<p>In the case of this problem, you are assuming that the opportunity cost of the architect is zero (and the same for the builder), since you are saying that his payoff from refusing the contract is zero. </p>

<p>Remember that this is a theoretical game. You could include a different payoff for the opportunity cost, but it would be a different problem from the one you are presenting. </p>

CC BY-SA 3.0
2017-11-12T22:35:23.400Z
How would you include it?
Bensstats
CC BY-SA 3.0
2017-11-12T22:37:13.380Z
Note that  oppourtunity cost is not even considered in the question as an assumption
Bensstats
CC BY-SA 3.0
2017-11-12T22:41:09.243Z
Since it is not considered, it means that it is zero. You could include it by changing the zero payoff to something else. For example, if the architect could make \$100,000 from doing something else, you would compare \$100,000 to 40%*(dollar amount of the contract in the question). If the opportunity cost was larger, then he would not sign the contract. Otherwise, he would sign it.
python_enthusiast
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2017-11-12T22:12:49.063Z
2017-11-12T22:12:49.063Z
python_enthusiast
<p>Recall that <a href="https://en.wikipedia.org/wiki/Opportunity_cost" rel="nofollow noreferrer">Oppurtunity Cost</a> is referred to the benefit forgone by choosing the other option.</p>

<p>In your example of a single player game, opportunity cost exists since the architect is completely in control of the benefit he receives. In this case the opportunity cost for signing the contract is 0 (and conversely -40 for not signing the contract).</p>

<p><strong>However this is only applicable in a single person game</strong>.</p>

<p>In a case where the business owner and Architect were actively negotiating, it would appear that there would not be any practical ramifications for considering opportunity cost because the payoffs change depending on the other player and can only be seen after the fact.</p>

<p>for example consider a single period 2x2 game such that:
$$\left[\begin{matrix}(10,5)&amp;(2,2)\\(2,2)&amp;(5,10)\end{matrix} \right]$$</p>

<p>From the horizontal/vertical player's position his payoffs range from 10,5 and 2. He does not choose with respect to costs, he chooses based on what he thinks the payoffs will be.</p>

<hr>

<p>To answer the broader question which  you are probably wondering about.<br>
<strong>Opportunity cost is only considered when a buy in for a specific game is necessary</strong><br></p>

<p>You'd have to consider expected value of a game compared to the cost. (however that only provides a fair price when the game is played infinity, you would also have to consider how many times you'd have to play a game and end up with a positive profit) using this formula: </p>

<p>$$n=\left(\frac{1.96\sigma}{p-\mu}\right)^2$$</p>

<p>I suggest reading up on <a href="https://en.wikipedia.org/wiki/Martingale_(betting_system)" rel="nofollow noreferrer">Martingales</a> and the <a href="https://en.wikipedia.org/wiki/St._Petersburg_paradox" rel="nofollow noreferrer">St. Petersberg Paradox</a> for more info.</p>

CC BY-SA 3.0
2017-11-12T23:32:19.560Z
2017-11-13T00:19:37.897Z
2017-11-13T00:19:37.897Z
EconJohn
<p>Morton Davis in his book <a href="https://www.amazon.ca/Game-Theory-Nontechnical-Morton-Davis/dp/0486296725" rel="nofollow noreferrer">Game Theory: A non-Technical introduction</a> brings the
following example of a <a href="http://www.businessdictionary.com/definition/non-zero-sum-game.html" rel="nofollow noreferrer">non-zero sum game</a> (pg.73) :</p>
<blockquote>
<p><strong>A Buisness Partnership</strong></p>
<p>A builder and an architect are jointly offered a contract to design and construct a building. They are offered a single lump sum as a payment and are given a week to decide whether they accept. The approval of both is required, so they must decide how the lump sum will be divided. The architect writes to the builder suggesting that the profits be divided equally. The builder replies, committing himself to the contract in writing provided he receives 60 percent of the profits. He informs the architect moreover, that he is going on a two week vacation, that he cannot be reached, and it is up to the architect to accept the contract on these terms or reject it entirely.</p>
<p>The architect feels like he is being exploited. He feels that his services are valuable as the builder's and that each should receive half the profits. On the other hand, the probable profit is large, and under different circumstances, he would consider 40 percent of such a total an acceptable fee. Should he accept the builder's offer? Note that the builder has no more options; on the architect has the choice- to accept or reject the contact. This is reflected in the payoff matrix shown:</p>
<p><span class="math-container">$$\left[\begin{matrix}(0.40,0.60)\\(0, 0)\end{matrix} \right]$$</span></p>
</blockquote>
<h1>My question :</h1>
<p>The way the case seems to be presented is that the architect is <em>forced</em> to choose 40 percent in light of the alternative where there is no profits to be gained. What about the architect's <a href="https://en.wikipedia.org/wiki/Opportunity_cost" rel="nofollow noreferrer">opportunity cost</a>? Isn't there what to be gained from the architect when refusing this split of profits in a 40-60 split as far as opportunity cost in concerned?</p>

CC BY-SA 3.0
2017-11-12T20:19:01.490Z
Could you please make your last sentence more clear. Right now I can't understand it at all and it seems crucial.
Giskard
CC BY-SA 3.0
2017-11-12T20:23:38.140Z
@denesp edited 1char
Bensstats
CC BY-SA 3.0
2017-11-12T20:38:09.503Z
"Isn't there what to be gained" Huh?
Giskard
<game-theory><opportunity-cost>
Does Game theory consider opportunity cost?
Bensstats
# Does Game theory consider opportunity cost?

(Asked by: username_0 on 2017-11-12)

Morton Davis in his book [Game Theory: A non-Technical introduction](https://www.amazon.ca/Game-Theory-Nontechnical-Morton-Davis/dp/0486296725) brings the
following example of a [non-zero sum game](http://www.businessdictionary.com/definition/non-zero-sum-game.html) (pg.73) :

> **A Buisness Partnership**
>
> A builder and an architect are jointly offered a contract to design and construct a building. They are offered a single lump sum as a payment and are given a week to decide whether they accept. The approval of both is required, so they must decide how the lump sum will be divided. The architect writes to the builder suggesting that the profits be divided equally. The builder replies, committing himself to the contract in writing provided he receives 60 percent of the profits. He informs the architect moreover, that he is going on a two week vacation, that he cannot be reached, and it is up to the architect to accept the contract on these terms or reject it entirely.
>
> The architect feels like he is being exploited. He feels that his services are valuable as the builder's and that each should receive half the profits. On the other hand, the probable profit is large, and under different circumstances, he would consider 40 percent of such a total an acceptable fee. Should he accept the builder's offer? Note that the builder has no more options; on the architect has the choice- to accept or reject the contact. This is reflected in the payoff matrix shown:
>
> $$\left[\begin{matrix}(0.40,0.60)\\(0, 0)\end{matrix} \right]$$

# My question :

The way the case seems to be presented is that the architect is *forced* to choose 40 percent in light of the alternative where there is no profits to be gained. What about the architect's [opportunity cost](https://en.wikipedia.org/wiki/Opportunity_cost)? Isn't there what to be gained from the architect when refusing this split of profits in a 40-60 split as far as opportunity cost in concerned?

**Tags:** game-theory, opportunity-cost
> **Comments:**
> **username_1**: Could you please make your last sentence more clear. Right now I can't understand it at all and it seems crucial.  
> **username_0**: @denesp edited 1char  
> **username_1**: "Isn't there what to be gained" Huh?  

---

## 2 answers

### Answer by username_3 on 2017-11-12. Score: 3 | Accepted answer

Recall that [Oppurtunity Cost](https://en.wikipedia.org/wiki/Opportunity_cost) is referred to the benefit forgone by choosing the other option.

In your example of a single player game, opportunity cost exists since the architect is completely in control of the benefit he receives. In this case the opportunity cost for signing the contract is 0 (and conversely -40 for not signing the contract).

**However this is only applicable in a single person game**.

In a case where the business owner and Architect were actively negotiating, it would appear that there would not be any practical ramifications for considering opportunity cost because the payoffs change depending on the other player and can only be seen after the fact.

for example consider a single period 2x2 game such that:
$$\left[\begin{matrix}(10,5)&(2,2)\\(2,2)&(5,10)\end{matrix} \right]$$

From the horizontal/vertical player's position his payoffs range from 10,5 and 2. He does not choose with respect to costs, he chooses based on what he thinks the payoffs will be.

---

To answer the broader question which you are probably wondering about.  
**Opportunity cost is only considered when a buy in for a specific game is necessary**

You'd have to consider expected value of a game compared to the cost. (however that only provides a fair price when the game is played infinity, you would also have to consider how many times you'd have to play a game and end up with a positive profit) using this formula:

$$n=\left(\frac{1.96\sigma}{p-\mu}\right)^2$$

I suggest reading up on [Martingales](https://en.wikipedia.org/wiki/Martingale_(betting_system)) and the [St. Petersberg Paradox](https://en.wikipedia.org/wiki/St._Petersburg_paradox) for more info.


---

### Answer by username_2 on 2017-11-12. Score: 0

In the case of this problem, you are assuming that the opportunity cost of the architect is zero (and the same for the builder), since you are saying that his payoff from refusing the contract is zero.

Remember that this is a theoretical game. You could include a different payoff for the opportunity cost, but it would be a different problem from the one you are presenting.

> **Comments:**
> **username_0**: How would you include it?  
> **username_0**: Note that  oppourtunity cost is not even considered in the question as an assumption  
> **username_2**: Since it is not considered, it means that it is zero. You could include it by changing the zero payoff to something else. For example, if the architect could make \$100,000 from doing something else, you would compare \$100,000 to 40%*(dollar amount of the contract in the question). If the opportunity cost was larger, then he would not sign the contract. Otherwise, he would sign it.  

---

