The Economics Theory Game - Case Study Example

The Economics Theory Game The Game Itself In this game, there are 5 pirates who are very rational. Assuming each one is assigned a number that is, 1, 2, 3, 4, and 5, for the sake of reference, these pirates luckily find 100 coins made of gold. The problem is that they must make a decision on how to share the gold coins. However, the pirates already have a strict seniority order, in the case that: 5 is superior to 4, who is superior to 3, who is superior to 2, who is superior to 1. The distribution that is to take place must follow some rules from the pirates’ world. These rules assert that the distribution of the coins must be proposed by the pirate who is the most senior. The pirates, with the inclusion of the proposer, then cast votes to decide on whether to accept the proposed distribution. If, in the votes that are casted, 50% of the voters agree with the proposal, the gold coins are divided as the proposal was made. If after the votes there is a tie, the pirate who proposed the distribution has the casting vote (Hoena & Stevenson, 2013, p 45-48). If the pirates accept the distribution proposal, the disbursement of the coins takes place, and here the game ends. If the distribution proposal is not accepted, the pirate who had made the proposal is thrown overboard by the other pirates off their ship and dies. Once he is thrown, the pirate who is next most senior takes over the task of making a distribution proposal and begins the system again. The decisions of the pirates are deeply founded on three aspects. The first aspect is that all pirates seek to survive despite the proposal. The second aspect is, given that they survive, each pirate is extremely greedy, and each has the goal to get the maximum number of gold coins he will receive. The third and the last aspect is that, if all other outcomes are otherwise equal, every pirate will prefer throwing one another overboard. The problem in making the decision is that the pirates do not have trust in each other, and they will neither opt to make nor honor any promises that are made by the pirates, unless it is the main proposal (Li, 2014). The big question now lies on, what could be the proposal of the pirate who is most senior? The assumption is that they put the three aspects in much consideration in the sense that they are extremely greedy and very intelligent and that there is no pirate who prefers to die. The solution to the game First, it is essential to gain a clear understanding of what a 50% of the votes mean. It implies that for the distribution proposal to be adopted, it must get the votes of three pirates since there is a total of five pirates for it to pass. If there are four pirates, the proposal needs 2 votes, and it will need 2 votes if the pirates are three, in order to make it adoptable. When this kind of puzzle is given to people to solve it, most of them give answers that suggest that the pirate who is senior most will take half the amount of gold coins and will divide the remainder among the pirates who are the least senior. This is never true, and these people miss the point since they ignore the factor that states that the pirates are extremely greedy and very clever. Any answer that lacks a particular logic behind it is considered invalid because it will not make sense if a question is posed to know why pirate 5 would give a certain number of gold coins to pirate 1 and the response is that pirate 5 is nice. The reason is that these pirates don’t have trust in each other, and, therefore, no one would dare do that (Chatterjee & Samuelson, 2014, p. 90). The perfect solution to the puzzle of the pirates and the gold coins now comes. Pirate 5, being the most senior understands that he is in charge of making the distribution proposal, and that he requires getting two other pirates to vote for his solution so that he does not get executed by the other pirates. The big question again is, who is ready to vote for him, and what is the reason that can make them choose to cast the vote in his favor. The thought that, pirate 4 will never choose to vote for him due to the reason that he would opt to have pirate 5 executed and take the position of the most senior pirate and be in charge of making the proposal, is still close to the answer. Unfortunately, this puzzle is getting more complicated. Assuming that the gold coins were discovered by one pirate, the obvious solution is that he would be free to take it all for himself without anybody complaining about it. Again, if there were two pirates who discovered the gold coins, pirate 2 being the most senior, he would simply vote for himself, garnering a total of 50% of the votes. This implies that he will keep all the gold coins for himself and still, nobody would complain about it. If the gold coins were discovered by three pirates, in the attempt to come up with a distribution proposal, pirate 3 will have to convince an additional one person to support him in his proposal. So, who can pirate 3 convince out of the three and how is he going to do it? The leap that requires to be considered to get a solution to this problem is here: pirate 3 knows that if his plan fails to be adopted, he will be executed, and the gold coins will be left to only two pirates. Already, he understands what will happen if the gold coins are left to the two pirates, just as we have figured out above. What happens is that pirate 2 will take all the money, keep it to himself, and give nothing to pirate 1. This, therefore, implies that pirate 3 proposes to take 99 gold coins and give the other 1 coin to pirate 2. Pirate 2 will as well say that one gold coin is better than none, and he knows again that if he fails to vote for pirate 3, he will not get anything and thus he should vote for this distribution proposal (Li, 2014, p 57-59). Now, up to this level, it is clear that we are all aware of what will happen if there are only three pirates. The question again is what will happen if the gold coins are discovered by four pirates? Well, pirate 4 has to convince another one pirate to vote for his plan to avoid being executed. He understands that if he is thrown overboard and dies, pirate 3 will get 99 gold coins while pirate 2 will get 1 gold coin. Pirate 4, could choose to give pirate 2 two gold coins. This will surely make the pirate 2 vote for his plan since two gold coins are better than the one that he will get from pirate H incase I is executed. Let’s not forget that pirate I is extremely greedy, and he would opt not to part with the entire two gold coins. He discovers that if he faces execution, then the scenario of pirate 3 will happen and pirate 1 will get the shaft in the scenario, that is; he won’t get any coin at all. Therefore, pirate 4 chooses to give one gold coin to pirate 2, and pirate 2 seeing that one gold coin is better than none, he will automatically vote for the plan proposed by pirate 4. The general objection is that, it is not a guarantee that pirate 2 will vote for this distribution proposal since he might have the hope for a situation where there will only be two pirates where he will pocket all the gold coins to himself. But we should not forget the fact that all these pirates are very intelligent. Pirate 2 discovers that pirate 3 will be clever enough to come up with the optimal proposal, and thus he discovers that the scenario where there are only two pirates will never arrive, since pirate 3 is not ready to die and we have just figured out the winning proposal that Pirate 3 can come up with so that he can win (Hoena & Stevenson, 2013 pp.54-60) At this point, the summing up could be made of the above information in the table below. Pirate 1 2 3 4 5 5 ? ? ? ? ? 4 0 1 0 99 - 3 1 0 99 - - 2 0 100 - - - 1 100 Once we look at the pattern keenly, all the above information gains clarity. It is essential to recognize that if the proposal plan of one pirate fails to succeed then it implies that the situation remains one pirate is missing. In the case of pirate 1 alone, he does not need any other people to vote for him. Therefore, he votes gives himself the votes and pockets all the gold coins. In the case of two pirates, pirate 2 votes for himself and takes up all the gold coins and pirate 1 does not get any. Additionally, pirate 3 requires one more pirate to vote for him. He, therefore, offers one gold coin to pirate 1 so that he can get his vote and enable him avoid execution and get the money. If the situation forces the pirates to remain two in number after 3 is executed, pirate 1 will not gain anything, and thus he will consider the offer of pirate 3 of one gold coin. In that case, pirate 3 gathers 99 gold coins, and pirate 2 does not get any gold coin. In the case scenario 4, pirate 4 requires one additional person to give him the vote he needs (Hoena & Stevenson, 2013, p. 64). He then offers one coin to pirate 2. Considering the result if the number is reduced to 3 pirates, pirate 2 accepts the coin and votes for pirate 4 since he may end up not getting any coin in the case pirate 4 is executed. In that case, pirate 4 will have 99 coins, pirate 2 and 3 will not have any and pirate 1 gets one gold coin. Li (2014) argues that if it is in the situation where there are five pirates, pirate 5 requires an additional of two other pirates to vote in his favor. It is now clear that the two people he is supposed to convince are the two pirates who will get shafted in the scenario with four pirates, that is, pirate 1 and pirate 3. So he will have to give each one of them one gold coin, a coin that seems to be better than none (what they would otherwise get in the scenario of four pirates), and he will, therefore, retain the 98 coins for himself. It will, therefore, be a win for pirate 5 if he gives one coin to pirate 1 and another coin to pirate 3 so that he gets their votes. The Extension of the Game The solution of the game will follow the same collective pattern for the other numbers of the pirates and/or coins that are involved. However, the character of the game changes, when the extension of the number of the pirates goes beyond twice as many as the gold coins, is. Ian Stewart, who is a writer, wrote about the extension of Steve Omohundro to a random number of available pirates and gave a description of the rather complicated pattern that emerges in the solution. Supposing that there are 100 gold coins that are available, then the following is the solution. If pirate 201 is the captain, the only way he can stay alive is by offering all the gold coins to the odd-numbered pirates and keep none of them. Again, if pirate 202 is the captain, the only way to live is only through offering all the gold coins to the even-numbered pirates and keep none of them. If pirate 203 is the captain, there will not be sufficient gold coins to bribe the majority, and he will, therefore, die (Hoena & Stevenson, 2013, p 64). If pirate 204 is the captain, he has the vote of 203 secured without giving a bribe since 203 will only survive if 204 survive too. This will therefore imply that 204 will be on the safe side if he makes a similar offer as that of 201, giving a bribe to the odd-numbered pirates between 1 and 100, who won’t get anything from 202 if both 203 and 204 die. Since 204 is safe, 203 will have nothing concerning him if 205 dies (Chatterjee & Samuelson, 2014, p 105-108). This will then imply that 205 will be in trouble if he becomes the captain, and the same case will be observed in 206 and 207. The self-preservation votes from pirates 205, 206, and 207are sufficient to ensure that pirate 208 is safe, if his offer is similar to that of 202, that is, giving bribe to the first 100 pirates who are even-numbered, who will not be in a position to get anything from 204 if pirates 205 and 208 die. Reference list: Chatterjee, K., & Samuelson, W. (2014). Game theory and business applications. New York, Springer. Hoena, B. A., & Stevenson, R. L. (2013). Robert Louis Stevenson's Treasure Island. Li, D.-F. (2014). Decision and game theory in management with intuitionistic fuzzy sets. Read More