Game Theory
Answer the following questions. Each of your answers should be an essay of 250 to 350 words (with a typical font and spacing this will be about 1 to 1-1/2 pages). Refer to the lectures and the texts as needed. 1. You are player 2 in the Ultimatum Game. Player 1 has offered you $10. Does it make a difference to you if player 1 is dividing $12, $20, or $100? Why? Does it make a difference to you if player 1 is offering his own money, dividing money that he won in a previous game, or dividing money given to him for division? Why? Does it make a difference if player 1 is an individual, an organization, or a computer? Why? 2. Discuss any “tragedy of the commons” example not already discussed in the lectures or texts, analyzing the elements involved using game theory. 3. We saw in our hawk/dove game that a polymorphic ESS exists with a population of 70 percent hawks and 30 percent doves. But we could consider a mutant phenotype in this game that acts as a hawk 70 percent of the time and a dove 30 percent of the time. Show that this phenotype is a monomorphic ESS—it cannot be successfully invaded by either hawks or doves.
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Game Theory
Response to question 1
I am Player 2 in the Ultimate Game. Player 1 has offered me $10. It actually makes a difference to me if Player 1 is dividing $12, $20, or $100. This is primarily because I need to know how the split was made. I need to know how Player 1 divided the sum between the two of us, and my decision to either reject or accept the proposal will be dependent on this knowledge. If I reject the proposal, none of us will get anything. If the offer is less than 20% of the sum, I will reject it. As such, if the sum was $12 or $20, I will accept since the $10 that Player 1 is offering me is more than 20%. Nonetheless, I will reject the offer if the sum was $100 since Player 1 would be offering me less than 20%. Small offers are often rejected. The choice of correct offer is formed by using some concepts of equity, hence offers which offend the receivers fundamental sense of fairness are rejected (Stevens, 2008).
It makes a difference if the money belongs to Player 1, if it is the money he won in the previous game, or money given for division. If the money belongs to him, then it is okay and fair if he offers me $10 even if the sum was $100; I will accept the offer. It also does not make any difference if it is the money which he won in a previous game, since the money is his and I will accept the offer not considering the sum or how the division was made. However, it makes a difference if the money was given to him for division since the money is not his and the division has to be fair and equitable. It does not make a difference if Player 1 is a computer, an individual, or an organization since both of us are players and the rules of the game have to be followed; an offer would be rejected or accepted depending on where the money is coming from and/or the size of the offer proportionate to the sum.
Response to question 2
Tragedy of the commons essentially takes place whenever people ignore the group’s or the society’s well-being as they pursue their own personal gains. Examples include the following: assuming there are 10 neighboring farmers who keep various animals. If they increase the quantity of their animals living on a shared parcel of land, in the end the land would become depleted and unable to support all the animals, something that is disadvantageous to all farmers. In this example, the grassland is open to all herders to herd their animals, and this commons is availa...