http://kedarsoman.wordpress.com/2007/05/27/mathematical-simulation-of-election-in-democracy-india-and-usa/

            This article is about game theory and how it relates to democratic systems in India and the USA.  The writer describes the electoral system in the United States with respect to game theory, then goes on to extrapolate what kinds of systems would work best in India.  In democracy, the votes are considered random if people vote with respect only to their own preferences, and do not vote as a block.  If people vote in a block, such that all the people in that block vote exactly the same way, then political candidates must concentrate on winning that block regardless of how small it is, because the remaining distribution of votes will be random.  Therefore, it is in the candidate’s best interests (a dominant strategy) to please the block, as he either gets the entire block or doesn’t, but the candidate must balance his policy decisions with respect to pleasing the group and pleasing the other constituents.  The problem is that the creation of one unified group hurts democracy in that the candidate will change his strategies to cater to the one group more than to the interests of the public in general.  A Nash equilibrium must be found where the candidate can balance the desire of the groups and the candidates not in groups.  Another beneficial alternative is the presence of several groups that make the voter distribution more random than the presence of only one group. 

            A complication of the voting system is that only a majority of a certain block needs to be won for the candidate to get that entire set of votes.  In the United States, states can be considered blocks of people; regardless of what the voting distribution is within the state, a majority within the state guarantees all the votes to that candidate.  Thus the voting distribution of the people of the United States is less important than getting majorities in every states, making the winning of states as blocks very important to the election process.  This detracts from democracy by not making the votes of all people equally important.  However, as described above, the candidate can use game theory to help assess how to balance the desires of the American majority and success in the election.  The article also describes an election simulation to assess what type of system would be best in India, based on the election system here.  The algorithm is complex and takes in account many factors such as individual voters and special interest groups.  The simulation assesses a failed election if the candidate that wins is one that is disliked by a majority of people.  It is interesting to see that game theory arguments can be used to assess whether our election system if flawed: catering to small blocks of people as opposed to the entire set of people goes against democratic principles, and could result in a president unpopular to the majority. 

http://www.sciam.com/article.cfm?chanID=sa006&articleID=7750A576-

E7F2-99DF-3824E0B1C2540D47&ref=rss

The link above leads to a very well known game, much like the Prisoner’s Dilemma, created by Cornell University professor Kaushik Basu. The problem is as follows: Two people are returning home from vacation on a plane and both have brought back with them an identical souvenir. Upon arriving at the airport after their trip, they both discovery that each of their souvenirs were damaged. The airlines is willing to compensate each of them for the loss, however, it does not know how much the souvenir costs, and for the sake of argument, each traveler did not save a receipt. So, the airlines decides to compensate them as follows, it asks both travelers to write down the amount they paid for the item but without talking to one another. If they both write the same amount, then the airlines will believe them and compensate them with that amount. If they write differing amounts, then the airlines will assume that the person who wrote the higher price is lying and trying to scam more money away from the company, so they will pay each traveler the lower amount. However, they will also give a bonus to the “truthful” traveler and pay him an extra $2 for not lying and take away $2 from the traveler who lied and wrote the larger amount. Here’s an example, is Traveler 1 writes down $60 and Traveler 2 writes down $100, then Traveler 1 gets $62 and Traveler 2 gets $58. The question is, what amount would you write if you were one of the travelers?

This problem has been experimented with many people and many answers have been given. When giving the actual value of the item, many write down that value, when told to write an answer between $2 and $100 many write a number in the $90s range. However, the intriguing part about this question, and what makes it a dilemma, is that the answer goes against rationality to some degree. The answer that game theory analysis gives us is $2, that is to say, if you were one of the travelers, you should write $2. We come up with this answer through a sort of backward induction. For example, if you were told to write a number between 2 and 100, many would assume that the other traveler would write 100 and therefore you should as well so that you both receive $100. However, if you believe this, then you should deviate to write down 99 so that you would receive $101 and the other traveler would receive $97. But, because of common knowledge, the other traveler knows you know this so he will write 99 as well and both of you will receive $99. Then again, from here, if you deviate to 98 then you will receive $100 dollars. This backward argument can be made for both all the way down until both players reach $2. This is what makes it odd, that game theory states the answer should be $2, however, no one would write down $2, if they were truly “rational.”

This problem is another example to one we learned in class where the “game theory” answer doesn’t always lead to a socially optimal solution as in the Prisoner’s Dilemma. In the PD, both should confess, however, if both would have not confessed then they both would have been better off. The Traveler’s Dilemma is a great game and if you want to learn a lot more about it, I encourage you all to read more about it in the article linked above!

http://edition.cnn.com/2008/WORLD/meast/02/28/mideast/index.html

This news article is mainly on reporting the escalating violence between Israel and Palestine.  The news article reports that Israel has launched an air-strike in response to the rocket attacks from militants of Palestinian terrorist group, Hamas.  The Israeli air-force targeted Gaza in attempt to terminate the Palestinian terrorist group, which resulted in death of several terrorists and peaceful bystanders.  In retaliation, Hamas also launched attacks in Israeli territory, which inflicted deaths and injuries in Israeli civilian population.  The article eventually went on to the responses of UN and human’s rights organizations on the attacks.  This article is relevant to the course material because we can explain the behavior of both Israeli and Palestinian with game theory.

            Let’s start by constructing a game theory table with two players.  On one side, we have Israel, and on the other side, we have Palestinian terrorist.  Each side is given two choices of action.  One of them is to strike and the other one is not to strike.  The numbers inside of the column represent approval rating of people in Israel and Palestine, and the approval number is in the scale of 0 to 5.  5 is the highest rating and 1 is the lowest rating.  On the top left column, we have a situation where both sides decide to strike which earn them an approval rating of 3 each.  The top right corner of the table is when Palestine strikes and Israel chooses not to strike.  That gives Israel an approval rating of 1 and Palestine an approval rating of 5.  The bottom left column of the table is exactly opposite of the top right column, which gives Israel an approval rating of 5 and Palestine an approval rating of 1.  The bottom right column of the table is when both sides chooses not to strike which give both side an approval rating of 0 since nothing has happened.  From the table we can tell that the dominant strategy for both sides is to strike.  That is why the fighting never stops since the best thing for the both side to do in this situation is to strike back.      

http://www.antiwar.com/henderson/?articleid=12395 The following article describes the embargo the United States has imposed on Cuba.  Cuba, holding its position as a communist nation, has been suffering long economic and social grief for the past 48 years.  With the embargo in place, America has forced the Cuban people into a worse economic dilemma.  Although America has created this embargo as a response to the Castro administration, the embargo has done nothing but weakened the country and its people, without eliminating Castro.  Many questions have been brought up, such as why would the embargo go against a communist country, while America freely trades with China or why has the embargo worsened the situation, instead of making it better?  If America is really the land of the free, why have people been restricted from visiting or entering Cuba, without special permission?  Given the right to visit Cuba, by Americans, would increase the economic status of the country and give Cubans more freedom, seeing that the American dollar would have a strong affect there. 

Relating to the subject of Networks, America represents this great structural hole, and through the embargo placed, has robbed Cuba of any potential of trade.  This can be visualized on a graph in which there would normally be buyers, traders and sellers, but the traders have been forced out of work, eliminating any possible transfer of goods or products.  This can also be seen as a 3 node graph where America is in the middle and can trade with any other country except Cuba, unless America’s demands are met.  With this observation in mind, Cuba has two options, meet America’s demands and have a lower payoff or establish good trade relations with other countries, which would be too difficult for a country that has been weakened by harsh rule and bad economy.  Is there really a right decision?  As discussed in class, players have expected payoffs, based on the idea that every player is acting rationally, trying to maximize his/her payoff, but is the idea of rationality present in politics?  What rationality is seen when a superpower such as America has placed an embargo on Cuba?  What is there to gain?  The embargo has lead to nothing but suffering for the people, and has done nothing to the government of Cuba.  Relieving this embargo would allow trade between the two countries, and when is trade ever a bad thing?  So the answer is no, in this situation there is no rationality. 

Reference: http://en.wikipedia.org/wiki/Tit_for_tat

On homework 2, we were asked to consider the Prisoner’s Dilemma where it was played twice, and both players knew that the game was to be placed twice. The optimal solution for both players was to confess both games. Now, what would happen if the players were told that the game would go on for an unknown number of times, and then against a larger pool of players? That is to say, there will be a pool of 2^m players, who will each play eachother for an unknown number of rounds. Since the players cannot reason about the last game first, they must use forward logic to try and predict what the best move is.

There are two choices the players can make on the first round. They can either confess or not confess. If played only once, confessing is clearly the optimal strategy. But, since the game will most likely be played again, and more than once, the players might consider a different strategy. An effective strategy for this type of game is called Tit for Tat. The rules are simple. A player will not confess unless otherwise provoked (his opponent confessed). A player is quick to forgive other players. That is to say, he will forgive an opponent who does not confess.

Now, consider two players playing against eachother. Player A uses Tit for Tat, while Player B will always confess. Against player B, player A will lose initially, and then always confess. Thus, Player A will be slightly behind. However, if player A plays against an opponent who is also playing Tit for Tat, both players will always not confess, leaving each player with a substantially less penalty then if each confessed.

As described in the link above, the Tit for Tat player will always come out ahead in such a game. The results of such a game, however, are quite surprising. Using such a method changes the Nash Equilibrium from always (Confess, Confess) to (Not Confess, Not Confess). Thus, depending on the desired outcome, whoever is running the game should choose which details to tell the players and which to not. For instance, if the players are 2 criminals wanted for a crime, it is in the interest of the Police to tell them that they will only have 1 chance. If, on the other hand, the criminals know that they will multiple chances to confess, or multiple charges to confess to, it would be in the best interest of the criminals to not confess and see what happens, and carry the result into the next round. But, this is contingent on the fact that the criminals cannot now how many times the game will be played. If it is known, they will always confess.

The emergence of the internet has disrupted the equilibrium in the entertainment world and radically changed the way content providers and users interact. It was no longer just through televisions or radios at a certain set time but also through the web on-demand available 24/7 with just a click of a button. The music industry was the first to be affected by such change. File sharing networks such as Napster and Limewire forever changed the industry’s definition of distributing contents. With the internet, new business models surfaced, creating the concept of online music store. On the not so bright-side, however, the Recording Industry Association of America (RIAA) has been blaming illegal downloads for the decrease in record sales.

Naturally, same transitions occurred within the media industry. Many media giants saw big potentials in distributing their contents through the internet to reach a wider audience. As broadband access become cheaper and more widespread, more “edges” are forming in the internet world. On the other hand, they had to deal with illegal downloads of television shows and movies through programs such as BitTorrent. They are also running into difficulties because there are not many options in the market to make profit off of. Video sharing websites such as Youtube are constantly under fire because of copyright infringements. While distribution through such venues could be used as a marketing tool for promotion, content owners cannot profit from it without commercials. Apple’s iTunes Store, the dominating download service provider in U.S., offers “profitable” business solution, selling television shows and movies at a certain price and letting the users download them to their computers or their iPods. Couple month ago, however, media giant NBC Universal decided not to renew its contract with Apple because NBC had limited options in terms of pricing and packaging its shows. This happened because Apple dominated the market of handheld video device with the iPod and thus have a wide distribution platform that no rivals can match. Its high “betweenness” gives the company more bargain power in deals with the media content providers.

As a reaction to this, many media giants are looking for alternatives. Majors have each opened their own website with their contents. NBC and News Corp. have teamed up to create new online video venture, Hulu. NBC Universal and GE Commercial Finance launched a $250 million Peacock Equity Fund in April to invest in media and technology companies that are developing products of relevance to NBC. Many have also teamed up with existing services such as Amazon Unbox, SanDisk’s Fanfare, Vudu, AOL, Comcast, MSN, MySpace, and Yahoo. They are trying create competition in the market by creating more distribution path, weakening their dependence on Apple and thus making the situation more favorable to them. Currently, the industry is trying to find its position in the new internet market, testing out different business models to figure out the user’s habits, which is now just taking place.

References:

http://www.forbes.com/2007/08/06/nbc-internet-video-biz-media-cx_lh_0806kliavkoff.html

http://www.nytimes.com/2007/12/02/business/02frame.html?_r=2&oref=slogin&oref=slogin

Referenced Article: http://www.guardian.co.uk/environment/2008/feb/18/conservation.aaas

There are many situations that involve a finite amount of a very valuable resource. Everybody involved has an interest in procuring portions of that resource (often as much of it as possible), but it is in nobody’s interest alone to conserve or maintain that resource. There is a conflict between adhering to self-interest and improving the common good (social welfare) for everyone. This type of situation is known as the “tragedy of the commons”, wherein the valuable resource in question is spent faster than it can be replenished, which ultimately results in scarcity, and in some cases, total extinction of that resource.

Worldwide overfishing provides a perfect example of the tragedy of the commons. This article discusses in particular the overfishing of sharks, which is made possible by the lack of restrictions on shark fishing in international waters. Indeed, nations with coastlines are especially eager to sweep the seas in order to gather as many resources as possible to try to gain a competitive edge over each other in the global fish market. In doing so, these nations ignore the pleas, recommendations, and warnings sent out by the hundreds of environmental and wildlife organizations each year that point out the wider spectrum of dire consequences (both economic and environmental) resulting from an eventual extinction of fish species. This harkens back to the outcome of the prisoner’s dilemma. Even though both prisoners could shorten their overall prison time by cooperating with each other and agreeing not to confess, each prisoner’s individual dominant strategy is still to confess. Of course, this does not lead to social welfare maximization, because both prisoners end up spending longer times in prison. Similarly, in the case of overfishing, all nations could agree to fish at a predetermined amount so the fish will replenish themselves faster than they are plucked from the sea. This will produce the maximum social welfare because there will not come a time in which an economic slump arrives due to the depletion of fish. However, it is every nation’s dominant strategy to fish as much as possible to gain a market advantage over one another. This then leads to a result that is not social-welfare-maximizing. Therefore, the solution to the problem of worldwide overfishing is not just the drafting of treaties and trade agreements between nations to keep their fishing levels below predetermined limits. Almost always, there needs to be a central regulating authority such as the UN (as suggested in the article) to make sure that these nations cooperate with each other and do not surpass the fishing limit. And only with cooperation can we hope to arrive at the social-welfare-maximizing result.

Referenced Paper: http://delivery.acm.org/10.1145/1090000/1080199/p116-jun.pdf?key1=1080199&key2=1552844021&coll=GUIDE&dl=GUIDE&CFID=18506295&CFTOKEN=73653288

BitTorrent is a protocol for downloading large files, and is often a faster alternative to regular client-server downloading. Essentially, BitTorrent is able to increase download speeds by utilizing a network of people downloading the same file at the same time. The network of people, in BitTorrent terminology, is referred to as a swarm. Every person in the swarm downloads different parts of a file from their peers in the network. Unlike other clients however, you simultaneously upload parts of the file you are downloading to other peers who need it the parts you have. An interesting caveat with the system is that BitTorrent requires users to upload to each other and also requires that there exist a few altruistic “seeders” who are willing to upload the entire file they possess.

As a user it may be tempting to refuse to upload to others and just download your file, but it turns out that you will be punished by the BitTorrent system. Your “leech” behavior and refusal to upload to others forces the BitTorrent system to “choke” you and reduce your download speed. Therefore, a dominant strategy is to share what you are downloading. In the paper referenced, this system is referred to as TFT (tit-for-tat) and is relevant to our prisoner’s dilemma problem when played multiple times. The TFT system always cooperates at first, and then copies the user’s previous move in order to end up at a Nash equilibrium all the time.

As we know from class, when the prisoner’s dilemma is played once, both players should “confess”, but with BitTorrent, the players are concerned with the future. Users are continually playing the prisoner’s dilemma game in order to download parts of the file they need. Therefore, in the long run, it is beneficial to coordinate. Essentially, if both people choose to coordinate they get better download speeds than if they do not coordinate. If they coordinate at not uploading, then they end up at a non-focal Nash equilibrium which is not the prediction of play because both players uploading would be more desirable. Additionally, the focal point Nash equilibrium (where both choose to upload) is a Pareto optimal solution because no change can be made where both players can achieve a higher payoff.

In the end, while the TFT solution has worked substantially better than other solutions, the referenced paper argues that the TFT system induces “free-riding”. Therefore, the authors of the paper propose a slightly better “incentive mechanism” for improving the results of the TFT method. For more information on this, click the link provided above.

http://irl.eecs.umich.edu/jamin/courses/eecs494/fall06/lectures/lecture12-balance.pdf

The link above is a pdf file that describes how game theory is used to make games more interesting. As an example, the balance among the three races of Starcraft:Broodwar showed up. The three races are Zerg, Terran, and Protoss. One of the reasons that this computer game has been such a hit is that the three races are fairly balanced in their units and the build orders, so who wins is mostly determined by who is the better player.

There are many aspects of the races that make them so well-balanced. Each race has about 13 types of units, 18 buildings, and each units have strengths and weaknesses. As a result, there are hundreds of possible armies you can make with these units, and they will all fit the rock-paper-scissors model. For example, a group of zealots(Protoss units) is superior over a group of zerglings(Zerg units); a group of firebats and medics(Terran units) is superior over a group of zealots; a group of lurkers and hydras(Zerg units) are superior over a group of firebats and medics; and so on. Each of these incidences could be formed into a game theory model, but since there are so many possibilities, it is not practical.

However, there is a general aspect about the game that can be fit into a rather simple game theory - the build orders. Basically, there are three general build orders for each race. Strategy one, S1, is staying with one base, staying poor, and going for a quick rush. Strategy two, S2, is staying with one or two bases, staying fairly rich, and going safely by responding passively. Strategy three, S3, is having two bases, staying very rich but with very little units, and leading a long match.

S1 would have a great advantage over S3 because S1 can attack very quickly before S3 produces sufficient number of units.

S2 would have a great advantage over S2 because S1 starts poor, and by the time S1’s units attack S2, S2 will have sufficient number of units to defend and rush back.

S3 would have a great advantage over S2 because S3 is richer than S2, and by the time S2’s units attack S3, S3 would have sufficient number of units to defend. Also, S3 will produce even more units as the game goes on.

As a result, the game theory model of Starcraft:Broodwar Build Order may look something like this:

If (a, b) = (Player A’s strategy, Player B’s strategy),

(S1, S1) = (0,0) ; (S1, S2) = (0,1) ; (S1, S3) = (1,0) ;

(S2, S1) = (1,0) ; (S2, S2) = (0,0) ; (S2, S3) = (0,1) ;

(S3, S1) = (0,1) ; (S3, S2) = (1,0) ; (S3, S3) = (1,1) ;

So, there is no dominant strategy for each player, which is essential to make a game interesting. However, in reality, gamers are able send scouts to see what build order the other player is planning, so it may not be a perfect model of game theory. Still, there are also many ways to prevent other player’s scouts from discovering your build. Besides, when I watch the Korean Starcraft League, it seemed that S1 beats S3, S2 beats S1, and S3 beats S2 when the players were about the same in skills.

http://www.egwald.ca/operationsresearch/chickengame.php

The link above describes a variation of the Hawk/Dove game theory, as presented in a popular James Dean movie. In this game, there is no dominant strategy for each player. Two people drive their cars towards a cliff or each other; the first person to jump out is the chicken, while the last is the “hero”. Therefore, the four outcomes are chicken, hero (and vice versa) and death for both players, which is a highly undesirable outcome. This game was also compared to nuclear brinkmanship since an element of uncontrollable risk is introduced.

The game of chicken differs from games such as the prisoner’s dilemma because both players do not have a dominant strategy, and there is a disparity in cost. Jumping at the same time gives both players a favourable outcome, but the payoff is very low. Player preference ranks being the hero over tying, tying over being the chicken, and being the chicken over crashing. Since both players would use different strategies for their best outcomes, this is an anti-coordination game, like the Hawk/Dove game theory that we covered in class. On the other hand, it shares similarities with the prisoner’s dilemma game because the mutual solution is often unstable, causing both players to avoid it.

An equilibrium for this game utilizes mixed strategies, which is most appropriate due to the anti-coordination. The players randomize their strategy choice and there is a probability of playing each strategy. The expected payoffs then for each player in this equilibrium would be in fraction form, since it factors in the probability of each eventual outcome. Neither player can “improve” the strategy despite changing their choices because of the unstable situation. There is no one Nash equilibrium. However, each player can harm the other by choosing not to be the chicken. When this happens, the least desirable outcome (death) occurs. So….try not to play this game.