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同主题阅读：面试题 - white elephant gift exchange
[版面：金融工程] [首篇作者：person] , 2006年10月29日12:21:10
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发信人: person (幸福的黄马甲), 信区: Quant
标 题: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 12:21:10 2006)
上来他问我只不知道white elephant gift exchange，我说不知道，于是他介绍问题如下
设置
1. 2n (n>3)个礼物，价值依次为1至2n的整数，标价公开
2. 有2n个人，编号1至2n， 人分两组，编号为奇数的一组，编号为偶数的一组
3. 胜负：
游戏终止时，若编号为奇数的一组拿到礼物总值大于n(n+1)，奇数的一组赢
若编号为偶数的一组拿到礼物总值大于n * n，偶数的一组赢
否则平
规则
1. 开始时，没有人有礼物，
2. 由没有礼物的编号最大的人选礼物
他/她可以选一样还没人要的礼物，
或他/她可以抢一样已经有人要的礼物，但是
这个礼物不能是上一轮中刚被抢过的礼物
也不能是已被抢过三次的礼物
3. 若不是每个人都有礼物了，返回第2条
问哪个组可以必胜，如何？
--
我花开后百花杀
满城尽带黄马甲
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 69.110.]
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skydive
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发信人: skydive (跳跳~~备战备荒为人民), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 12:25:45 2006), 转信
被抢过礼物的人转变成没礼物的？
下一轮立刻可以参与？
【 在 person (幸福的黄马甲) 的大作中提到: 】
: 上来他问我只不知道white elephant gift exchange，我说不知道，于是他介绍问题
如下
: 设置
: 1. 2n (n>3)个礼物，价值依次为1至2n的整数，标价公开
: 2. 有2n个人，编号1至2n， 人分两组，编号为奇数的一组，编号为偶数的一组
: 3. 胜负：
: 游戏终止时，若编号为奇数的一组拿到礼物总值大于n(n+1)，奇数的一组赢
: 若编号为偶数的一组拿到礼物总值大于n * n，偶数的一组赢
: 否则平
: 规则
: 1. 开始时，没有人有礼物，
: ...................
--
※ 来源:·BBS 未名空间站 mitbbs.com·[FROM: 69.118.]
person
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发信人: person (幸福的黄马甲), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 12:29:30 2006)
是
只是由于规则不能把刚被抢走的礼物抢回来
【 在 skydive (跳跳~~备战备荒为人民) 的大作中提到: 】
: 被抢过礼物的人转变成没礼物的？
: 下一轮立刻可以参与？
: 如下
--
我花开后百花杀
满城尽带黄马甲
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 69.110.]
juedr
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发信人: juedr (我的不是你的我的前世今生), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 14:55:25 2006)
平。
分析一下可以看出：
1，偶数方先拿，然后奇数方，如此循环下去，无论发生抢夺与否。
2，任何一个数三次易手后就定了。所以先选择这个数的一方最后肯定得不到这个数。
3，由2知，最佳策略是选择没有OPEN的数里面最小的一个。把大数的初夜权留给对方，
最终再夺过来。
因此，偶数方选择的是开始的选择次序是1，3，5。。。奇数方选择的是2，4，6。。。
最后双方交换。
所以最后结果是平。
"上来他问我只不知道white elephant gift exchange，我说不知道，于是他介绍问题
如下
设置
1. 2n (n>3)个礼物，价值依次为1至2n的整数，标价公开
2. 有2n个人，编号1至2n， 人分两组，编号为奇数的一组，编号为偶数的一组
3. 胜负：
游戏终止时，若编号为奇数的一组拿到礼物总值大于n(n+1)，奇数的一组赢
若编号为偶数的一组拿到礼物总值大于n * n，偶数的一组赢
否则平
规则
1. 开始时，没有人有礼物，
2. 由没有礼物的编号最大的人选礼物
他/她可以选一样还没人要的礼物，
或他/她可以抢一样已经有人要的礼物，但是
这个礼物不能是上一轮中刚被抢过的礼物
也不能是已被抢过三次的礼物
3. 若不是每个人都有礼物了，返回第2条
问哪个组可以必胜，如何？"
--
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 24.61.]
person
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发信人: person (幸福的黄马甲), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 16:38:19 2006)
谢谢， 但我不是很明白你的解答
1，“偶数方先拿，然后奇数方，如此循环下去，无论发生抢夺与否”
如编号为2n的人先挑x，编号为2n-1的人抢x, 编号2n的人再挑y，
下面轮到编号2n-2的人挑或抢
所以此时序列是偶数方，奇数方，偶数方，偶数方....
2. "先选择这个数的一方最后肯定得不到这个数"
若如你的例中所说“偶数方选择的是开始的选择次序是1.. ”
奇数方以后可永不抢1号礼物啊，那1号礼物不就死在偶数方了？
【 在 juedr (我的不是你的我的前世今生) 的大作中提到: 】
: 平。
: 分析一下可以看出：
: 1，偶数方先拿，然后奇数方，如此循环下去，无论发生抢夺与否。
: 2，任何一个数三次易手后就定了。所以先选择这个数的一方最后肯定得不到这个数。
: 3，由2知，最佳策略是选择没有OPEN的数里面最小的一个。把大数的初夜权留给对方，
: 最终再夺过来。
: 因此，偶数方选择的是开始的选择次序是1，3，5。。。奇数方选择的是2，4，6。。。
: 最后双方交换。
: 所以最后结果是平。
: "上来他问我只不知道white elephant gift exchange，我说不知道，于是他介绍问题
--
我花开后百花杀
满城尽带黄马甲
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 69.110.]
zgsun
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发信人: zgsun (源泉), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 17:06:27 2006)
How do you define next round?
Does round mean at least a new item should be openned? Or it means someone
makes a decision steal/getnew?
【 在 person (幸福的黄马甲) 的大作中提到: 】
: 上来他问我只不知道white elephant gift exchange，我说不知道，于是他介绍问题
如下
: 设置
: 1. 2n (n>3)个礼物，价值依次为1至2n的整数，标价公开
: 2. 有2n个人，编号1至2n， 人分两组，编号为奇数的一组，编号为偶数的一组
: 3. 胜负：
: 游戏终止时，若编号为奇数的一组拿到礼物总值大于n(n+1)，奇数的一组赢
: 若编号为偶数的一组拿到礼物总值大于n * n，偶数的一组赢
: 否则平
: 规则
: 1. 开始时，没有人有礼物，
: ...................
--
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 24.98.]
person
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发信人: person (幸福的黄马甲), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 17:53:38 2006)
我从没提到过next round啊
如果一定要的话，应该是
someone makes a decision steal/getnew
当每个人都有礼物的时候，游戏就结束了，没有下一轮
【 在 zgsun (源泉) 的大作中提到: 】
: How do you define next round?
: Does round mean at least a new item should be openned? Or it means someone
: makes a decision steal/getnew?
: 如下
--
我花开后百花杀
满城尽带黄马甲
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 69.110.]
zgsun
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发信人: zgsun (源泉), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 19:48:29 2006)
I mean this.
这个礼物不能是"上一轮"中刚被抢过的礼物
Suppose A just steal x from B, and B steals y from C, now can C steal from A?
If next round is defined that "only one new gift is open", C cannot steal
from A.
【 在 person (幸福的黄马甲) 的大作中提到: 】
: 我从没提到过next round啊
: 如果一定要的话，应该是
: someone makes a decision steal/getnew
: 当每个人都有礼物的时候，游戏就结束了，没有下一轮
--
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 24.98.]
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发信人: bushel (失乐园), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 19:59:15 2006), 转信
我怎么觉得是后拿的必胜阿
也就是单号必胜阿
【 在 person (幸福的黄马甲) 的大作中提到: 】
: 上来他问我只不知道white elephant gift exchange，我说不知道，于是他介绍问题
如下
: 设置
: 1. 2n (n>3)个礼物，价值依次为1至2n的整数，标价公开
: 2. 有2n个人，编号1至2n， 人分两组，编号为奇数的一组，编号为偶数的一组
: 3. 胜负：
: 游戏终止时，若编号为奇数的一组拿到礼物总值大于n(n+1)，奇数的一组赢
: 若编号为偶数的一组拿到礼物总值大于n * n，偶数的一组赢
: 否则平
: 规则
: 1. 开始时，没有人有礼物，
: ...................
--
※ 来源:·BBS 未名空间站 mitbbs.com·[FROM: 71.58.]
person
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发信人: person (幸福的黄马甲), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 20:00:00 2006)
sorry
yes, suppose A just steal x from B, and B steals y from C, now can C steal
from A.
【 在 zgsun (源泉) 的大作中提到: 】
: I mean this.
: 这个礼物不能是"上一轮"中刚被抢过的礼物
: Suppose A just steal x from B, and B steals y from C, now can C steal from
A?
: If next round is defined that "only one new gift is open", C cannot steal
: from A.
--
我花开后百花杀
满城尽带黄马甲
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oolong
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发信人: oolong (乌龙茶), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 20:18:34 2006), 转信
后拿的最后要求的分数也高阿
【 在 bushel (失乐园) 的大作中提到: 】
: 我怎么觉得是后拿的必胜阿
: 也就是单号必胜阿
: 如下
--
※ 来源:·BBS 未名空间站 mitbbs.com·[FROM: 137.132.]
person
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发信人: person (幸福的黄马甲), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Sun Oct 29 22:52:34 2006)
若even numbers好，the odd side也可以上来就抢even numbers啊
【 在 cashine (Who Am I) 的大作中提到: 】
: You're right.
: Basically no one will go for no.1, so there are really just 2n-1 gifts.
: At most they can be snatched (2n-1)*3 times which is odd.
: Now the gift-picking process is a rotation between even and odd number, so
: it is definite that the last snatch is from an even number person instead
of
: the odd number person.
: This means that "1" belongs to the odd group, hence they will lose.
: The even side should win.
: My strategy is, they always go for even numbers (2,4,...) or snatch odd
: numbers from the odd side, and the odd side will have to snatch these even
: ...................
--
我花开后百花杀
满城尽带黄马甲
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 69.110.]
zgsun
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发信人: zgsun (源泉), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Mon Oct 30 01:55:21 2006)
应该是偶数组赢.可以用归纳法证明偶数组至少能拿到2-2n的偶数(如果奇数组尽量使自
己的数字和大的话).
假设n=k-1的时候成立.并且这2k-2个数字是从3到2n.
最后拿数字的奇数组只能拿3,所以只可能有三种情况:(注)
A) 4被抢过一次.
B) 4被抢过两次.
C) 4被抢过三次.
n=k,考虑多两个数字1和2.两个组抢.图上画一下就知道任何哪种情况偶数组总能拿到4
和2(甚至4和3).
【 在 person (幸福的黄马甲) 的大作中提到: 】
: 上来他问我只不知道white elephant gift exchange，我说不知道，于是他介绍问题
如下
: 设置
: 1. 2n (n>3)个礼物，价值依次为1至2n的整数，标价公开
: 2. 有2n个人，编号1至2n， 人分两组，编号为奇数的一组，编号为偶数的一组
: 3. 胜负：
: 游戏终止时，若编号为奇数的一组拿到礼物总值大于n(n+1)，奇数的一组赢
: 若编号为偶数的一组拿到礼物总值大于n * n，偶数的一组赢
: 否则平
: 规则
: 1. 开始时，没有人有礼物，
: ...................
--
※ 来源:·BBS 未名空间站 http://mitbbs.com·[FROM: 24.98.]
Vishnu
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发信人: Vishnu (Time Dealer), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Mon Oct 30 06:31:16 2006), 转信
A same-group member can grab a high-numbered gift from his own group in
order to secure a gift, can't he?
【 在 zgsun (源泉) 的大作中提到: 】
: 应该是偶数组赢.可以用归纳法证明偶数组至少能拿到2-2n的偶数(如果奇数组尽量使自
: 己的数字和大的话).
: 假设n=k-1的时候成立.并且这2k-2个数字是从3到2n.
: 最后拿数字的奇数组只能拿3,所以只可能有三种情况:(注)
: A) 4被抢过一次.
: B) 4被抢过两次.
: C) 4被抢过三次.
: n=k,考虑多两个数字1和2.两个组抢.图上画一下就知道任何哪种情况偶数组总能拿到
4
: 和2(甚至4和3).
: 如下
: ...................
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发信人: person (幸福的黄马甲), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Mon Oct 30 06:32:08 2006)
谁说得对呢？
【 在 diehard75 (diehard) 的大作中提到: 】
: By the analysis, the even team will leave the gift 2n to player 1 because
: they know they have no chance to keep it.
: So we can reduce the problem to "we have gift 2n-1, 2n-2, ..., 1 and
player
: 2,
: 3, 4,..., 2n." By the same argument, player 2 can keep the gift 2n-1 (
player
: 1 won't take gift 2n-1 since he will take gift 2n).
: So recursively, odd team will have gift 2n, 2n-2, ... 2 and even team will
: have gift 2n-1, 2n-3, .. 1. So in the end, it will be a draw.
: This is just my analysis.
【 在 zgsun (源泉) 的大作中提到: 】
: 应该是偶数组赢.可以用归纳法证明偶数组至少能拿到2-2n的偶数(如果奇数组尽量使自
: 己的数字和大的话).
: 假设n=k-1的时候成立.并且这2k-2个数字是从3到2n.
: 最后拿数字的奇数组只能拿3,所以只可能有三种情况:(注)
: A) 4被抢过一次.
: B) 4被抢过两次.
: C) 4被抢过三次.
: n=k,考虑多两个数字1和2.两个组抢.图上画一下就知道任何哪种情况偶数组总能拿到
4
: 和2(甚至4和3).
: 如下
--
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发信人: Vishnu (Time Dealer), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Mon Oct 30 06:34:45 2006), 转信
It seems neither is a concrete proof.
【 在 person (幸福的黄马甲) 的大作中提到: 】
: 谁说得对呢？
: player
: player
: 4
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发信人: loveleader (hatefree), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Mon Oct 30 12:10:19 2006), 转信
偶数组赢. 下面是偶地理解,不知道对不对,请指正.
因为偶数组首先开始抢礼物,并且
如果偶数组想赢,就需要至少占据一个偶数号礼物.
因为每个礼物最多被抢三次,并且不能抢刚被抢过地.
所以基本第一次选地都会被抢走,但是除了接近
边界地时候不一样. 所以最后一轮抢夺会决定胜负.
那么偶得策略是: 让2n尽量抢最大地,
然后用2n-2最后中介,尽量hold住最大地,
显然这个最大地会被2n-1最后占有.
但是没有关系,这样可以保证最后会赢.
如果2n-1不这么干,那就更要输.
2n 抢 2n
2n-1 抢 2n-1
2n-2 抢 2n
2n 抢 2n-1
2n-1 抢 2n (2n done)
2n-2 抢 2n-1 (2n-1 done)
2n 抢 2n-2 ....
...
2n 抢 2(win)
1 抢 1.
假设n=4. 抢地过程是这样地:
8 -> 8 ( x-> y means x gets gift y)`
7->7
6->8
8->7
7->8 (8 done)
6->7 (7done)
8->6
5->5
4->6
8->5
5->6 (6done)
4->5 (4done)
8->4
3->3
2->4
8->3
3->4 (4done)
2->3(3done)
8->2 (win)
1->1
game over.
final even group (7,5,3,2) odd group (8,6,4,1)
【 在 person (幸福的黄马甲) 的大作中提到: 】
: 上来他问我只不知道white elephant gift exchange，我说不知道，于是他介绍问题
如下
: 设置
: 1. 2n (n>3)个礼物，价值依次为1至2n的整数，标价公开
: 2. 有2n个人，编号1至2n， 人分两组，编号为奇数的一组，编号为偶数的一组
: 3. 胜负：
: 游戏终止时，若编号为奇数的一组拿到礼物总值大于n(n+1)，奇数的一组赢
: 若编号为偶数的一组拿到礼物总值大于n * n，偶数的一组赢
: 否则平
: 规则
: 1. 开始时，没有人有礼物，
: ...................
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发信人: cashine (Who Am I), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Mon Oct 30 14:56:52 2006), 转信
I guess I was wrong in the previous post.
Think of it this way, each gift can be picked or snatched at most three
times, therefore gives a maximum of being in the hand of 4 people.
No one is going to snatch the "1" gift, therefore there are in total 4*(2n-1
)+1 rounds of picking or snatching, which is an odd number, since the
picking or snatching alternates from even to odd, this means the last person
to pick (because all other gifts have been snatched 3 times) will be from
the even group, so they have to pick 1.
The following argument does not apply to the case when people in each group
can snatch from each other.
Now think of the first person, he would not pick the large ones since they
will be snatched and finally in the hands of the opposite, so he should
start from the smallest, i.e., 2, the opposite won't need to snatch it, but
pick 3 instead, then the even group pick 4, none of them need to snatch from
the others because ultimately each group will have exactly what the other
group has after odd number of snatches, before anyone picks 1 and the game
ends.
So I guess the final result will be tied.
【 在 person (幸福的黄马甲) 的大作中提到: 】
: 若even numbers好，the odd side也可以上来就抢even numbers啊
: of
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发信人: cashine (Who Am I), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Mon Oct 30 14:57:51 2006), 转信
Think of 2 people playing the game,
with two gifts, 1 and 2.
you pick first, how can you win?
【 在 loveleader (hatefree) 的大作中提到: 】
: 偶数组赢. 下面是偶地理解,不知道对不对,请指正.
: 因为偶数组首先开始抢礼物,并且
: 如果偶数组想赢,就需要至少占据一个偶数号礼物.
: 因为每个礼物最多被抢三次,并且不能抢刚被抢过地.
: 所以基本第一次选地都会被抢走,但是除了接近
: 边界地时候不一样. 所以最后一轮抢夺会决定胜负.
: 那么偶得策略是: 让2n尽量抢最大地,
: 然后用2n-2最后中介,尽量hold住最大地,
: 显然这个最大地会被2n-1最后占有.
: 但是没有关系,这样可以保证最后会赢.
: ...................
--
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发信人: skydive (跳跳~~备战备荒为人民), 信区: Quant
标 题: Re: 面试题 - white elephant gift exchange
发信站: BBS 未名空间站 (Mon Oct 30 15:49:31 2006), 转信
n>3
that might matter.
【 在 cashine (Who Am I) 的大作中提到: 】
: Think of 2 people playing the game,
: with two gifts, 1 and 2.
: you pick first, how can you win?
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Just off Revolution Avenue in the Russian city of Voronezh 15 years ago stood a state-owned pelmennaya, a grubby cafe where surly matrons slopped grey dumplings into chipped bowls. Today, it is a franchise of Mango, the Spanish fashion chain – all smoked mirrors, halogen spotlights and low-rise jeans.
“The prices are still quite high for us,” muses Vera Cherkasova, a lawyer with a property company, admiring a tailored woollen cardigan. “But Russian women are prepared to spend a bit on looking nice.”
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Next door, the former Niva food store, which in the Soviet Union’s dying days sold little beyond tinned fish and lumps of lard, is now an Adidas franchise. The once-dowdy Rossiya department store nearby is a mini-mall with franchises of Benetton and Diesel. Grocery shoppers can choose from numerous modern supermarkets, two Russian-owned hypermarkets and a cash-and-carry run by Germany’s Metro. Little by little, cappuccino bars and mobile phone stores, McDonald’s outlets and Irish pubs are transforming this 1m-strong regional capital – even though the roads and other government services are worse than ever.
What is happening in Voronezh, 300 miles south of Moscow, is a powerful new phenomenon. Western-style retailing and international brands, largely confined a decade ago to metropolitan Moscow and St Petersburg, are spreading to cities across Russia. After the hardships of the 1990s, Russia is finally witnessing the rise of a prosperous post-Soviet middle class.
Politically and economically, this has become one of the most important, and least talked-about, trends in Russia today. While international attention has focused on President Vladimir Putin’s increasingly authoritarian approach, that tends to obscure what many Russians believe to be his main legacy – the extent to which they have, materially, become better off under his presidency.
Some international observers feel, moreover, that if democracy, press freedom and the rule of law are to flourish in Russia, that may depend on an assertive middle class pushing for such rights.
Those economic conditions are being created. Although the country is known abroad primarily as an exporter of raw materials, companies from carmakers to cosmetics giants now list Russia alongside China and India among their most dynamic consumer markets.
“What’s happening here is very exciting. We’re running to keep up,” says A G Lafley, chairman of Procter & Gamble, who was in Moscow last month to celebrate the consumer group’s 15th anniversary in Russia. Richard Smyth, general manager in Russia for Mars, echoes this, pointing to new production lines at a $200m (£105m, €157m) chocolate factory south of the capital. “Basically”, he says, “we can’t build it fast enough”.
The consumer boom is the fruit of nearly eight years of economic growth averaging 6.6 per cent – thanks in part to record oil and natural gas prices – since Russia’s debt default and financial crisis in 1998. Real wages and consumer spending are growing twice as fast. The average monthly wage was up 13.6 per cent year-on-year in September to $415 – still low, but four times what it was when Mr Putin became president in 2000.
Low housing and utility costs mean a relatively high proportion of Russians’ wages goes straight into disposable income. A lingering suspicion of banks, born of the 1998 crisis, also means spare cash is more likely to go into flat-screen television sets or washing machines than into savings accounts.
Russians are less wary of borrowing, however. Consumer credit has mushroomed from zero a few years ago to about $40bn – though at barely 5 per cent of gross domestic product, one-tenth of western European levels, there is plenty of room for growth.
Yet despite the progress, yawning inequalities exist – and overall trends are not wholly encouraging. Tatyana Maleva, a sociologist at Moscow’s Independent Institute for Social Policy, led a study in 2000-01 of Russia’s social structure. Analysing salaries and factors such as savings and property ownership, she classed fewer than 1 per cent of Russians as a super-rich elite. At the other extreme, 10 per cent of the 144m population lived in real poverty.
In between, 20 per cent formed a more-or-less comfortable middle class; just under 70 per cent were lower middle class – struggling, but able to afford a few consumer luxuries.
The picture already differed sharply from Soviet times. Then, too, says Ms Maleva, there was a privileged elite and poor underclass. But 80-90 per cent of Russians formed a middle layer where modest income differences were partly smoothed out by the Soviet command economy’s inability to produce goods for people to buy. (Many Russians amassed big rouble savings, only to see them wiped out by hyperinflation triggered by the 1990s “shock therapy” reforms.)
Six years after her study, Ms Maleva says the overall picture has not changed. Russia’s middle class is still around 20 per cent, but has got richer – because it includes those in thriving economic sectors such as natural resources and banking. The poor class has shrunk a little, thanks partly to government social programmes. But few of the 70 per cent lower middle class have made the jump to the next rung, its members working largely in the public sector or less successful parts of the economy.
“While incomes have been rising, there are those who have been winners and those who received much less,” says Ms Maleva.
But with tens of millions of Russians now having at least a foot in the door of the consumer society, foreign and domestic investors are starting to look beyond oil and gas. Apart from a few big energy and metals deals, acquisitions by Coca-Cola and Heineken and a big domestic retail merger have been among the largest transactions of the past 18 months.
Russia’s “oligarchs” have spotted the consumer market as a growth opportunity largely free of the political risk and state interference now associated with energy. Mikhail Fridman, head of the Alfa Group conglomerate, is a big shareholder in the TNK-BP oil joint venture but has consumer exposure through Alfa Bank and a stake in Vimpelcom, a mobile phone group.
In his biggest consumer venture yet, Mr Fridman in April merged his Perekryostok supermarket chain with Pyaterochka, a St Petersburg-based discounter, to create Russia’s biggest grocery retailer with nearly 900 stores and a target of $6bn annual sales by 2008.
“We believe retailing generally, and especially food retailing, will develop very fast here. And we are at the leading edge,” says Mr Fridman.
Even $6bn sales would give the chain only a few percentage points of a large but unconsolidated food retail market, which the Economist Intelligence Unit forecasts will grow from $113bn last year to $203bn in 2010. It expects total retail sales will double in the same period from $245bn to $526bn – taking Russia from 12th- to ninth-biggest retail market in the world.
With “modern” formats – rather than markets, street kiosks or unrefurbished Soviet-era stores – accounting for less than one-third of the retail market, the opportunity is huge.
Strangely, perhaps, retailing’s global giants have been slow to take up the challenge. Wal-Mart of the US, France’s Carrefour and the UK’s Tesco have so far stayed away, citing the risks and difficulties of operating in Russia. But Auchan of France, Germany’s Rewe as well as Metro and Turkey’s Migros Turk have all entered the Russian grocery market. France’s Leroy Merlin, Germany’s OBI and the UK-based Kingfisher are chasing consumers’ roubles in the home improvement sector. Britain’s Dixons last year acquired an option to buy Eldorado, a Russian electrical retailer, for $1.9bn by 2011.
Sweden’s Ikea is playing a pioneering role by developing not just its own furniture stores but shopping malls alongside, housing partner retailers such as Auchan and OBI, multiplex cinemas and fast food courts. After three such Mega-Malls opened in Moscow since 2002 and one in Kazan, more are due to arrive over the next year in other 1m-plus cities – St Petersburg, Nizhny Novgorod, Yekaterinburg, Samara, Rostov-on-Don and Novosibirsk.
While other foreign retailers dither, budding Russian chains are scurrying to raise expansion capital before the competition arrives. Retailers are well represented among the flood of Russian initial public offerings on the London Stock Exchange.
In a headquarters surrounded by new shopping centres and apartments in a St Petersburg suburb, Oleg Zherebtsov, chief executive of Lenta, is one such retailer. He jokes that when his chain opened its first warehouse-style store in 1999, “we thought we had invented the concept”. Now aware that it did not introduce hypermarket retailing to the world, Lenta still hopes to pioneer it in many Russian cities. It opened last month in Astrakhan and Novosibirsk, adding to nine existing St Petersburg hypermarkets with $700m annual sales.
Foreigners already dominate some consumer segments. Scottish & Newcastle and Carlsberg – which jointly own Baltika, the market leader – along with InBev and Heineken control much of a beer market that has doubled since 1999 to become the world’s fifth biggest.
Similar changes are now expected in higher-value sectors. Sales of foreign cars grew 58 per cent last year to about 400,000, overtaking sales of local brands for the first time, and Boston Consulting Group forecasts they will reach 900,000 by 2010. That could put pressure on Avtovaz, maker of the Lada, which still churns out 70 per cent of all cars assembled in Russia.
Avtovaz is a rare case of state intervention in a consumer segment: Rosoboronexport, a state arms agency, seized control of the struggling Soviet-era behemoth last year and pledged huge investment. That may reflect the social and political importance of a manufacturer employing 120,000 and reckoned directly or indirectly to support up to half a million people.
But the government has encouraged foreign manufacturers to open assembly plants, provided they use some local components. Ford is adding more expensive models to lines that produce the Focus, Russia’s best-selling foreign car. VW, Toyota, Nissan, General Motors and China’s Great Wall are among 15 foreign manufacturers with existing or planned assembly lines, set to double the country’s output to 2m cars a year within a few years.
As Russians get richer, entertainment and travel should also flourish. Restaurant menus are being translated into Russian in resorts across Europe, while Turkey and Egypt are becoming to Russians what Spain was for Britons in the 1970s. Mohamed Rachid, Egypt’s trade minister, says 1m Russians visited last year, and the total could reach 1.5m in two years.
“Russian tourists coming to Egypt are the highest spenders,” he adds. “They might take cheaper packages, but once there they spend more than all the other Europeans.”
Could today’s boom be followed by a 1998-style bust? With Russia’s public coffers overflowing with petrodollars, and big efforts in recent years to reduce debts, a default looks a remote possibility. But dependence on energy and raw material exports makes the economy vulnerable to any correction in commodity prices. Even if the good times continue, growth in disposable incomes is expected to slow towards the level of overall GDP growth by about 2010.
One other big question remains: Why is Russia’s Mango-clad, Ford-driving, Egypt-holidaying middle class not becoming more politically assertive? Some suggest Russians are too busy enjoying the comparative stability and prosperity the Putin years have brought to protest about the accompanying erosion of political and media freedom.
“In the early 1990s our people were paupers – and it’s ridiculous to say they were free,” Vladislav Surkov, a senior aide to Mr Putin seen as the Kremlin’s chief ideologist, said recently. “When you have a car to ride in and things to buy – that’s freedom.”
A poll this month by the Levada Center, an independent pollster, showed how successful United Russia, the political party whose main credo is loyalty to Mr Putin, has been at capturing the support of the middle class (which Levada estimates at 15 per cent of the population rather than 20 per cent).
Middle-class support for United Russia was 55 per cent, against 48 per cent among the rest of the population. And support for the Communist party in the middle class was markedly lower than by others (8.5 per cent against 22 per cent). Support for the liberal Yabloko party – perhaps the closest Russia has to a western-style social democratic party – was a mere 5 per cent among the middle class and 3 per cent among the rest.
Stephen Jennings, chief executive of Renaissance Capital, a Moscow investment bank, believes pressure for change may grow out of more prosaic, but concrete, issues.
“You have a good job, you have money, you have a nice dacha, but you can’t get there because the roads are so terrible,” he says. “I think the next big wave of change will be more bottom-up. That’s why this middle-class phenomenon is so powerful.”