人工智能博弈论中的功利主义与平等主义分配
假设我有两个玩家：玩家 A 和玩家 B，他们对资源有偏好（让我们笼统地使用术语“资源”）。他们的偏好可能是：
{p} {q} {p,q} {}
A 10 15 20 0
B 5 5 10 1
这表示两个玩家可以拥有一种资源，也可以两者都拥有，也可以没有。数字越大，玩家就越想要它。
我相信“功利主义”观点是最大化总体分配，因此这将是以下两种分配：
A：{p，q}和 B：{}，
因为即使 B 不太高兴，它也会增加到 21 [幸福 1 :-( ]。
我的问题是平等主义者会做什么（参见 wiki：1) 分配是（如果有的话）？我不确定如何从上表中正确计算这一点？
谢谢:)。
Let's say I have two players: Player A and Player B and they have preferences over what resources (let's just be general and use the term 'resource'). Their preferences could be:
{p} {q} {p,q} {}
A 10 15 20 0
B 5 5 10 1
This says that the two players can have one resource, both or none. The greater the number the more the player wants it.
I believe the 'utilitarian' view would be to maximise the allocation overall so this would be the following two allocations:
A: {p,q} and
B: {}
because it adds to 21 even though B is not very happy [happiness 1 :-( ].
My question is what would the egalitarian (see wiki: 1) allocations be (if there are any)? I'm not sure how this would be properly calculated from the above table?
Thanks :).
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在严格平等的解决方案中，每个人都获得相同的价值。在示例中这是不可能的。
然而，平等主义的社会福利解决方案被定义为最大化任何代理人收到的最小价值的解决方案（参见我的多智能体系统教科书）
在这种情况下，两种解决方案之间存在联系：
您可以根据自己的需要进一步完善平等主义社会福利解决方案概念。
In a strictly egalitarian solution everyone receives the same value. That is not possible in the example.
However, the egalitarian social welfare solution is defined as that which maximizes the minimun value received by any agent (see page.79 of my multiagent systems textbook)
In this case, there is a tie between two solutions:
You can further refine egalitarian social welfare solution concept as you see fit.
假设：
1. 不能将相同的资源提供给两个玩家。
2. 资源被标识为 p 或 q。
3. 所有资源必须分配给一个或另一个玩家。
4.“平等分配”意味着两个玩家获得相同的分数。
那么这是不可能的，因为除了可以为两个玩家提供 p 的组合之外，A 行和 B 行中的分数都不相同。
假设：
4.“平均分配”意味着两个玩家的分数之间的差异被最小化。
那么可能性是：
给 A:{p} B:{q} 的最小差值为 5
假设：
3. 所有资源可以分配给一个玩家或另一个玩家，也可以不分配给任何一个玩家。
那么可能性是：
A:{} B:{} 的最小差值为 1
Assuming:
1. That the same resource cannot be given to both players.
2. That resources are identified as either p or q.
3. That all resources must be allocated to one player or the other.
4. That "egalitarian allocations" mean that both players get the same score.
Then it is not possible, since none of the scores are the same in the A and B rows, except for a combination that would supply p to both players.
Assuming instead:
4. That "egalitarian allocations" mean that the difference between the scores of the two players is minimized.
Then the possibilities are:
Giving a minimum difference of 5 for A:{p} B:{q}
Assuming instead:
3. That all resources may be allocated to one player or the other, or given to neither.
Then the possibilities are:
Giving a minimum difference of 1 for A:{} B:{}