From a strict game theory perspective, zero sum games have a technical definition, ie being zero sum, that is rarely met in practice. A zero sum game is one where the opponents are perfectly opposed to each other. So it does not contain any outcomes that all players consider bad. In a zero some game, for one player to win, another must loose. For one player to loose, another must win. (Game theory usually only talks about 2 player zero sum games, because these have a nice mathematical structure. )
If we take a perfectly zero sum game, and give one player the opportunity to headbutt a wall (which gives them −1 util and doesn’t effect the rest of the game) then the game is no longer zero sum. If you take 2 zero sum games and play one after the other, the result is not in general zero sum.
To see this consider Alice and Bob, two expected money maximisers playing a game that always has exactly one winner. They each get a (possibly different) prize for winning. (and can’t transfer money between each other) A game where Alice can win £10, or Bob can win £1 is zero sum (up to Linear transformation of utility function). But follow that with a game where Alice can win £1, and Bob can win £10, and the result is no longer zero sum.
The set of games I think you are really talking about are the games where there is a big difference between the Nash equilibria society often lands in, and the Parito optimal.
In a war, a parito improvement would involve neither side making any weapons, and working together to divide up resources in proportion to how they would be divided if they did have a war.
In status games, a parito improvement might be neither side buying expensive status symbols, instead buying something they will actually enjoy.
It depends on the utilities. And what the other option is. Take a war between Aland and Bland. Look at the results. Does Aland take all Blands territory? The parito improvement is to just do that without shooting at each other first.
In status games, what exactly do you mean by status. Is it possible for everyone to just decide to hand bob high status. If so, a parito improvement is just to hand status out in the same way.
Here is a toy model of war. Each country has a utility of 100 for winning (say winning control over a disputed stretch of land), and a utility of −1 for buying tanks, whichever side has more tanks wins. Both sides buy lots of tanks, and one side wins. A parito improvement would be for that neither side buys any tanks, and the side that would win the war gets the land.
The war Pareto improvement is not realistic from a game-theory perspective if both of the players act rationally. Obviously, one can always imagine some deus-ex-machina-Pareto-improvement (A silly example would be to imagine that one of the sides creates a god that changes the game completely and prevents the war, and brings both sides to a post-scarcity utopia). Still, I think it misses the point as the idea is to play within the realistic versions of the games. Your toy model solution requires a level of cooperation/ability to predict the future that doesn’t exist.
Status is hierarchical and always relative; by increasing the status of bob, you effectively lower the status of all the other players. If you increased the status of everyone by 10% (whatever that means...), reality wouldn’t change at all.
A pareto improvement is a change that harms no one and helps at least one person. The options I’ve outlined don’t always happen. (Although countries often don’t go to war, it isn’t clear if this is cooperating in a prisoners dilemma, or that they expect going to war to be worse for them.) The point of a Pareto improvement is that it is something within the combined action space. Ie something they would do if they somehow gained magical coordination ability. It doesn’t realy on any kind of magical capabilities, just different decisions. If both agents are causal decision theorists, and the war resembles a prisoners dilemma situation, “cooperate—cooperate” might be unrealistic, but its still a pareto improvement.
From a strict game theory perspective, zero sum games have a technical definition, ie being zero sum, that is rarely met in practice. A zero sum game is one where the opponents are perfectly opposed to each other. So it does not contain any outcomes that all players consider bad. In a zero some game, for one player to win, another must loose. For one player to loose, another must win. (Game theory usually only talks about 2 player zero sum games, because these have a nice mathematical structure. )
If we take a perfectly zero sum game, and give one player the opportunity to headbutt a wall (which gives them −1 util and doesn’t effect the rest of the game) then the game is no longer zero sum. If you take 2 zero sum games and play one after the other, the result is not in general zero sum.
To see this consider Alice and Bob, two expected money maximisers playing a game that always has exactly one winner. They each get a (possibly different) prize for winning. (and can’t transfer money between each other) A game where Alice can win £10, or Bob can win £1 is zero sum (up to Linear transformation of utility function). But follow that with a game where Alice can win £1, and Bob can win £10, and the result is no longer zero sum.
The set of games I think you are really talking about are the games where there is a big difference between the Nash equilibria society often lands in, and the Parito optimal.
Can you provide an example of how you can get a significant Pareto improvement in the mentioned games?
In a war, a parito improvement would involve neither side making any weapons, and working together to divide up resources in proportion to how they would be divided if they did have a war.
In status games, a parito improvement might be neither side buying expensive status symbols, instead buying something they will actually enjoy.
These are not Pareto Improvements as they will lower the utility of the winning side...
It depends on the utilities. And what the other option is. Take a war between Aland and Bland. Look at the results. Does Aland take all Blands territory? The parito improvement is to just do that without shooting at each other first.
In status games, what exactly do you mean by status. Is it possible for everyone to just decide to hand bob high status. If so, a parito improvement is just to hand status out in the same way.
Here is a toy model of war. Each country has a utility of 100 for winning (say winning control over a disputed stretch of land), and a utility of −1 for buying tanks, whichever side has more tanks wins. Both sides buy lots of tanks, and one side wins. A parito improvement would be for that neither side buys any tanks, and the side that would win the war gets the land.
The war Pareto improvement is not realistic from a game-theory perspective if both of the players act rationally. Obviously, one can always imagine some deus-ex-machina-Pareto-improvement (A silly example would be to imagine that one of the sides creates a god that changes the game completely and prevents the war, and brings both sides to a post-scarcity utopia). Still, I think it misses the point as the idea is to play within the realistic versions of the games. Your toy model solution requires a level of cooperation/ability to predict the future that doesn’t exist.
Status is hierarchical and always relative; by increasing the status of bob, you effectively lower the status of all the other players. If you increased the status of everyone by 10% (whatever that means...), reality wouldn’t change at all.
A pareto improvement is a change that harms no one and helps at least one person. The options I’ve outlined don’t always happen. (Although countries often don’t go to war, it isn’t clear if this is cooperating in a prisoners dilemma, or that they expect going to war to be worse for them.) The point of a Pareto improvement is that it is something within the combined action space. Ie something they would do if they somehow gained magical coordination ability. It doesn’t realy on any kind of magical capabilities, just different decisions. If both agents are causal decision theorists, and the war resembles a prisoners dilemma situation, “cooperate—cooperate” might be unrealistic, but its still a pareto improvement.