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Game Theory Presentation

Transcript: Topic Understanding how Game Theory Solved a Religious Mystery Talmud : Division of Estate The Story Person X has an accidental death There are three creditors whom he owes debt Person A's claim = 100 Person B's claim = 200 Person C's claim = 300 But Person X did not leave behind sufficient estate to pay all the creditors What is the solution? The Story Behind 100 200 300 Division of Estate Division of Estate 33 1/3 33 1/3 33 1/3 50 75 75 50 75 150 100 75 75 Equal Division 25 Estate = 100 Estate = 300 Proportionate Division Estate= 200 Logic ? The Mystery 1. Israeli mathematicians and professors Robert Aumann and Michael Maschler finally cracked the code. (1980) 2. They justified their answer by examining other Talmudic texts . 3. They also explained that equal division of the contested sum was then a social custom. It seems strange to us, but it was natural in their culture. 4. The conflicted/ contested portion between the players is always equally divided. Equal Division of Contested Sum The division of the estate among the three creditors is such that any two of them divide the sum they together receive, according to the principle of equal division of the contested sum. An Example Claim by A : Half of the pizza = 1/2 Claim by B : Whole pizza = 1 How should the pizza be divided? Understanding through an Example According to the principle of Equal Division of Contested Sum, Contested Sum = 1/2 Half of Contested Sum = 1/4 This half should be provided to both A and B! Remaining Sum = 1/2 This should be provided to the individual with the higher claim! Equal Division of Contested Sum Claim A = 1/2 Received = 1/4 Claim B = 1 Received = 3/4 1/4 + 3/4 = 1 The Answer 1.Order the creditors from lowest to highest claims. 2.Divide the estate equally among all parties until the lowest creditor receives one half of the claim. 3.Divide the estate equally among all parties except the lowest creditor until the next lowest creditor receives one half of the claim. 4.Proceed until each creditor has reached one-half of the original claim. 5.Now, work in reverse. Start giving the highest-claim money from the estate until the loss, the difference between the claim and the award, equals the loss for the next highest creditor. 6.Then divide the estate equally among the highest creditors until the loss of the highest creditors equals the loss of the next highest. 7.Continue until all money has been awarded Seven Step Algorithm The Mystery Resolved

Game Theory Presentation

Transcript: Sponsored by: Roaring Dino Co. By: Jonathan The Use of Game Theory in Elections Summary Game theory can be applied in many fields, including politics. Game theory can help a presidential candidate decide which state to visit, and calculate his chances of winning. When applied in swing states, where much of the decisions lie, an understanding of game theory can be critical. You can determine dominant strategies and equilibriums to decide which state to campaign to. Summary Application of Game Theory Pt 1 Game Theory in Campaigns Pt 1 Example 1: In this scenario, we will use candidates Biden and Trump. They can campaign in swing states Arizona, or Florida. They can only go for one state. If we give probabilities for the states, it can be easily determined which result is better. Biden has a 30% chance in Florida and 70% chance in Arizona and Trump has the opposite. Visiting a state increases your chances by 10%. If Biden visits Arizona and Trump visits Florida. Biden has a 20% chance in Florida and 80% chance in Arizona, multiplying to a 16% chance of victory. Example 1 Example 1 However, if Biden visits Florida and Trump visits Arizona, Biden now has a 40% chance in Florida and 60% chance in Arizona, multiplying up to a 24% chance of winning the election. Note that the same applies to Trump, the other way around Dominant Strategies and Nash Equilibrium Dominant Strategies and Nash Equilibrium Based on previous results, it shows that it would be better for Biden to campaign in Florida. However, this is also the case for Trump. Both going to Florida is the Nash Equilibrium. Application of Game Theory Pt 1 Example 2: In this scenario, we will add another swing state, Georgia. Consider if they had 50-50-50 odds in each state. What would be the best choice? If Biden has 80-60-20 odds in Arizona, Georgia, and Florida, what would be the best? Game Theory in Campaigns Pt 2 Mixed Strategies Mixed Strategies If they both have 50-50-50 odds in each state, then there obviously is no dominant strategy. So they have to go with mixed strategies. If they go to the same state, Biden will then have a 50% x 50% x 50% = 12.5%. However, if they go to different states, he will have a 50% x 60% x 40% = 12% chance to win. If they pick randomly. Biden will then have a 33% x 12.5% + 67% x 12% = 12.167% Widely Separated Odds Widely Separated Odds This is even still true if we take into account Trump's possible choices. Going to Florida is still the best option for Biden. In the case of the second set of odds, with 80-50-20 odds, it would be best for Biden to go to Florida, giving him 80% x 50% x 30% = 12% odds. If Biden campaigns in Georgia, it would give him 80% x 60% x 20%, it would give him 9.6% odds. If Biden goes to Arizona, then he would have 90% x 50% x 20% = 9% chance to win. Florida Arizona Georgia 8% 7.2% 4.5% Arizona 8% 4.8% Georgia 8.4% Florida 10.5% 9.6% 8% Conclusion This is a major oversimplification, but it somewhat shows that game theory can be used to determine different odds when running for president. This does not take into account how certain states have more electoral college votes, nor the other 47 states. Real-world scenarios are just far too complicated to be expressed in a matrix. Conclusion Works Cited Bibliography Article: Ellenberg, Jordan. “Bush and Kerry Do Swing-State Math.” Slate Magazine, Slate, 25 Oct. 2004, Calculator:

Game Theory Presentation

Transcript: Free rider Problem Solution Game theory Investigating how the interaction of participants influences their payoffs Methods Using dynamic and complete information game model impossible for all participants to get information about what others do or obtain information about the P2P network Algebraic Illustration Assumption: 1. Two categories of players: Free riders & Altruist (Selfish and Selfless) 2. Altruist has extra gains through uploading while free rider does not. 3. Two different strategies for each player: Upload & Not Upload 4. The payoff is the net gain of cost 5. Non-cooperative Variables: 1. Quantity of resources: d for downloading & u for uploading 2. Profit function: Pd for downloading & Pu for uploading 3. Cost function: Cu for uploading GAME MATRIX Simplify to 2 person : Altruist and Free rider Simplify to one time payoff of player -- Pu: upload profit Cu : upload cost Pd download profit Can be in terms of reputation , downloading speed etc. TIT FOR TAT A player is first cooperate, then subsequently replicate an opponent's previous action e supervisory probability MIXED NASH EQUILIBRIUM Consider 2 person only: Mary and Sally. Both are White collar Background Origin First used in economic theory of public goods Similar concepts have been applied in to other contexts, including : 1. Collective bargaining, 2. Antitrust law, 3. Psychology, and 4. Political science, etc Thank You :) Wage problem GAME MATRIX The Kyoto Protocol ( UNFCCC ) Nash equilibrium Non – Cooperative Game!! Free riding can be found in various situations. Our presentation has focused on the three areas: - Peer to peer network - Environmental protection policy among countries - General paid jobs Thanks to inspiration of game theory, we are able to observe the struggling in a more mathematical way, in which we found that the COST of not participating, not working or not uploading contributes much to whether free-riding occurs. 3. Altruist vs. Free rider grant some peers with supervising privilege can identify whether other are free-riding or not Change to cooperative game What is mean by cooperative / selfish is not definite here payoff of player – supervision cost (h) cooperative cost (g) found selfish profit(w) assumed cooperative profit(w) w>g; w>h Communism Definition Situation Improvement (How to avoid having free riders?) Assume total cost of abating carbon emission in Sweden and Germany is X without the trade After the trade : X’ = X – P – P’ By defining a reasonable C , reduction of carbon emission is encouraged Nash Equilibrium To improve the situation… Algebraic Illustration A factory will not have 2 workers only Not all workers are free riders Do not know if others is free rider or not Have not consider incentives other than salaries: Self-satisfaction, promotion… Examples : 1. Music, 2. Movies, and 3. Documents, etc What is “free riding”? Participants only download resources from others, but share none PEER TO PEER NETWORK The Emission Trading In the Perspective of Game Theory A Game between two countries In a NEW situation * The quantity of resources downloaded by player 1 equals The quantity of resources uploaded by player 2 (u1=d2, u2=d1), so we replace d1 and d2 by u2 and u1 respectively. * g2(x)-c(x)>0 for Altruist Statistics: 10% users provide 87% files 20% users provide 98% files Situation Will Nash Equilibrium = both of them produce nothing? Environmental Protection Kyoto, Dec,1997 >> Repeated N-person non cooperative game >> People are rational and strategic Will Nash Equilibrium = both of them produce nothing? Money Sharing Game 2. Free rider vs. Free rider By IEEE, Peers make a portion of their resources, such as disk storage, available to other network participants, without the need for coordination by servers or hosts Examples : Gnutella , Napster supervision cost (h)cooperative cost (g)found selfish profit(w)assumed cooperative profit(w) Inspiration The peer-to-peer (P2P) system on the Internet P2P system Comprised of voluntary peers that contribute their own resources to the resources of others Users can play roles of server or client depending on whether they provide or request resources Background Reduction of emissions of greenhouse gases in Industrialized countries Algebraic Illustration GAME THEORY APPROACH Old China with communism Resources were evenly distributed Big pot  To work = Not to work A Game between two countries -to address the free-riding problem Suppose there are two countries Germany and Sweden The amount of emission need to be reduce is different for different country Rreq (Germany < Sweden) For countries that can reach their own Rreq before P, they can have profit through the trade More applications It can be seen that for both players, “Not upload” dominants “Upload”! supervision cost (h) cooperative cost (g) found selfish profit(w) assumed cooperative profit(w) UGEB 2530 Games & Strategic Thinking Presentation (Group 5) - Free rider Problem Free rider Someone who benefits from

social behaviour

Transcript: Cwillis92(July 17, 2010) Hunting Behaviour of the Wolf. Hubpages. Retrieved from International Wolf Center.(2013)Teaching the World about Wolves. Retrieved from Lawrence R.D. (1993).Trail of the Wolf. Toronto, Ontario: Key Porter Books. Miles.K (2002) Wolfdog training.The wolfdog. Adapted from the works of L. David Mech, Erik Zimen, L. Partignani & Ricordi. Retrieved from Savage, C. (1996). The Nature of Wolves. Vancouver B.C. Greystone Books. The Wolf Pack. Retrieved from Owen, J. (2004, December 9). National geographic news. Retrieved from Rice , R. (2007). Smithsonian national zoological park . Retrieved from Climate change and birds. (n.d.). Retrieved from Audubon society. (n.d.). Retrieved from Gallagher, J. (2013, February 23). Crows return after west nile die-off. Retrieved from off/article_76f29e15-946b-5594-b6e8-7336b09066e7.html Crows and their night roosts. (2013). Retrieved from Behavior&id=13 Westerfield, M. (2011, November 15). Retrieved from Urbanization Beta and Omega - Fatal to the crow species - Used it to its greater advantage Axel (2013). Retrieved from Black Hat Gringo blog, (October 20, 2011). Wolf and Crow. Retrieved from Crivello, J.( January 13, 2011.) Timber Wolves. National Geographic. Retrieved from Dutcher, J.(2013) The Alpha Male Gray Wolf, Canis Lupus, Dominates the Omega Wolf. All posters. Retrieved from Dominates-the-Omega-Wolf-Posters_i4207408_.htm Foxtails and fashion (2013) retrieved from imgur (2013) retrieved from London, C. (11 December 2012.) Retrieved from Megaamegan. (2013) Social behaviour . Retrieved from O’Connell, S. (2013). Magical Nature Tour. Retrieved from Purdue University (2010). Track identification guide. Wildlife Conflicts. Retrieved from Sotgiu ,M.(May 2012) The wolf and the crow, Retrived from mirko Tourofduty. (2013). Wolf paw print. IMVU. Retrieved from Wolves against hunters (2013). Omega wolf. Wolves against hunters. Retrieved from Conclusion How ranks are established problem solving techniques Adaptations continued... Social Behavior Of Animals (Sibley, 2012) (Black Hat Gringo, 2012) •Rank order is established through a series of ritualized fights and posturing •Wolves prefer psychological warfare to physical confrontations • the dominant wolf will stare, snarl or growl at the subordinate •It lies on the ground, side and belly exposed. Population strain - Ability to remember and recognize (Taylor, 2011) (Crivello, 2011) (Lynn, 2007) -strong social ingenuity Introduction - Trial and error -Survival skills (Britannica, 2011) - Ability to imitate other sounds •Wolves work as one unit to take down prey. •Old, young, sick or weak. •Pose less of a threat to the wolves themselves. •wolves will usually wait and take turns testing the prey. •Plan ambushes -Adaptations - Team work established Problem solving clip... vocalization (London, 2012) -Social ingenuity of Crows Introduction - Quick learners Conclusion •howling, barks, and whimpers to communicate •Wolves use scent marking to border their boundaries, mark the kill sites and trails. • Use their faces, much like people to tell the other members how they are feeling. • Combinations of facial gestures and tail gestures mean different things. - Independent and no hierarchy Section 61 Vocalization - Scattered the population Social Structure of Wolves -Roles -How they communicate -Hunting References Beta •The Beta wolves are the second in command • well-respected within the pack. •They enforce what the alphas choices Omega •Punching bag of

Social behaviour

Transcript: Other factors that influence pro social behaviour Situational factors Altruism Reciprocity norm: that we should help others who help us Social responsibilities: that we should help those who need help because it is our responsibility or duty to do so Smoked filled room When people act in their own interest, they can sometimes help others as well. However, in other circumstances, people can harm themselves and others by acting in their own self-interest. This sort of situation is called a social trap. Global warming is an example of a social trap: it is occurring because people act in their own self-interest when they buy fuel-inefficient cars. Noticing the situation Social behaviour Pro-social behaviour is intended to help or benefit another person, group or society Factors that influence pro social behaviour These internationally famous rock stars and movie actors are deeply involved in various activities to benefit starving or disadvantaged people in poor and/or war torn countries. Q: can their pro-social behaviour be described as alturism? is helping behaviour which is not motivated by personal gain or reward Social behaviour – refers to any behaviour where interaction occurs between two or more people.May include: smiling at someone, receiving advice etc Social behaviour and relationships Taking responsibility for helping Social relationship – is used to describe the connection or association between two or more people, especially with regard to how they think, feel and behave towards each other The case of Kitty Genovese Audience inhibition Factors influencing reluctance to help Diffusion of responsibility Procedure: Participants sat in a room completing a questionnaire. In one condition the participant was alone, in the other there were 3 participants. Steam which looked like smoke stared to pour into the air vent, this continued for 6 minutes. Findings: Participants failed to report smoke even though they were bothered. Conclusion: Only defined as emergency if majority of bystanders agree, in another study they found that if an individual thought they were the only ones to see emergency 85% helped this dropped to 35% if they were in a group. Social influence - Diffusion of responsibility - Audience inhibition - Cost-benefit analysis - Social influence Anti social behaviour any behaviour that is disruptive or harmful to the wellbeing or property of another person or to the function of a group and society Empathy: More likely to help if feel sorry for them or understand their feelings and difficulties (feel concern for them) – want suffering to end which can motivate to help Mood: More likely to help when in a good mood b/c helping makes us feel good people sometimes help in order to stay in a good mood Competence: People with abilities or training relevant to a situation in which help is required are more likely to help Relevant training makes help more likely to be offered and more likely to be effective Belief that in a situation where help is required and others are present one or more OTHER people will or should take responsibility for helping Leads each individual to feel less responsible for helping than when alone b/c assume someone else will take on the responsibility of helping Explains why no one helps when many people are present in a situation where help is required Genovese was murdered in a New York street in 1964 at around 3am after returning home from work in a bar – she was attacked by a man with a knife She tried to escape but her attacker caught her and repeatedly stabbed her Kitty’s scream for help woke 38 of her neighbors – many switched on their lights and watched for up to 35 minutes Only one called the police – no one went to her aid Learning objectives for this lessons – characteristics of, and factors influencing, pro-social behaviour: situational (bystander intervention and effect), social norms-reciprocity principle; social responsibility norm; personal (empathy, mood, competence); altruism – characteristics of, and factors influencing diffusion of responsibility; audience inhibition; social influence; cost-benefit analysis The bystander effect: Factors that influence pro social behaviour in situational factors Weighing up personal and social costs of helping against the benefits of helping BENEFITS = Rewards – monetary reward, feeling good, increased self esteem or social approval (cheers from crowds) or thrill of making evening news COSTS = effort and time required, risks such as personal injury Eg giving a friend a kidney People may stand back and not help because they do not want to embarrass themselves or feel foolish, especially if help is not actually needed The presence of others at the scene = an audience and this increases the chances of being embarrassed or feeling foolish This can INHIBIT/STOP someone from helping Latane & Darley 1968 Social norms is the tendency for individuals to be less likely to help another person when other bystanders are present, or

Presentation Social Behaviour Research

Transcript: - Social Topic - Technology - Research area: Rotterdam - Focus group: Students aged 12-25 - Requirement: Primary data and Secondary data - Gained knowledge and insights By: Suliendra Pantophlet Tim Hofma Varsha Sewradj Niels Vaartjes Jordy Rodriquez Sanchez Eric Spencer Andrade From: Surveys and Interviews Final report presentation Conclusion - miscommunication and misunderstandings - ethical issues Hypothesis Any questions? - Guideline that provides information and tips to prevent the negative impact of usage of social media, phones and tablets for communication. Research Findings Is the constant use of social media and devices such as mobile phones and tablets making the youth anti-social? Identification of concepts: - "Social Capital" - Social group Primary data and secondary data Sampling factors Limitations of the research 1. Justification of our research topic 2. Research Question 3. Literature Review 4. Hypothesis 5. Research Design 6. Research Findings 7. Conclusion 8. Recommendations Research Question - Articles - Topic is known - Multiple research already has been done Justification of the research topic This was our presentation Social media > Primary source of communication The usage of social media and devices such as smartphones and tablets has a negative impact among the youths to a certain extend. - Invest in disturbers (to block access on social media sites) at high schools and universities. Literature Review Recommendations Research Design Youth, devices and social media. Table of Content - Expected relationship between the youth using social media and mobile devices, and becoming anti-social.

Game Theory Presentation

Transcript: Definition: A section of mathematics focused on strategic decision making within a competitive situation, where the actions of the other participant affect the outcomes Game Theory derived from chess games Believed to be one of three consequences: 1: Black could win 2: White could win 3: Draw Nash proved equilibria exist in non-cooperative games with set payoffs. Now, cleverly titled "Nash Equilibrium" The costs of allowing the Soviet Union to surpass us in nuclear power were too great to take the risk of bargaining. Game Theory + The Military As shown, Game Theory was used constantly by the military Guessing opponents moves Running scenarios with possible reactions by other countries This is a more dramatic version of "Chicken" To win, appear as if you do not mind losing Rothert implies JFK knew this: "the greatest danger would be to do nothing" Mixed Strategies Based of probabilities EQUATION (essentially Expected Value): p(payoff 1) + (1-p)(payoff 2) = p(payoff 3) + (1-p)(payoff 4) USSR: 0p - 1(1-p) = p - 2(1-p) p = .5; 1-p = .5 America: 0q - q(1-q) = q - 2(1-q) q = .5; 1-q = .5 The U.S. will "Do nothing" 50% of the time and "Blockade" 50% of the time. The U.S.S.R. will "Retreat" 50% of the time and "Continue" 50% of the time. Note that this is not how the game was played, only an example of mixed strategies When you purchase a stock, the value is based on your analysis When you sell a stock, you typically believe it to have "peaked" Why? This peak is based off what you believe society to value that specific stock. While the stock market would never reach zero, participants attempt to find the best time to sell their shares. They value society's value of their stocks in order to do this, the same way people attempt to guess everyone's guess in the 2/3 Game. The Games of Game Theory Outcome: both vote for yourselves, giving you a worse chance of winning the extra points had you cooperated. Game Theory Prisoner's Dilemma Both choose A Nash Equilibrium are not required to take into account the benefit of the entire group. This is not a Nash Equilibrium Each side had two options America: blockade/do nothing Russia: continue sending missiles/retreat Payoff Matrix: Tony Chen & Joe Mashburn This guy This is a solution to a common Game Theory paradox: Prisoner's Dilemma Voting for the best project in Math Pearls, you promise your best friend in the class you'll vote for them if they vote for you. You calculate this will give each of you a 50% chance to win. Let's try it, before we give you the definition. Jump to 1950: John von Neumann - 1928 Questioned how players should act based off potential plays by opponent Was there an equilibrium point? Realistic example: U.S. vs U.S.S.R. Cold War nuclear arms race John Nash: PhD Student at Princeton / Schizophrenic Age 22: solves von Neumann's question and receives PhD Later receives Nobel Prize for this feat Definition of Prisoner's Dilemma: The Nash Equilibrium of a game results in lower payoffs because the incentive to deviate from the other player is too great. For example: Stocks Pagent Jacek Rothert: Game Theory & The Cuban Missile Crisis Let's talk about Russel Crowe for a second Recall the bar epiphany This is not a Nash Equilibrium. Stocks and Game Theory A derivation from Keynes' "Beauty Pageant" You are a judge in a beauty pageant Purpose is to have your pick win the beauty pageant Keynes believed you would pick what you thought other judges would pick, to maximize the chance your person won the contest Example Game: Guess 2/3 the average Numbers range from 0-100 Play with multiple people Person closest to 2/3 of the average of the guesses wins 66.67 = 2/3 of the highest possible, so everything above that can be eliminated 44.44 = 2/3 of 66.67, so everything above 44.44 can be eliminated This continues, and the Nash Equilibrium for this game results in 0. retreat do nothing blockade continue sending missiles 0,0 1, -1 -1, 1 -2, -2 U.S.A. USSR

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