THE STRATEGIST th
29 April,2012
First Edition
The KGPian Game Theory Society
STRATEGIES
QUIZZES / PUZZLES
A BEAUTIFUL MIND
LETS PLAY A GAME
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here are 5 rational pirates who are looking for a certain treasure chest when they found 100 gold coins. Greedy as they are, they must decide how to distribute them. The pirates have a strict order of seniority: The pirate world's rules of distribution are that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution or not. If the proposed allocation is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again. Pirates base their decisions on three factors . First of all, each pirate wants to survive. Second, given survival, each pirate wants to maximize the number of gold coins he receives. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal. The pirates do not trust each other, and will neither make nor honor any promises between pirates apart from the main proposal You are the captain of the ship and hence the senior most. How would you divide the gold so that your life is not at stake? Think for a while. Should you be fair or should you be shrewd? Is it necessary for you to pay everyone or only a few? Think of what the other pirates
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might think! Lets name the pirates in order of seniority: Alex (YOU), Billy, Colin, Duncan and Eddie. Consider the case with only 2 Pirates left : Duncan splits the coins 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal. 3 Pirates: Colin splits the coins 99 : 0 : 1. Eddie will accept this deal (getting just 1 coin), because he knows that if he rejects the deal there will be only two pirates left, and he gets nothing. 4 Pirates: Billy splits the coins 99 : 0 : 1 : 0. By the same reasoning as before, Duncan will support this deal. Billy would not waste a spare coin on Colin, because Colin knows that if he rejects the proposal, he will pocket 99 coins once Billy is thrown overboard. Billy would also not give a coin to Eddie, because Eddie knows that if he rejects the proposal, he will receive a coin from Colin in t h e n e x t r o u n d a n y w a y .
AN INTRODUCTION.....
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he game you played above is just a tiny example of the principle of Game Theory- Life is a game and you are the player. Every time , the situations in life present a new game to you. But beware! You are not alone! There are many other players and all of them want to maximize their gain. You may adopt any strategy you like but remember that you can only control your move, not your opponents, and the game that you are playing is a part of a much bigger game! Even the dog that wags his tail to your whistle is doing so to maximize his profit, for he knows that soon that obnoxious ape calling his name will throw him a bone out of his plate! You cannot play your opponents move, but you can predict their motives based on your rationale and make the best response possible. You can fool him into misjudging your intentions and make him play the move that you want him to. But only he can play his moves, not you! That is the essence of game theory- To put yourself in your opponent's shoes and maximize your payoff. The games in this theory range from playing Chess to managing your sex life, on field strategies to business decisions, hall politics to wars between nations. All these games require some skill and knowledge but most importantly they require the best strategy. Let's take a look at how strategic thinking helped the legendary investor, Warren Buffet. In an article promoting election campaign finance reform, the Oracle of Omaha, Warren Buffett, proposed raising the limit on individual contributions from $1000 to $5000 and banning all other contributions. No corporate money, no unions, no black money. Sounds great, except that no one would pass it! Campaign finance reform is hard to pass because the legislators that have to pass it are the ones who gain the most from fund raising. How do you get them to do something against their own interests? Put them in what we call the Prisoner's dilemma! According to Buffett:
Pirates: You now have the option of being fair and giving considerable amount to each. But will that really help you? Suppose you split the coins 98 : 0 : 1 : 0 : 1. By offering a gold coin to Colin (who would otherwise get nothing if Billy had his way) you are assured of a deal! So u stay alive and Note that in the final deal you should not give a coin to Billy, who knows he can pocket 99 coins if he votes against your proposal and you go overboard. Likewise, you should not give a coin to Duncan, because Duncan knows that if he votes against the proposal, you will be voted overboard and Billy will propose to offer Duncan the same single coin as you. All else equal, Duncan would rather see you go overboard and collect his one coin from Billy. The method that we have used in this popular example is called Backward Induction and is just one of many techniques that are found in the pockets of a game theorist!
-Vaibhav Bhargava “Well, suppose some eccentric billionaire (not me :P) were to make the following offer: If the bill for this reform was defeated the party that had given the most votes for getting it passed will receive a donation of $1 billion from me. Thus through this diabolic application of Game Theory this bill would pass through easily and our billionaire doesn't need to pay anything!� Put yourself in shoes of these parties- the Democrats and the Republicans. If you think that the other party will support the bill and you try to defeat it then you'll only be handling them enough monetary resources to beat you hands down in the next face-off. So no matter what the other party does you'll have to support the bill and yet hope that it doesn't pass! Now since all parties think the same the bill would definitely pass and they all end up losing! That's what game theory can do. Can we adopt a similar strategy for the Jan Lokpal bill? During the cold war of 1962 the Soviet Union under its leader Khrushchev began installing Nuclear Missiles on Cuba, 90 miles from American mainland. A week after he got this news President John F. Kennedy ordered preparations for a naval quarantine of Cuba. Had the Soviet Union accepted this challenge it could have led to an all out Nuclear War. The risk was mutual and deliberately created. After a few days General Khrushchev pulled back in a face saving compromise of withdrawal of US missiles from Turkey. Thus the possibility of a big catastrophe was eliminated by the creation of a bigger mutual risk! It was a battle of minds and Kennedy won! Be it a gambler or a politician, a husband or a Casanova, a clerk or a CEO, a writer or an athlete, a horse or a donkey! It always helps to put yourself in your opponent's shoes, to be able to calculate your profit and make the best move. That's what Game Theory does! As you can see, it's not a separate science but a part of your life.