Reciprocity problem set anthropology

Reciprocity problem set anthropology

1. Is rock, paper, and scissors a game?
2. If your opponent chooses the rock strategy, what is your best response?

 

3. If you choose the paper strategy, what is your opponent’s best response?

 

Evolutionary game theory is a useful tool for studying the evolution of alternative designs of organisms because the process of evolution by natural selection is a process by which relatively better designs (better = achieve higher fitness payoffs) are selected to spread in the population. So, the evolutionary process sets different designs (different alleles) against each other in games (situations) that recur across generations.  An understanding of game theory gives us insights into the process and results of evolution.  Depending on the “game”, designs can be said to have strategies at the molecular level (e.g., the rate of cell growth, types of immune system), the morphological level (e.g., differences in body size), and the behavioral strategy (e.g., help close kin, defer when overmatched) etc.

 

4. Suppose there is a population of organisms all of whom are wired to play the rock strategy. (a) What happens when they play each other? Does the population evolve?  Suppose further that these organisms survive and reproduce based on their rates of winning. Now consider the fate of a mutation that appears with the paper strategy appears and starts to interact with the other rock strategy organisms. (b) What would happen in this population in terms of the relative frequency of the two strategies?  (When an allele spreads and becomes 100% of the population, it is said to go to fixation.)

 

 

5. An evolutionarily stable strategy (or ESS) is a strategy which, if adopted by a population of players, cannot be outcompeted by any alternative strategy that is initially low frequency. Now suppose the rock strategy organisms in the population in the previous question are fully supplanted by the paper strategy organisms. Is this paper strategy in this population an evolutionarily stable strategy? What would happen if one mutant with the scissors strategy appears and start to interact with other paper strategies?

 

6. Can you predict possible long term group dynamics in this population in terms of the rock, paper, and scissors strategy frequencies? Would any strategy go to a fixation? Or would the population shows some cyclical pattern?

 

 

Part 2. The prisoner’s dilemma

 

		Igor
		don’t bring gun(cooperate)	bring gun(defect)
You	don’t bring gun(cooperate)	get cocaine, get $20,000	lost $20,000, gets cocaine & $20,000
	bring gun	get cocaine & keep $20,000 / loses cocaine	get nothing, get nothing

 

 

Or this is a general version of prisoner’s dilemma payoff matrix

		Player B
		Cooperate	Defect
Player A	Cooperate	A’s payoff R, B’s payoff R(informally: win-win)	A’s payoff S, B’s payoff T(informally: big loss, big win)
	Defect	A’s payoff T, B’s payoff S(informally: big win, big loss)	A’s payoff P, B’s payoff P(informally: lose, lose)

Where T stands for Temptation to defect, R for Reward for mutual cooperation, P for Punishment for mutual defection and S for Sucker’s payoff. To be defined as prisoner’s dilemma, the following inequalities must hold: T > R > P > S.

7. What is your best response to Igor’s choice, if Igor was not bringing a gun?
8. What is your best response to Igor’s choice, if Igor was bringing a gun?
9. Given your answers to question 7 and 8, what would you choose to do, if your only goal were attaining the best payoff for yourself?
10. What about Igor? What should Igor do if his only goal is obtaining the best payoff?
11. What is the payoff that each of you end up with? Compare it with the payoff that each of you would have received, had both of you chosen the other strategy.

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