<p>For clarity, let's first understand what &quot;stake&quot; means. According to <a href="https://www.merriam-webster.com/dictionary/stake" rel="nofollow noreferrer">Merriam-Wester</a>, the word &quot;stake&quot; has several meanings, the most relevant to economics is the following:</p>
<blockquote>
<p>3 a: something that is <a href="https://www.merriam-webster.com/dictionary/staked" rel="nofollow noreferrer">staked</a> [i.e. <a href="https://www.merriam-webster.com/dictionary/bet" rel="nofollow noreferrer">betted</a> or <a href="https://www.merriam-webster.com/dictionary/wager" rel="nofollow noreferrer">wagered</a>] for gain or loss<br />
b: the prize in a contest<br />
c: an interest or share in an undertaking or enterprise</p>
</blockquote>
<p>Whether a stake counts as benefit or cost depends on which sense the word is used in.</p>
<p><strong>a.</strong> If stake refers to a wager for potential gain or loss, it can be viewed as a cost.</p>
<p><strong>b.</strong> If stake refers to the prize in a contest, then it's a benefit.</p>
<p><strong>c.</strong> If stake refers to a share or an interest in something being consequential (financially or otherwise) to a stakeholder, then it is essentially a lottery ticket (in the sense used in expected utility theory), which may be a benefit or a cost depending on its expected value (<em>ex ante</em>) or realization (<em>ex post</em>). In other words, it can be either, depending on the context.</p>
<hr />
<p>Now, to the items on which you seek clarifications:</p>
<blockquote>
<p>do stakes affect—increase or decrease—B, C, or both e.g. B-C? Are there strong reasons to think about it in one of these ways?</p>
</blockquote>
<p>It depends on the context, particularly the sense in which the word &quot;stake&quot; is used. See discussion above.</p>
<blockquote>
<p>if one’s anticipated gain is another’s loss: how is it translated into B and C? Both agents have something at stake. But are the terms so encompassing that one’s gain is possible B while another’s loss is possible C?</p>
</blockquote>
<p>If <span class="math-container">$i$</span>'s gain is <span class="math-container">$j$</span>'s loss, then we simply write <span class="math-container">$B_i = C_j$</span>, where <span class="math-container">$B_i$</span> enters positively in <span class="math-container">$i$</span>'s utility and <span class="math-container">$C_j$</span> enters negatively in <span class="math-container">$j$</span>'s utility.</p>
<blockquote>
<p>An agent might lose what’s at stake irrespective of the initial calculus. So after the fact one might have lost and another might have benefitted. Before the fact, which is the time of decision making or the reason for action, the stakes may be thought of as benefits.</p>
</blockquote>
<p>This is consistent with the view of stake as lottery, whose value may differ between <em>ex ante</em> and <em>ex post</em>.</p>
<blockquote>
<p>is it up to the individual agent to judge what the stakes are? Perhaps because one cares more deeply than the other. How are the terms affected? Is caring deeply the same as perceiving high stakes and thus 0&lt;B-C?</p>
</blockquote>
<p>For stake-as-a-wager or prize, there is usually little room for individual differences in how it is perceived. But for stake-as-a-lottery, individual differences in perception can exist, for example, due to differences in access to information, psychological predispositions, etc. While wagers/prizes are sure outcomes (i.e. there's no uncertainty of what they are), lotteries consist of a set of outcomes and their associated probabilities. It is the probabilities that can be perceived differently by different individuals. Objective probabilities can be misperceived <em>a la</em> Kahneman-Tversky/prospect theory, and subjective probabilities are, well, subjective. That's why wagers/prizes cannot be perceived differently, but lotteries can.</p>
<p>Now, &quot;caring deeply&quot; should be thought of as having an intense preference for or a high valuation of an outcome, and can be modeled with a cardinal utility such as quasilinear or vNM utility. But whether it can be interpreted as &quot;perceiving high stakes&quot; will have to be determined by further details from the context.</p>

CC BY-SA 4.0
2024-09-06T07:50:03.620Z
Thank you very much. I added from the comments under the question a fifth bullet point concerning potential theoretical implications such as for expected utility theory, which you indeed mention in your answer. You are very welcome to expand on that too although I already accepted your answer.
Johan
CC BY-SA 4.0
2024-09-06T07:55:11.593Z
How do you suggest one may think about an agent making an action/decision if B must outweigh C but the anticipated (ex ante) stakes are construed/seen as costly? Wouldn't that entail C>B and thus inaction?
Johan
CC BY-SA 4.0
2024-09-06T08:08:50.993Z
Your last comment made me very curious. Can you explain a bit more why there is little room for individual differences in perceived wagers and prizes but not lotteries? Moreover, do you mind expanding on (or suggest where to read more about it) that degree of care and perceived stakes can be modelled or what it requires? I would be happy to ask a new question for that purpose.
Johan
CC BY-SA 4.0
2024-09-06T08:18:42.703Z
Are there indeed fundamental differences between a wager, a share, a bet, a lottery, and a prize? _Wagers and bets_: agents set the amount of the C/B themselves, and in some cases the agents differently affect the outcome. _Lotteries_: the amount of the C/B is typically set exogenously and agents never influence the outcome. _Prizes_: the amount of the B is set exogenously. ... However, I would tend to believe that in all cases (from wagers to prizes) individuals may differ in how they perceive the utility/cost/benefit.
Johan
CC BY-SA 4.0
2024-09-06T08:58:58.650Z
To the question _do stakes affect—increase or decrease—B, C, or both e.g. B-C? __Are there strong reasons to think about it in one of these ways?___ you suggest that "It depends on the context, particularly the sense in which the word "stake" is used" cf. Merriam-Webster. I take it that you agree that there is no strong a priori reason to presume either possibility, right?
Johan
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2024-09-07T01:37:34.290Z
@Johan: To your [second comment](https://economics.stackexchange.com/questions/59060/what-are-stakes-in-cost-benefit-terms-clarifying-five-examples-contentions/59118?noredirect=1#comment98209_59118), a rational decision-maker should consider the C/B balance of all available options. Just because C>B for an option does not necessarily mean it should be forsaken; one has to consider the C/B balance of the other options and pick one that has the highest B against C, even if the balance is still negative.
Herr K.
CC BY-SA 4.0
2024-09-07T01:48:33.273Z
@Johan: To your [third comment](https://economics.stackexchange.com/questions/59060/what-are-stakes-in-cost-benefit-terms-clarifying-five-examples-contentions/59118?noredirect=1#comment98211_59118), to me wagers/prizes are objective facts over which disagreement should be minimal. Lotteries involve uncertainty. Individuals with different risk attitudes may value the same lottery differently.
Herr K.
CC BY-SA 4.0
2024-09-07T02:05:47.623Z
@Johan: We've been talking about C-B analysis as if it's always possible to linearly separate the two. Sometimes it's not; namely, it's impossible to put C and B on different sides of an inequality. In those cases, we'd have look at net benefit (NB) and see if NB<>0. It's natural to think that NB is captured by a utility function. However, econ theory also posits that utility is ordinal, meaning that in general utility doesn't have a unit. This implies that, if you want to model intensity of preference, you'd have to use special utility functions (e.g. quasilinear) that have a unit (e.g. \$)
Herr K.
CC BY-SA 4.0
2024-09-07T02:08:41.670Z
@Johan: To your [fifth comment](https://economics.stackexchange.com/questions/59060/what-are-stakes-in-cost-benefit-terms-clarifying-five-examples-contentions/59118?noredirect=1#comment98213_59118), you're right. I don't have a reason to think that stakes generally affect cost-benefit analysis in one particular direction.
Herr K.
CC BY-SA 4.0
2024-09-07T02:21:03.463Z
@Johan: Your [fourth comment](https://economics.stackexchange.com/questions/59060/what-are-stakes-in-cost-benefit-terms-clarifying-five-examples-contentions/59118?noredirect=1#comment98212_59118) touches on C-B analysis vis-a-vis utility maximization, which I alluded to in an earlier comment. I think it warrants a different post.
Herr K.
CC BY-SA 4.0
2024-09-07T16:22:39.137Z
I really appreciate your commentary. RE 2) I get that the least costly outcome, including inaction, is rational to pursue. Doing something is more costly than doing nothing, ceteris paribus, hence my question.  Now I better see that stakes-as-costs can still entail action considering opportunity cost. RE 3 & 4) I’m happy to ask another question, but right now I am not sure how to formulate it, in other words, what the question is. RE x) I don’t quite understand how preference intensity goes beyond ordinal utility (unless intensity requires an interval scale), so I might ask about that too.
Johan
CC BY-SA 4.0
2024-09-15T11:25:06.763Z
It seems to leave me with two questions: 1) how to theorize wagers/bets, lotteries, and prizes in cost-benefit analysis and in utility maximization and perhaps other economic frameworks (with respect to agent’s impact on outcomes, risk attitudes [i.e. preference for high/low probabilities], uncertainty of outcomes [i.e. known probabilities], and individual differences)? 2) why does ordinal utility imply no unit such as preference intensity? @HerrK. Do you mind commenting briefly, please; then I’ll open new questions?
Johan
CC BY-SA 4.0
2024-09-15T14:19:07.277Z
@Johan: 1) Expected utility theory is a very mature framework for understanding risks (known probabilities), while (Knightian) uncertainty or ambiguity is addressed in certain areas of behavioral economics. 2) See this [Wikipedia article](https://en.wikipedia.org/wiki/Ordinal_utility) or any intermediate micro textbook for a discussion.
Herr K.
CC BY-SA 4.0
2024-09-15T16:58:44.907Z
Thank you @HerrK. . Your reference for 2) sufficed. Briefly RE 1), if Knightian econ studies uncertainty, what is meant by uncertain events with possible outcomes in [subjective expected utility](https://en.m.wikipedia.org/wiki/Subjective_expected_utility)? I thought uncertainty (cf. Savage) was about not knowing the probabilities of outcomes (e.g. unlike known probabilities of outcomes in certain games). Yet it is referred to as expected utility theory and decisions under risk. I ask wrt your comment on wager/lottery/prize: “C-B analysis vs utility max. I think it warrants a different post”
Johan
CC BY-SA 4.0
2024-09-16T16:46:42.450Z
@Johan: In economics, risk and uncertainty differs in whether the probabilities (subjective or otherwise) of relevant outcomes are known. Risk refers to known probabilities and uncertainty to unknown ones. To avoid equivocation, uncertainty in this sense is also referred to as [Knightian uncertainty](https://en.wikipedia.org/wiki/Knightian_uncertainty), following Frank Knight who first proposed the distinction. Savage's SEUT would be considered decision under *risk*, because probabilities, albeit subjective, are still "known" to the decision-maker.
Herr K.
CC BY-SA 4.0
2024-09-16T18:01:01.770Z
That confirms how I thought about it initially. Except I thought that Savage's contribution was (to) decision-making under uncertainty, not under risk. In particular his minimax regret criterion has been described as such, but I see that is contrasted with the utility maximization criterion, which is probably the crucial point I missed or confused, cf. https://web.stanford.edu/~mfiorina/Fiorina%20Web%20Files/Paradox.pdf). I understand how you may describe subjective utility, conversely, as risky decision-making. Thanks again for your help!
Johan
CC BY-SA 4.0
2024-09-18T04:40:15.397Z
HerrK. said: _wagers/prizes cannot be perceived differently but they can be valued differently. One would have to be delusional to perceive a 1m dollar prize as a 2m dollar prize, or a cheeseburger as French fries. Accepting such misperception (of outcomes) would be a radical departure from the conventional economic framework. However, it is perfectly consistent with economic theory to have different people valuing the same outcome, be it $1m or a cheeseburger, differently._
Johan
CC BY-SA 4.0
2024-09-18T04:51:37.207Z
... _I think you can gain much clarity on the concepts by reading a proper textbook treatment of EUT. I'd recommend Ch. 6 of [MWG](https://www.hawkinqian.com/uploads/media/2014/09/Microeconomic_Theory.pdf#page=85), though Ch. 2 of [Tadelis](https://students.aiu.edu/submissions/profiles/resources/onlineBook/Y5z2A2_Game_Theory_An_Introduction.pdf#page=33) is more accessible._
Johan
CC BY-SA 4.0
2024-09-18T04:59:42.567Z
Thank you very much for elaborating on perceptions of prize/wager vs lottery. It makes much more sense now. However, in my opinion it is now also clearer that the three examples of stakes appear more different than similar because they emphasize outcomes vs. probability of outcomes, respectively. Recasting stakes-as-prize in terms of stakes-as-contest-for-prize makes it more similar, fundamentally, to the lottery concept. And the wager example can also be viewed as outcomes (what is there to win/lose) and as probability of outcome (who wins?).
Johan
CC BY-SA 4.0
2024-09-18T14:17:08.983Z
@Johan: As shown in my improved edit, I'm back-tracking a bit on my original comment on "caring deeply as perceiving high stake", because I was to a certain extent also confusing perception with valuation.
Herr K.
CC BY-SA 4.0
2024-09-18T14:36:16.147Z
Cheers! In my book, ‘caring deeply’, ‘an intense preference for an outcome’, and ‘perceiving high stakes or stakes as being high’ are in the same ballpark (I’m primarily having political contexts in mind). Are you not sure about what to conclude on that particular aspect of the question/answer? Perhaps it is a possibility worthy of empirical scrutiny.
Johan
CC BY-SA 4.0
2024-09-06T03:58:43.917Z
2024-09-18T13:57:48.173Z
2024-09-18T13:57:48.173Z
Herr K.
<p>HerrK. answered</p>
<blockquote>
<blockquote>
<p>do stakes affect—increase or decrease—B, C, or both e.g. B-C? Are there strong reasons to think about it in one of these ways?</p>
</blockquote>
</blockquote>
<blockquote>
<p>It depends on the context, particularly the sense in which the word ‘stake’ is used.</p>
</blockquote>
<blockquote>
<p>Whether a stake counts as benefit or cost depends on which sense the word is used in.</p>
</blockquote>
<p>I would like to add that the three meanings of stakes don’t differ much considering that all regard 1) a probability distribution on outcomes (chance/risk of reward) and 2) outcomes (what is there to win/not win/lose).</p>
<p>It is not useful to focus too much on a prize itself (an outcome) because that compares less directly with e.g. a lottery. Conversely, the contest for a prize is comparable with a lottery.</p>
<p>The exception regards wagers/bets i.e. risking to jeapordize current (privately held, personal) value for the possibility of gaining more value (handed by the losing party) or the honor of not losing. In that case, the outcome itself seem to differ from outcomes like a prize or an outcome of a lottery, which are mostly not already private but rather up for grabs.</p>

CC BY-SA 4.0
2024-09-18T08:42:03.943Z
2024-11-01T08:55:19.857Z
2024-11-01T08:55:19.857Z
Johan
<p>Please excuse me if this is off-topic, and don't be offended if it is stupid.</p>
<p>Scholars theorize that the stakes matter for rational decision making or cost-benefit calculations (under uncertainty or risk).</p>
<p>But I haven't found a reference clearly explaining how the concept of stakes is understood, and how it enters the terms of the calculus, B and C (are stakes considered a B or a C?). I have come across the concept as if it is known and not needed to be interpreted in formal terms (perhaps this is because there is no reason to do so - something I am not aware of or have yet to understand). These are some of the examples I am thinking about but haven't seen discussed or explained clearly in literature but would appreciate clarification of:</p>
<ul>
<li>do stakes affect—increase or decrease—B, C, or both e.g. B-C? Are there strong reasons to think about it in one of these ways?</li>
<li>if one’s anticipated gain is another’s loss: how is it translated into B and C? Both agents have something at stake. But are the terms so encompassing that one’s gain is possible B while another’s loss is possible C?</li>
<li>An agent might lose what’s at stake irrespective of the initial calculus. So after the fact one might have lost and another might have benefitted. Before the fact, which is the time of decision making or the reason for action, the stakes may be thought of as benefits.</li>
<li>is it up to the individual agent to judge what the stakes are? Perhaps because one cares more deeply than the other. How are the terms affected? Is caring deeply the same as perceiving high stakes and thus 0&lt;B-C?</li>
<li>is the interpretation of stakes in formal terms mere semantics or does it have theoretical interpretations i.e. for debates about rational choice, expected utility, prospect theory (loss'/gain's domains), decision making under risk (known outcomes and probabilities of outcomes) vs. uncertainty (unknown probabilities of outcomes), game theory, etc.?</li>
</ul>
<p>Can you either please clearly explain or refer me to a reference that does that? (or refer me to a better forum or Q&amp;A site for this). My immediate view tends to be that stakes are encompassed as benefits rather than costs. But there may be reasons you can help me understand to not view it like that or to say that an alternative view is equivalent or preferable. Thank you.</p>

CC BY-SA 4.0
2024-08-28T01:28:23.743Z
Are you asking if a stake should be considered a cost or a benefit? BTW, the word *stake* has the same meaning in economics as it does outside economics. See for example [here](https://www.merriam-webster.com/dictionary/stake) and [here](https://dictionary.cambridge.org/us/dictionary/english/stake).
Herr K.
CC BY-SA 4.0
2024-08-28T18:17:39.197Z
@HerrK., yes that is an alternative way of asking the question, thank you.
Johan
CC BY-SA 4.0
2024-08-28T21:24:25.050Z
I think this is more of a semantic question than an economic one. Someone who has bet \$500 on a horse race has a stake---the \$500 bet---in the game. In this case, the stake is a cost, incurred for the potential gain from the bet. In contrast, a citizen may have a stake in a government policy. However, the stake here is not a cost incurred  but the potential benefit (possibly negative) of the policy to the stakeholders. So it depends on the context. Nevertheless, in neither scenario does the cost-benefit analysis depend on the labeling of stake as B or C; what matters at the end is (B-C).
Herr K.
CC BY-SA 4.0
2024-08-29T09:00:28.987Z
Thanks for engaging with the question anyhow, @HerrK. (meaning despite semantics, which is derogatory for cheap talk). In my view, that discussion is entirely useful for the sake of being clear about what is asserted. Not least if we desire to operationalize the model empirically. It might also be that the question taps into a debate between e.g. expected utility theory and prospect theory (where potential losses have greater effects than potential gains on decisions) and thus fundamental disagreement among economists/social scientists. ...
Johan
CC BY-SA 4.0
2024-08-29T09:08:36.923Z
Indeed B-C is the calculus by the end of the day. Don't you think stating that 'what the stakes are depends on the context' implies prospect theory? - and whether the agent is in the loss or winners domain? If we consider that one takes decisions under risk or uncertainty, then I would say that if one's potential gain is another's potential loss, then it also means that the potential loser has a possibility to gain something; meaning that we needn't cast it as a cost or a benefit depending on the outlooks of specific agents involved.
Johan
CC BY-SA 4.0
2024-08-29T17:17:18.747Z
As I repeatedly mentioned, the word "stake" is not an economic terminology (unlike e.g. "[cheap talk](https://en.wikipedia.org/wiki/Cheap_talk)", which you happened to refer to). The reason why economists have not found a need to formally define the term "stake" is probably that it is not needed and that its introduction would complicate more it simplifies. Just because it's not straightforward to relabel terms (i.e. cost and benefit) that are well-understood within the discipline into some neologism does not invalidate existing theories or lend credence to one model over another.
Herr K.
CC BY-SA 4.0
2024-08-29T17:28:48.310Z
Also, neither rational choice theory nor expected utility theory require a clear distinction between cost and benefit. Only (B-C) matters because cost is negative benefit and benefit is negative cost. I would argue that even prospect theory does not require the distinction of C from B, only gains from losses, which are conceptually different from C&B, though the difference is more nuanced. This is why I think the focus on separating cost from benefit---and on top of that, labeling stake as cost vs stake as benefit---is just semantics and really misses the point of economic theorizing.
Herr K.
CC BY-SA 4.0
2024-08-29T17:37:20.973Z
We should avoid extended discussions in comments. But I'd suggest that you consider revising your question to have a better focus, such as getting clarifications on the 3 examples (especially the last two) in your question. I sense from them that you have some misunderstanding of a few elementary concepts in economics.
Herr K.
CC BY-SA 4.0
2024-08-29T18:31:03.020Z
All that help is much appreciated @HerrK. I edited the question. Thank you. BTW I realized I shouldn’t have used the term cheap talk in this context, because it has the specific meaning you referred to and that I was aware of but did not think about at the time of writing.
Johan
<game-theory><decision-theory><expected-utility><model>
what are stakes in cost-benefit terms? Clarifying five examples/contentions
Johan
# what are stakes in cost-benefit terms? Clarifying five examples/contentions

(Asked by: username_0 on 2024-08-27)

Please excuse me if this is off-topic, and don't be offended if it is stupid.

Scholars theorize that the stakes matter for rational decision making or cost-benefit calculations (under uncertainty or risk).

But I haven't found a reference clearly explaining how the concept of stakes is understood, and how it enters the terms of the calculus, B and C (are stakes considered a B or a C?). I have come across the concept as if it is known and not needed to be interpreted in formal terms (perhaps this is because there is no reason to do so - something I am not aware of or have yet to understand). These are some of the examples I am thinking about but haven't seen discussed or explained clearly in literature but would appreciate clarification of:

* do stakes affect—increase or decrease—B, C, or both e.g. B-C? Are there strong reasons to think about it in one of these ways?
* if one’s anticipated gain is another’s loss: how is it translated into B and C? Both agents have something at stake. But are the terms so encompassing that one’s gain is possible B while another’s loss is possible C?
* An agent might lose what’s at stake irrespective of the initial calculus. So after the fact one might have lost and another might have benefitted. Before the fact, which is the time of decision making or the reason for action, the stakes may be thought of as benefits.
* is it up to the individual agent to judge what the stakes are? Perhaps because one cares more deeply than the other. How are the terms affected? Is caring deeply the same as perceiving high stakes and thus 0* is the interpretation of stakes in formal terms mere semantics or does it have theoretical interpretations i.e. for debates about rational choice, expected utility, prospect theory (loss'/gain's domains), decision making under risk (known outcomes and probabilities of outcomes) vs. uncertainty (unknown probabilities of outcomes), game theory, etc.?

Can you either please clearly explain or refer me to a reference that does that? (or refer me to a better forum or Q&A site for this). My immediate view tends to be that stakes are encompassed as benefits rather than costs. But there may be reasons you can help me understand to not view it like that or to say that an alternative view is equivalent or preferable. Thank you.

**Tags:** game-theory, decision-theory, expected-utility, model
> **Comments:**
> **username_1**: Are you asking if a stake should be considered a cost or a benefit? BTW, the word *stake* has the same meaning in economics as it does outside economics. See for example [here](https://www.merriam-webster.com/dictionary/stake) and [here](https://dictionary.cambridge.org/us/dictionary/english/stake).  
> **username_0**: @HerrK., yes that is an alternative way of asking the question, thank you.  
> **username_1**: I think this is more of a semantic question than an economic one. Someone who has bet \$500 on a horse race has a stake---the \$500 bet---in the game. In this case, the stake is a cost, incurred for the potential gain from the bet. In contrast, a citizen may have a stake in a government policy. However, the stake here is not a cost incurred  but the potential benefit (possibly negative) of the policy to the stakeholders. So it depends on the context. Nevertheless, in neither scenario does the cost-benefit analysis depend on the labeling of stake as B or C; what matters at the end is (B-C).  
> **username_0**: Thanks for engaging with the question anyhow, @HerrK. (meaning despite semantics, which is derogatory for cheap talk). In my view, that discussion is entirely useful for the sake of being clear about what is asserted. Not least if we desire to operationalize the model empirically. It might also be that the question taps into a debate between e.g. expected utility theory and prospect theory (where potential losses have greater effects than potential gains on decisions) and thus fundamental disagreement among economists/social scientists. ...  
> **username_0**: Indeed B-C is the calculus by the end of the day. Don't you think stating that 'what the stakes are depends on the context' implies prospect theory? - and whether the agent is in the loss or winners domain? If we consider that one takes decisions under risk or uncertainty, then I would say that if one's potential gain is another's potential loss, then it also means that the potential loser has a possibility to gain something; meaning that we needn't cast it as a cost or a benefit depending on the outlooks of specific agents involved.  
> **username_1**: As I repeatedly mentioned, the word "stake" is not an economic terminology (unlike e.g. "[cheap talk](https://en.wikipedia.org/wiki/Cheap_talk)", which you happened to refer to). The reason why economists have not found a need to formally define the term "stake" is probably that it is not needed and that its introduction would complicate more it simplifies. Just because it's not straightforward to relabel terms (i.e. cost and benefit) that are well-understood within the discipline into some neologism does not invalidate existing theories or lend credence to one model over another.  
> **username_1**: Also, neither rational choice theory nor expected utility theory require a clear distinction between cost and benefit. Only (B-C) matters because cost is negative benefit and benefit is negative cost. I would argue that even prospect theory does not require the distinction of C from B, only gains from losses, which are conceptually different from C&B, though the difference is more nuanced. This is why I think the focus on separating cost from benefit---and on top of that, labeling stake as cost vs stake as benefit---is just semantics and really misses the point of economic theorizing.  
> **username_1**: We should avoid extended discussions in comments. But I'd suggest that you consider revising your question to have a better focus, such as getting clarifications on the 3 examples (especially the last two) in your question. I sense from them that you have some misunderstanding of a few elementary concepts in economics.  
> **username_0**: All that help is much appreciated @HerrK. I edited the question. Thank you. BTW I realized I shouldn’t have used the term cheap talk in this context, because it has the specific meaning you referred to and that I was aware of but did not think about at the time of writing.  

---

## 2 answers

### Answer by username_1 on 2024-09-06. Score: 1 | Accepted answer

For clarity, let's first understand what "stake" means. According to [Merriam-Wester](https://www.merriam-webster.com/dictionary/stake), the word "stake" has several meanings, the most relevant to economics is the following:

> 3 a: something that is [staked](https://www.merriam-webster.com/dictionary/staked) [i.e. [betted](https://www.merriam-webster.com/dictionary/bet) or [wagered](https://www.merriam-webster.com/dictionary/wager)] for gain or loss  
> b: the prize in a contest  
> c: an interest or share in an undertaking or enterprise

Whether a stake counts as benefit or cost depends on which sense the word is used in.

**a.** If stake refers to a wager for potential gain or loss, it can be viewed as a cost.

**b.** If stake refers to the prize in a contest, then it's a benefit.

**c.** If stake refers to a share or an interest in something being consequential (financially or otherwise) to a stakeholder, then it is essentially a lottery ticket (in the sense used in expected utility theory), which may be a benefit or a cost depending on its expected value (*ex ante*) or realization (*ex post*). In other words, it can be either, depending on the context.

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Now, to the items on which you seek clarifications:

> do stakes affect—increase or decrease—B, C, or both e.g. B-C? Are there strong reasons to think about it in one of these ways?

It depends on the context, particularly the sense in which the word "stake" is used. See discussion above.

> if one’s anticipated gain is another’s loss: how is it translated into B and C? Both agents have something at stake. But are the terms so encompassing that one’s gain is possible B while another’s loss is possible C?

If $i$'s gain is $j$'s loss, then we simply write $B\_i = C\_j$, where $B\_i$ enters positively in $i$'s utility and $C\_j$ enters negatively in $j$'s utility.

> An agent might lose what’s at stake irrespective of the initial calculus. So after the fact one might have lost and another might have benefitted. Before the fact, which is the time of decision making or the reason for action, the stakes may be thought of as benefits.

This is consistent with the view of stake as lottery, whose value may differ between *ex ante* and *ex post*.

> is it up to the individual agent to judge what the stakes are? Perhaps because one cares more deeply than the other. How are the terms affected? Is caring deeply the same as perceiving high stakes and thus 0

For stake-as-a-wager or prize, there is usually little room for individual differences in how it is perceived. But for stake-as-a-lottery, individual differences in perception can exist, for example, due to differences in access to information, psychological predispositions, etc. While wagers/prizes are sure outcomes (i.e. there's no uncertainty of what they are), lotteries consist of a set of outcomes and their associated probabilities. It is the probabilities that can be perceived differently by different individuals. Objective probabilities can be misperceived *a la* Kahneman-Tversky/prospect theory, and subjective probabilities are, well, subjective. That's why wagers/prizes cannot be perceived differently, but lotteries can.

Now, "caring deeply" should be thought of as having an intense preference for or a high valuation of an outcome, and can be modeled with a cardinal utility such as quasilinear or vNM utility. But whether it can be interpreted as "perceiving high stakes" will have to be determined by further details from the context.

> **Comments:**
> **username_0**: Thank you very much. I added from the comments under the question a fifth bullet point concerning potential theoretical implications such as for expected utility theory, which you indeed mention in your answer. You are very welcome to expand on that too although I already accepted your answer.  
> **username_0**: How do you suggest one may think about an agent making an action/decision if B must outweigh C but the anticipated (ex ante) stakes are construed/seen as costly? Wouldn't that entail C>B and thus inaction?  
> **username_0**: Your last comment made me very curious. Can you explain a bit more why there is little room for individual differences in perceived wagers and prizes but not lotteries? Moreover, do you mind expanding on (or suggest where to read more about it) that degree of care and perceived stakes can be modelled or what it requires? I would be happy to ask a new question for that purpose.  
> **username_0**: Are there indeed fundamental differences between a wager, a share, a bet, a lottery, and a prize? _Wagers and bets_: agents set the amount of the C/B themselves, and in some cases the agents differently affect the outcome. _Lotteries_: the amount of the C/B is typically set exogenously and agents never influence the outcome. _Prizes_: the amount of the B is set exogenously. ... However, I would tend to believe that in all cases (from wagers to prizes) individuals may differ in how they perceive the utility/cost/benefit.  
> **username_0**: To the question _do stakes affect—increase or decrease—B, C, or both e.g. B-C? __Are there strong reasons to think about it in one of these ways?___ you suggest that "It depends on the context, particularly the sense in which the word "stake" is used" cf. Merriam-Webster. I take it that you agree that there is no strong a priori reason to presume either possibility, right?  
> **username_1**: @Johan: To your [second comment](https://economics.stackexchange.com/questions/59060/what-are-stakes-in-cost-benefit-terms-clarifying-five-examples-contentions/59118?noredirect=1#comment98209_59118), a rational decision-maker should consider the C/B balance of all available options. Just because C>B for an option does not necessarily mean it should be forsaken; one has to consider the C/B balance of the other options and pick one that has the highest B against C, even if the balance is still negative.  
> **username_1**: @Johan: To your [third comment](https://economics.stackexchange.com/questions/59060/what-are-stakes-in-cost-benefit-terms-clarifying-five-examples-contentions/59118?noredirect=1#comment98211_59118), to me wagers/prizes are objective facts over which disagreement should be minimal. Lotteries involve uncertainty. Individuals with different risk attitudes may value the same lottery differently.  
> **username_1**: @Johan: We've been talking about C-B analysis as if it's always possible to linearly separate the two. Sometimes it's not; namely, it's impossible to put C and B on different sides of an inequality. In those cases, we'd have look at net benefit (NB) and see if NB<>0. It's natural to think that NB is captured by a utility function. However, econ theory also posits that utility is ordinal, meaning that in general utility doesn't have a unit. This implies that, if you want to model intensity of preference, you'd have to use special utility functions (e.g. quasilinear) that have a unit (e.g. \$)  
> **username_1**: @Johan: To your [fifth comment](https://economics.stackexchange.com/questions/59060/what-are-stakes-in-cost-benefit-terms-clarifying-five-examples-contentions/59118?noredirect=1#comment98213_59118), you're right. I don't have a reason to think that stakes generally affect cost-benefit analysis in one particular direction.  
> **username_1**: @Johan: Your [fourth comment](https://economics.stackexchange.com/questions/59060/what-are-stakes-in-cost-benefit-terms-clarifying-five-examples-contentions/59118?noredirect=1#comment98212_59118) touches on C-B analysis vis-a-vis utility maximization, which I alluded to in an earlier comment. I think it warrants a different post.  
> **username_0**: I really appreciate your commentary. RE 2) I get that the least costly outcome, including inaction, is rational to pursue. Doing something is more costly than doing nothing, ceteris paribus, hence my question.  Now I better see that stakes-as-costs can still entail action considering opportunity cost. RE 3 & 4) I’m happy to ask another question, but right now I am not sure how to formulate it, in other words, what the question is. RE x) I don’t quite understand how preference intensity goes beyond ordinal utility (unless intensity requires an interval scale), so I might ask about that too.  
> **username_0**: It seems to leave me with two questions: 1) how to theorize wagers/bets, lotteries, and prizes in cost-benefit analysis and in utility maximization and perhaps other economic frameworks (with respect to agent’s impact on outcomes, risk attitudes [i.e. preference for high/low probabilities], uncertainty of outcomes [i.e. known probabilities], and individual differences)? 2) why does ordinal utility imply no unit such as preference intensity? @HerrK. Do you mind commenting briefly, please; then I’ll open new questions?  
> **username_1**: @Johan: 1) Expected utility theory is a very mature framework for understanding risks (known probabilities), while (Knightian) uncertainty or ambiguity is addressed in certain areas of behavioral economics. 2) See this [Wikipedia article](https://en.wikipedia.org/wiki/Ordinal_utility) or any intermediate micro textbook for a discussion.  
> **username_0**: Thank you @HerrK. . Your reference for 2) sufficed. Briefly RE 1), if Knightian econ studies uncertainty, what is meant by uncertain events with possible outcomes in [subjective expected utility](https://en.m.wikipedia.org/wiki/Subjective_expected_utility)? I thought uncertainty (cf. Savage) was about not knowing the probabilities of outcomes (e.g. unlike known probabilities of outcomes in certain games). Yet it is referred to as expected utility theory and decisions under risk. I ask wrt your comment on wager/lottery/prize: “C-B analysis vs utility max. I think it warrants a different post”  
> **username_1**: @Johan: In economics, risk and uncertainty differs in whether the probabilities (subjective or otherwise) of relevant outcomes are known. Risk refers to known probabilities and uncertainty to unknown ones. To avoid equivocation, uncertainty in this sense is also referred to as [Knightian uncertainty](https://en.wikipedia.org/wiki/Knightian_uncertainty), following Frank Knight who first proposed the distinction. Savage's SEUT would be considered decision under *risk*, because probabilities, albeit subjective, are still "known" to the decision-maker.  
> **username_0**: That confirms how I thought about it initially. Except I thought that Savage's contribution was (to) decision-making under uncertainty, not under risk. In particular his minimax regret criterion has been described as such, but I see that is contrasted with the utility maximization criterion, which is probably the crucial point I missed or confused, cf. https://web.stanford.edu/~mfiorina/Fiorina%20Web%20Files/Paradox.pdf). I understand how you may describe subjective utility, conversely, as risky decision-making. Thanks again for your help!  
> **username_0**: HerrK. said: _wagers/prizes cannot be perceived differently but they can be valued differently. One would have to be delusional to perceive a 1m dollar prize as a 2m dollar prize, or a cheeseburger as French fries. Accepting such misperception (of outcomes) would be a radical departure from the conventional economic framework. However, it is perfectly consistent with economic theory to have different people valuing the same outcome, be it $1m or a cheeseburger, differently._  
> **username_0**: ... _I think you can gain much clarity on the concepts by reading a proper textbook treatment of EUT. I'd recommend Ch. 6 of [MWG](https://www.hawkinqian.com/uploads/media/2014/09/Microeconomic_Theory.pdf#page=85), though Ch. 2 of [Tadelis](https://students.aiu.edu/submissions/profiles/resources/onlineBook/Y5z2A2_Game_Theory_An_Introduction.pdf#page=33) is more accessible._  
> **username_0**: Thank you very much for elaborating on perceptions of prize/wager vs lottery. It makes much more sense now. However, in my opinion it is now also clearer that the three examples of stakes appear more different than similar because they emphasize outcomes vs. probability of outcomes, respectively. Recasting stakes-as-prize in terms of stakes-as-contest-for-prize makes it more similar, fundamentally, to the lottery concept. And the wager example can also be viewed as outcomes (what is there to win/lose) and as probability of outcome (who wins?).  
> **username_1**: @Johan: As shown in my improved edit, I'm back-tracking a bit on my original comment on "caring deeply as perceiving high stake", because I was to a certain extent also confusing perception with valuation.  
> **username_0**: Cheers! In my book, ‘caring deeply’, ‘an intense preference for an outcome’, and ‘perceiving high stakes or stakes as being high’ are in the same ballpark (I’m primarily having political contexts in mind). Are you not sure about what to conclude on that particular aspect of the question/answer? Perhaps it is a possibility worthy of empirical scrutiny.  

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### Answer by username_0 on 2024-09-18. Score: 0

HerrK. answered

> > do stakes affect—increase or decrease—B, C, or both e.g. B-C? Are there strong reasons to think about it in one of these ways?

> It depends on the context, particularly the sense in which the word ‘stake’ is used.

> Whether a stake counts as benefit or cost depends on which sense the word is used in.

I would like to add that the three meanings of stakes don’t differ much considering that all regard 1) a probability distribution on outcomes (chance/risk of reward) and 2) outcomes (what is there to win/not win/lose).

It is not useful to focus too much on a prize itself (an outcome) because that compares less directly with e.g. a lottery. Conversely, the contest for a prize is comparable with a lottery.

The exception regards wagers/bets i.e. risking to jeapordize current (privately held, personal) value for the possibility of gaining more value (handed by the losing party) or the honor of not losing. In that case, the outcome itself seem to differ from outcomes like a prize or an outcome of a lottery, which are mostly not already private but rather up for grabs.


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