<p>One thing that goes towards indifference happening in economics is <a href="https://en.wikipedia.org/wiki/Granularity" rel="nofollow">granularity</a>. In simple terms, making a <em>marginally better</em> offer to someone is not enough to offset preferences away from indifference as indifference is a zone of payment (say, $[a-\epsilon, a+\epsilon]$, with $\epsilon$ the granularity of the agent) rather than a single payment.</p>

<p>See for example <a href="https://www.sss.ias.edu/files/papers/econpaper76.pdf" rel="nofollow">bottom of page 8</a> here in <em>Consistency, Heterogeneity, and Granularity of Individual Behavior under Uncertainty</em>, Choi <em>et al.</em>, 2007</p>

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2015-12-19T14:14:24.323Z
While granularity is certainly interesting, how does this answer the question?
Giskard
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2015-12-19T14:23:45.847Z
@denesp because it renders marginal increments useless, thus answering the question: setting a "marginally" better payment is not feasible
VicAche
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2015-12-19T14:26:03.520Z
So why not set a payment that is discretely better? Say $a + \epsilon$? I think the OP wants to know why you can be sure of acceptance with indifference.
Giskard
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2015-12-19T14:28:25.287Z
@denesp if he makes a discretely better payment he has to choose to do so, at a distinguishable cost for himself (supposing comparable granularities for both agents), so it represents a different situation from the one presented in the provided paper.
VicAche
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2015-12-19T13:45:49.180Z
2015-12-19T13:45:49.180Z
VicAche
<p>Because otherwise you would not have subgame perfect equilibria. Suppose I have an item you need and the item is worthless to me. I would be happy to give you the item for any positive amount of money. If you give me no money for it, I am indifferent, both giving you the item and not giving you the item is an optimal choice for me. Just to be clear: we are not bargaining. You set I price and I will take it or leave it. </p>

<p>If you offer price 0 and I give you the item that is an equilibrium. No one could have made a better choice given the other person's choice.
<br> If you offer price 0 and I do not give you the item that is not an equilibrium, because I would give you the item for any small positive payment and you would be willing to pay that, so you could have made a better move.
<br> If you offer price $2a&gt;0$ I will give you the item. But this is not an equilibrium. You could also have offered me $a$, which is also positive, and I would also have given you the item then. So you could have saved some money, your original move was not optimal.</p>

<p>Because there is no smallest positive number, the only equilibrium in such cases is when one side is indifferent.</p>

CC BY-SA 3.0
2015-12-19T13:48:39.450Z
This supposes no negotiation power whatsoever from the seller side, which should be willing to sell at a gain if he's allowing the buyer to make a profit.
VicAche
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2015-12-19T14:11:41.693Z
@VicAche Indeed it does. It is an assumption frequently made in competitive markets. I also point out said assumption when I say that there is no bargaining.
Giskard
CC BY-SA 3.0
2015-12-19T14:19:16.623Z
@VicAche From the bottom of page 9 of the article referred by the OP:
"Because we assume that the wrestler offering the bribe has all of the bargaining power"...
Giskard
CC BY-SA 3.0
2015-12-19T14:22:21.430Z
you're right, I'll retract my downvote if you edit it. However the fact that the wrestler offering the bribe has all the bargaining power is not in accordance with the other assumptions the article makes (e.g. only one round)
VicAche
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2015-12-19T14:24:52.130Z
@VicAche I am not sure what you mean by the last sentence.
Giskard
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2015-12-19T14:26:59.573Z
with a single sell offer, take or leave, the buyer actually has some bargaining power on the seller. Also, there is a "smallest positive number" in economics, which is why I don't like that approach at all. It's interesting as a text book answer, but on such a case study would not convince me.
VicAche
CC BY-SA 3.0
2015-12-19T14:35:23.443Z
@Vicache "with a single sell offer, take or leave, the buyer actually has some bargaining power on the seller" If the buyer is the one making the offer, yes, if not, then no. I have yet to see convincing 'real world applicable' models of bargaining.
Giskard
CC BY-SA 3.0
2015-12-19T14:50:56.340Z
@VicAche I have just noticed this: "I'll retract my downvote if you edit it" Edit what? My answer makes the same assumption as the referred article. The assumption is stated in the answer.
Giskard
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2015-12-19T15:06:59.860Z
it's not a request for some particular edit, just the fact that I am not allowed to change my mind by the current voting system
VicAche
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2015-12-19T15:07:35.857Z
Ah, that's okay. I just did not understand what you wanted me to change.
Giskard
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2015-12-20T05:26:58.447Z
you may also want to add that you focus on subgame perfect equilibria. otherwise, offering 2a and accepting all offers equal to or above 2a is a nash equilibrium.
HRSE
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2015-12-21T09:17:05.573Z
@HRSE Good point, I'll edit the answer.
Giskard
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2015-12-22T18:09:30.507Z
@denesp, I think I understand most of your answer, but is there an assumption that 'pushes' toward equilibrium? In your first example, with the no bargaining assumption, what makes the equilibrium happen, i.e. give the item for the zero price when you have two different optimal choices? I understand that one reaches a stable equilibrium when the item is sold for the zero price, but if for some reason the item is not sold (as not selling is also an optimal choice) and I offer an arbitrary small amount instead for the item -- would that also qualify as an equilibrium?
John Doe
CC BY-SA 3.0
2015-12-22T21:03:52.480Z
@John Doe You say the item is not sold and you make a second offer, something I said is not possible. (Btw. I have one example throughout my answer.) That is okay, but you need to say more. Without exactly specifying what moves can be made (how many offers, counteroffers, in what order) and what cost is there to haggling, it is not possible to say what constitutes an equilibrium. I recommend reading about the Nash-equilibrium concept, and then something about bargaining. There are at least a dozen good books on the subject. (You have to see which suits your background and interests best.)
Giskard
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2015-12-23T12:53:20.400Z
@denesp, If you do know some chapters of textbooks that might answer some of what I've asked, I would be glad if you inform me o/
John Doe
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2015-12-23T13:08:21.603Z
@JohnDoe You really have to choose a book depending on your background. Dixit-Skeath: Games of Strategy is not very formal. Osborne: An Introduction to Game Theory is more formal. Both have chapters on bargaining.
Giskard
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2016-01-11T20:17:16.377Z
@denesp, I forgot to thank you for your references o/
John Doe
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2015-12-19T13:42:58.710Z
2015-12-21T09:17:21.597Z
2015-12-21T09:17:21.597Z
Giskard
<p>Take, for instance, that you have a game similar to the one proposed by Levitt and Duggan (2000) in sumo wrestling (link: <a href="http://www.nber.org/papers/w7798.pdf" rel="nofollow">http://www.nber.org/papers/w7798.pdf</a>, section II (pages 9-10) in which the paper describes the model). </p>

<p>Summarizing, a fighter maximizes a expected return in a non-rigged match. For a given fighter consider taking the bribe, the other minimizes a side payment (bribe) to the point of indifference between taking and not taking the bribe -- so, why would the fighter setting the side payment would not set the bribe so it would be <em>marginally</em> better to accept the bribe than not taking it? Why do the authors include the point of indifference among the possible solutions? </p>

CC BY-SA 3.0
2015-12-19T13:44:30.717Z
I changed the title because I believe this is more general and it reflects your actual question better. If you don't like it feel free to change it back.
Giskard
CC BY-SA 3.0
2015-12-20T00:06:35.650Z
I agree with the change in the title.
John Doe
<microeconomics><game-theory>
Indifferent choice assumption in economics
John Doe
# Indifferent choice assumption in economics

(Asked by: username_0 on 2015-12-19)

Take, for instance, that you have a game similar to the one proposed by Levitt and Duggan (2000) in sumo wrestling (link: <http://www.nber.org/papers/w7798.pdf>, section II (pages 9-10) in which the paper describes the model).

Summarizing, a fighter maximizes a expected return in a non-rigged match. For a given fighter consider taking the bribe, the other minimizes a side payment (bribe) to the point of indifference between taking and not taking the bribe -- so, why would the fighter setting the side payment would not set the bribe so it would be *marginally* better to accept the bribe than not taking it? Why do the authors include the point of indifference among the possible solutions?

**Tags:** microeconomics, game-theory
> **Comments:**
> **username_1**: I changed the title because I believe this is more general and it reflects your actual question better. If you don't like it feel free to change it back.  
> **username_0**: I agree with the change in the title.  

---

## 2 answers

### Answer by username_1 on 2015-12-19. Score: 6 | Accepted answer

Because otherwise you would not have subgame perfect equilibria. Suppose I have an item you need and the item is worthless to me. I would be happy to give you the item for any positive amount of money. If you give me no money for it, I am indifferent, both giving you the item and not giving you the item is an optimal choice for me. Just to be clear: we are not bargaining. You set I price and I will take it or leave it.

If you offer price 0 and I give you the item that is an equilibrium. No one could have made a better choice given the other person's choice.
  
 If you offer price 0 and I do not give you the item that is not an equilibrium, because I would give you the item for any small positive payment and you would be willing to pay that, so you could have made a better move.
  
 If you offer price $2a>0$ I will give you the item. But this is not an equilibrium. You could also have offered me $a$, which is also positive, and I would also have given you the item then. So you could have saved some money, your original move was not optimal.

Because there is no smallest positive number, the only equilibrium in such cases is when one side is indifferent.

> **Comments:**
> **username_2**: This supposes no negotiation power whatsoever from the seller side, which should be willing to sell at a gain if he's allowing the buyer to make a profit.  
> **username_1**: @VicAche Indeed it does. It is an assumption frequently made in competitive markets. I also point out said assumption when I say that there is no bargaining.  
> **username_1**: @VicAche From the bottom of page 9 of the article referred by the OP: "Because we assume that the wrestler offering the bribe has all of the bargaining power"...  
> **username_2**: you're right, I'll retract my downvote if you edit it. However the fact that the wrestler offering the bribe has all the bargaining power is not in accordance with the other assumptions the article makes (e.g. only one round)  
> **username_1**: @VicAche I am not sure what you mean by the last sentence.  
> **username_2**: with a single sell offer, take or leave, the buyer actually has some bargaining power on the seller. Also, there is a "smallest positive number" in economics, which is why I don't like that approach at all. It's interesting as a text book answer, but on such a case study would not convince me.  
> **username_1**: @Vicache "with a single sell offer, take or leave, the buyer actually has some bargaining power on the seller" If the buyer is the one making the offer, yes, if not, then no. I have yet to see convincing 'real world applicable' models of bargaining.  
> **username_1**: @VicAche I have just noticed this: "I'll retract my downvote if you edit it" Edit what? My answer makes the same assumption as the referred article. The assumption is stated in the answer.  
> **username_2**: it's not a request for some particular edit, just the fact that I am not allowed to change my mind by the current voting system  
> **username_1**: Ah, that's okay. I just did not understand what you wanted me to change.  
> **username_3**: you may also want to add that you focus on subgame perfect equilibria. otherwise, offering 2a and accepting all offers equal to or above 2a is a nash equilibrium.  
> **username_1**: @HRSE Good point, I'll edit the answer.  
> **username_0**: @denesp, I think I understand most of your answer, but is there an assumption that 'pushes' toward equilibrium? In your first example, with the no bargaining assumption, what makes the equilibrium happen, i.e. give the item for the zero price when you have two different optimal choices? I understand that one reaches a stable equilibrium when the item is sold for the zero price, but if for some reason the item is not sold (as not selling is also an optimal choice) and I offer an arbitrary small amount instead for the item -- would that also qualify as an equilibrium?  
> **username_1**: @John Doe You say the item is not sold and you make a second offer, something I said is not possible. (Btw. I have one example throughout my answer.) That is okay, but you need to say more. Without exactly specifying what moves can be made (how many offers, counteroffers, in what order) and what cost is there to haggling, it is not possible to say what constitutes an equilibrium. I recommend reading about the Nash-equilibrium concept, and then something about bargaining. There are at least a dozen good books on the subject. (You have to see which suits your background and interests best.)  
> **username_0**: @denesp, If you do know some chapters of textbooks that might answer some of what I've asked, I would be glad if you inform me o/  
> **username_1**: @JohnDoe You really have to choose a book depending on your background. Dixit-Skeath: Games of Strategy is not very formal. Osborne: An Introduction to Game Theory is more formal. Both have chapters on bargaining.  
> **username_0**: @denesp, I forgot to thank you for your references o/  

---

### Answer by username_2 on 2015-12-19. Score: 1

One thing that goes towards indifference happening in economics is [granularity](https://en.wikipedia.org/wiki/Granularity). In simple terms, making a *marginally better* offer to someone is not enough to offset preferences away from indifference as indifference is a zone of payment (say, $[a-\epsilon, a+\epsilon]$, with $\epsilon$ the granularity of the agent) rather than a single payment.

See for example [bottom of page 8](https://www.sss.ias.edu/files/papers/econpaper76.pdf) here in *Consistency, Heterogeneity, and Granularity of Individual Behavior under Uncertainty*, Choi *et al.*, 2007

> **Comments:**
> **username_1**: While granularity is certainly interesting, how does this answer the question?  
> **username_2**: @denesp because it renders marginal increments useless, thus answering the question: setting a "marginally" better payment is not feasible  
> **username_1**: So why not set a payment that is discretely better? Say $a + \epsilon$? I think the OP wants to know why you can be sure of acceptance with indifference.  
> **username_2**: @denesp if he makes a discretely better payment he has to choose to do so, at a distinguishable cost for himself (supposing comparable granularities for both agents), so it represents a different situation from the one presented in the provided paper.  

---

