each cow brings 5 units of utility to its owner. If one more 1Hardin, G. “The Tragedy of the Commons.” Science 1968, 162, 1243–1248. 1 cow is allowed to graze, the cows are not adequately fed, and the benefit from each cow reduces by 1. If instead two more cows are allowed in, the feed is fully inadequate for every cow because of overgrazing, and they bring zero benefit each to their owners. It is assumed that there is a tacit understanding between the two farmers that they will cooperate, that is, will allow in only one cow each. The payoff matrix for this model is given as follows: Table 1: The Tragedy of the Commons: TC1 ROW C D COLUMN C (5, 5) (4, 8) D (8, 4) (0, 0) Payoffs to: (Column, Row) The second model (TC2) changes the narrative to some extent. The local council de- cides that the two farmers can take a lease of part of the “commons” for a nominal fee, and use that part exclusively for grazing their own cows. However there is a constraint: each can take an independent decision of whether to lease 1 3 of the commons, or 1 4 . Either way, part of the commons will be left un-leased, and they will have equal grazing right over that un-leased part. Here we assume that the total commons has an area of 24, and each unit area provides one unit of benefit. Again there is the tacit understanding that the two farmers will cooperate, that is each will take out a lease on 1 4 of the commons. However there is incentive to defect, as the payoff matrix shows below. For instance, if one farmer cooperates, and the other defects, the cooperator receives 24 4 + 24−( 24 4 + 24 3 ) 2 = 11 units of benefit, while the defector will receive 24 3 + 24−( 24 4 + 24 3 ) 2 = 13 units. Table 2: The Tragedy of the Commons: TC2 ROW C D COLUMN C (12, 12) (11, 13) D (13, 11) (12, 12) Payoffs to: (Column, Row) 2 Task Specification The main issue is the representation of a strategy for playing a game like TC1 or TC2 as a bit string. Two papers are provided in the Assignment folder that will help you with this. You are recommended to start with the paper, an easy read, by Adnan Haider. You might want to also read the paper by Golbeck, if you find the topic interesting. Although it is possible to represent players/strategies in very many different ways, for parity in marking, you are strongly advised to employ the following representation: Figure 1: Representation of two players. With d as the memory depth, m = 22d. Total length of a player/chromosome: 22d + 2d. 1. BACKGROUND KNOWLEDGE ASSESSMENT [5 marks] (a) Consider the Cryptocurrency Mining. You may want to read this New Yorker article about the environmental impact of Bitcoin mining. Which of the two models of the Tragedy of the Commons, TC1 and TC2, is closer in spirit to this situation? Answer this question in no more than 50 words. (b) Find all Dominant Strategy Equilibria, Nash Equilibria and Pareto Optimal Strategy Profiles for the game TC1. (c) Find all Dominant Strategy Equilibria, Nash Equilibria and Pareto Optimal Strategy Profiles for the game TC2. (d) Analyse the results you obtained in items 1b and 1c above. Describe any inter- esting difference not noted between them. Why did you find those differences interesting? Answer this question in no more than 50 words. (e) Axelrod’s tournaments of Iterated Prisoner’s Dilemma show that that co-operation among players can emerge in a world of selfish agents. What do you ex- pect would happen if different strategies were to play Iterated TC1 (henceforth (ITC1) instead? What would you expect in the case of Iterated TC2 (henceforth (ITC2)? Explain your answer in no more than 50 words. Give particular at- tention to any difference in what you woudl expect in these two cases. 3 2. IMPLEMENTATION IN PYTHON [10 marks] (a) Implement the function: payoff_to_player1(player1, player2, game): returns payoff Note: player2 is the adversary, and payoff is determined by latest moves obtained from respective appropriate memory locations and the payoff matrix for the relevant game (TC1 or TC2). Assume memory-depth of 2. (b) Implement the function: next_move(player1, player2, game, round): returns player1’s move Note: player1’s next move is based on both the players’ earlier moves and player1’s strategy (encoded in player1’s chromosome). The move to be returned can be C/D or 0/1 depending on your representation. Note that in early rounds some default moves are made. Assume memory-depth of 2. (c) Implement the function: process_move(player, move, memory_depth): returns success / failure Note: player’s relevant memory bits are updated based on its latest move move and its memory depth. (d) Implement the function: score(player1, player2, m_depth, n_rounds, game): returns score to player1 Note: player1 iteratively plays the game game against player2 for n rounds number of rounds, and its score is returned. (e) You will be using the DEAP package for genetic evolution of strategies. As- sume a memory depth of 2. i. Implement genetic evolution of strategies for playing ITC1. ii. Modify the code you wrote as part of Task 2(e)i above so as to genetically evolve strategies for playing ITC2. 4 3. ANALYSIS [5 marks] (a) What is the best ITC1-strategy that you generated in Task 2(e)i via GA? What parameters (fitness function, type of crossover, mutation rate, etc.) did you use, and why? (b) Describe in English the behaviour of that ITC1-strategy (that you identified in Task 3a above). Does it align with the prediction you outlined in Task 1e earlier? Explain in no more than 50 words. (c) What is the best ITC2-strategy that you generated in Task 2(e)ii via GA? What parameters (fitness function, type of crossover, mutation rate, etc.) did you use, and why? (d) Describe in English the behaviour of the ITC2-strategy (that you identified in Task 3c above). Does it align with the prediction you outlined in Task 1e ear- lier? Explain in no more than 50 words. (e) Take an appropriate sustainability issue, and outline in no more than 50 words the implications that your results have in that context. What to Submit, and When You will submit two files:

1. code.py

2. report.pdf.
Your code file should include all the Python codes you wrote for this assignment.
Your report file should include all the answers (including the Python codes copied-and-
pasted). It must be submitted in the pdf format. It must have as cover page the one that has
been supplied (as part of the document template), duly filled and signed. Also, if relevant,
note in the last section anything relevant that is worth noting.
You will submit the files in two stages. In the first stage you must submit two draft files
(that you will be able to update) by 11:55pm, Friday Week 12:
(a) of the program file code.py including at
least the implementation of functions specified in Tasks 2a and 2b.
(b) of your report file report.pdf with an-
swers to Tasks 1a-1e. You can modify these files while preparing your final ver-
sion. However, failure to submit the two draft files by the required date will attract
a penalty of 2 marks. 
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ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 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