Quick philosophy/economics question

[Mo0o]

So our assignment involves looking at different reward structures to determine whether they're considered to be a prisoner's dilemma or not. Here's teh one presented:

.................b1...............b2
........a1...(6,6).............(3,10)
........a2...(10,3)............(4,5)

The matrix shows numerical positive objective payoffs as well as what choice each player must do to reach such payoffs. So in this matrix, both players have dominant stratgies, player A to choose option a2 and player B to choose option b2 to maximize their payoffs. So the requirement that both players have dominant strategies is fulfilled. But that situation (a2,b2) doesn't seem to be praeto-dominated by the usual option of (a1,b1) but rather two situations (a2,b1) and (a1,b2). Can an option by praeto-dominated by two different (and equal) options and still be considered a prisoner's dilemma?

edit; oh wait i think i answerd my own question. I wasn't clear on what praeto-dominated meant

 

[Goosemaster]

woah.

 

[fishmonger12]

Originally posted by: Mo0o
So our assignment involves looking at different reward structures to determine whether they're considered to be a prisoner's dilemma or not. Here's teh one presented:

.................b1...............b2
........a1...(6,6).............(3,10)
........a2...(10,3)............(4,5)

The matrix shows numerical positive objective payoffs as well as what choice each player must do to reach such payoffs. So in this matrix, both players have dominant stratgies, player A to choose option a2 and player B to choose option b2 to maximize their payoffs. So the requirement that both players have dominant strategies is fulfilled. But that situation (a2,b2) doesn't seem to be praeto-dominated by the usual option of (a1,b1) but rather two situations (a2,b1) and (a1,b2). Can an option by praeto-dominated by two different (and equal) options and still be considered a prisoner's dilemma?

pshh. Social science majors.

 

[BigJ]

Originally posted by: fishmonger12

Originally posted by: Mo0o
So our assignment involves looking at different reward structures to determine whether they're considered to be a prisoner's dilemma or not. Here's teh one presented:

.................b1...............b2
........a1...(6,6).............(3,10)
........a2...(10,3)............(4,5)

The matrix shows numerical positive objective payoffs as well as what choice each player must do to reach such payoffs. So in this matrix, both players have dominant stratgies, player A to choose option a2 and player B to choose option b2 to maximize their payoffs. So the requirement that both players have dominant strategies is fulfilled. But that situation (a2,b2) doesn't seem to be praeto-dominated by the usual option of (a1,b1) but rather two situations (a2,b1) and (a1,b2). Can an option by praeto-dominated by two different (and equal) options and still be considered a prisoner's dilemma?

pshh. Social science majors.

Game theory is also a mathematics course btw 😉

 

[fishmonger12]

Originally posted by: BigJ

Originally posted by: fishmonger12

Originally posted by: Mo0o
So our assignment involves looking at different reward structures to determine whether they're considered to be a prisoner's dilemma or not. Here's teh one presented:

.................b1...............b2
........a1...(6,6).............(3,10)
........a2...(10,3)............(4,5)

The matrix shows numerical positive objective payoffs as well as what choice each player must do to reach such payoffs. So in this matrix, both players have dominant stratgies, player A to choose option a2 and player B to choose option b2 to maximize their payoffs. So the requirement that both players have dominant strategies is fulfilled. But that situation (a2,b2) doesn't seem to be praeto-dominated by the usual option of (a1,b1) but rather two situations (a2,b1) and (a1,b2). Can an option by praeto-dominated by two different (and equal) options and still be considered a prisoner's dilemma?

pshh. Social science majors.

Game theory is also a mathematics course btw 😉

From what I understand, the core body of knowledge in mathematics doesn't revolve around using a bunch of trumped up vocabulary to overcomplicate simple problems.

 

[Mo0o]

Originally posted by: fishmonger12

Originally posted by: BigJ

Originally posted by: fishmonger12

Originally posted by: Mo0o
So our assignment involves looking at different reward structures to determine whether they're considered to be a prisoner's dilemma or not. Here's teh one presented:

.................b1...............b2
........a1...(6,6).............(3,10)
........a2...(10,3)............(4,5)

The matrix shows numerical positive objective payoffs as well as what choice each player must do to reach such payoffs. So in this matrix, both players have dominant stratgies, player A to choose option a2 and player B to choose option b2 to maximize their payoffs. So the requirement that both players have dominant strategies is fulfilled. But that situation (a2,b2) doesn't seem to be praeto-dominated by the usual option of (a1,b1) but rather two situations (a2,b1) and (a1,b2). Can an option by praeto-dominated by two different (and equal) options and still be considered a prisoner's dilemma?

pshh. Social science majors.

Game theory is also a mathematics course btw 😉

From what I understand, the core body of knowledge in mathematics doesn't revolve around using a bunch of trumped up vocabulary to overcomplicate simple problems.

it's not a simple problem... it's an interesting logic situation where all players acting out of self interest do not act in the interest of the group. and numbers play a great deal in modeling the situation

 

[Praxis1452]

explain simply. I understand the prisoner's dillemma. what is praeto-dominate?

 

[chcarnage]

A pareto-optimal field is one that one player alone can't leave in the next round of the game. In this example, (4,5) is pareto-optimal because each player would lose something by changing his strategy (and scoring only 3 points). And strategy 2 is therefor dominant.

But other than in the textbook prisioners' dilemma, the best outcome for the entire group of players isn't a1/b1 because the group scores higher if one player choses strategy 1 and the other strategy 2 (13 vs 12 points). And my opinion is that this is an essential characteristic of the prisioners' dilemma, where the sum for chosing strategy 1 is higher than for one player chosing strategy 1 and the other one strategy 2.