<p>One &quot;natural&quot; approach would be to base the price on the expected discounted revenue stream. Writing <span class="math-container">$R_t$</span> as the (random) revenue in period <span class="math-container">$t$</span> of one share, this then would be:
<span class="math-container">$$
p_t = \mathbb{E}\left(\sum_{t = 0}^T \frac{R_t}{(1+r)^t}\right) = \sum_{t = 0}^T \frac{\mathbb{E}(R_t)}{(1+r)^t}.
$$</span>
In addition, you might want to lower this price a bit, especially if the income stream is very volatile and if you would expect that individuals are risk averse.</p>
<p>One thing determine then is the rate <span class="math-container">$r$</span>. Ideally, this should be set equal to the rate of return of a risk-free asset (if you have this in your game). If the game does not last very long, I guess setting <span class="math-container">$r = 0$</span> also makes sense.</p>

CC BY-SA 4.0
2021-04-30T08:40:56.363Z
I think I see 2 problems with this:. The bank cannot (and should not) predict future revenue. That should be the players job. And I am not sure how this takes into account that shares may be dilluted over time by other players.
user2741831
CC BY-SA 4.0
2021-04-30T08:54:35.193Z
@user2741831 I'm not saying that the bank should predict the revenue, just that it should use the "real" expected revenue stream to set the price. 
If the bank sets the prices according to the expected return of the income stream, then the expected "profits" of the bank are in fact zero, so you can think of this as a perfectly competitive banking sector with zero profits.
I don't understand what you mean by "shares are diluted over time by other players"
tdm
CC BY-SA 4.0
2021-04-30T09:22:53.527Z
The income stream isn't set by the bank, its determined by player actions (otherwise they would be impossible to predict). So the bank has no idea what the income is going to be. The bank is also not a player so it can't predict it either. I don't know what you mean by "real expected revenue stream". Buying portions of the income stream must be possible at any time. So this means more shares are created, meaning the share pool gets "diluted" over time (100 shares may be 30% of the income stream at some point but turn into 20% as players create more shares by buying them).
user2741831
CC BY-SA 4.0
2021-04-30T08:26:23.247Z
2021-04-30T08:26:23.247Z
tdm
<p>I'm trying to create a game that's a bit like monopoly. The objective of the game is to earn money by investing money. The game has a limited amount of players and an increasing amount of money each game. That is done through regular stocks with a fixed supply but also through a system that involves buying shares of a revenue stream whose intensity changes through the course of the game.<br />
For the game, its very important that users can buy into that stream at any given time with any given amount of money. It should not be possible to limit access to that revenue stream by simply buying up all shares and then refusing to sell them at any price.<br />
I don't want to get into to much detail about how the game would work, its just important that this revenue stream remains open to all players at any given time for any lump sum.<br />
But that does not mean its always a good idea to invest in it, but it should still be profitable for the players to correctly predict incoming revenue.</p>
<p>The &quot;shares&quot; can be bought directly from the &quot;bank&quot; and traded amongst players (but it would not be a problem if buying directly from the bank would be a better option in every case).<br />
A share in the revenue stream would grant the player a portion of it. The revenue stream should always be divided amongst players as the money comes in (it should never flow to the bank). Also shares cannot be sold back to the bank.</p>
<p>Now since the &quot;bank&quot; would be an autmated system and not an active player in the game, it needs a system to automatically determine the price of the shares. And this is where I am stuck. How can I incentivize players to buy into a portion of something that is reduced over time? One idea that I had was to set the price of shares equal to the amount of shares. That way the shares should always arrive at the ideal equilibrium and people getting in early are rewarded. The problem with this is, that if the revenue stream is expected to go down, almost nobody will buy new shares, essentially cutting them off from buying it.<br />
So can somebody help me create a system like this? A system that</p>
<ul>
<li>rewards getting early</li>
<li>is always open to new investors</li>
<li>reduces equity as more people buy in</li>
</ul>

CC BY-SA 4.0
2021-04-29T14:15:21.720Z
Hi! I am into games and economic systems, but I have to ask (other members of the SE): is this on-topic?
Giskard
CC BY-SA 4.0
2021-04-29T14:46:17.067Z
I was pretty sure it isnt on topic on money st. So I posted it here
user2741831
CC BY-SA 4.0
2021-04-29T15:39:32.670Z
I am pretty sure it is not on-topic on History either, but that does not mean you should post it on Physics. You need not worry about this, question is for the other members, discussion will probably move to Meta.
Giskard
<game-theory><securities>
Form of security with a potentially infinite amount of equity for a continous payout for game?
user2741831
# Form of security with a potentially infinite amount of equity for a continous payout for game?

(Asked by: username_0 on 2021-04-29)

I'm trying to create a game that's a bit like monopoly. The objective of the game is to earn money by investing money. The game has a limited amount of players and an increasing amount of money each game. That is done through regular stocks with a fixed supply but also through a system that involves buying shares of a revenue stream whose intensity changes through the course of the game.  
For the game, its very important that users can buy into that stream at any given time with any given amount of money. It should not be possible to limit access to that revenue stream by simply buying up all shares and then refusing to sell them at any price.  
I don't want to get into to much detail about how the game would work, its just important that this revenue stream remains open to all players at any given time for any lump sum.  
But that does not mean its always a good idea to invest in it, but it should still be profitable for the players to correctly predict incoming revenue.

The "shares" can be bought directly from the "bank" and traded amongst players (but it would not be a problem if buying directly from the bank would be a better option in every case).  
A share in the revenue stream would grant the player a portion of it. The revenue stream should always be divided amongst players as the money comes in (it should never flow to the bank). Also shares cannot be sold back to the bank.

Now since the "bank" would be an autmated system and not an active player in the game, it needs a system to automatically determine the price of the shares. And this is where I am stuck. How can I incentivize players to buy into a portion of something that is reduced over time? One idea that I had was to set the price of shares equal to the amount of shares. That way the shares should always arrive at the ideal equilibrium and people getting in early are rewarded. The problem with this is, that if the revenue stream is expected to go down, almost nobody will buy new shares, essentially cutting them off from buying it.  
So can somebody help me create a system like this? A system that

* rewards getting early
* is always open to new investors
* reduces equity as more people buy in

**Tags:** game-theory, securities

> **Comments:**
> **username_1**: Hi! I am into games and economic systems, but I have to ask (other members of the SE): is this on-topic?  
> **username_0**: I was pretty sure it isnt on topic on money st. So I posted it here  
> **username_1**: I am pretty sure it is not on-topic on History either, but that does not mean you should post it on Physics. You need not worry about this, question is for the other members, discussion will probably move to Meta.  

---

## 1 answers

### Answer by username_2 on 2021-04-30. Score: 1 | Accepted answer

One "natural" approach would be to base the price on the expected discounted revenue stream. Writing $R\_t$ as the (random) revenue in period $t$ of one share, this then would be:
$$
p\_t = \mathbb{E}\left(\sum\_{t = 0}^T \frac{R\_t}{(1+r)^t}\right) = \sum\_{t = 0}^T \frac{\mathbb{E}(R\_t)}{(1+r)^t}.
$$
In addition, you might want to lower this price a bit, especially if the income stream is very volatile and if you would expect that individuals are risk averse.

One thing determine then is the rate $r$. Ideally, this should be set equal to the rate of return of a risk-free asset (if you have this in your game). If the game does not last very long, I guess setting $r = 0$ also makes sense.

> **Comments:**
> **username_0**: I think I see 2 problems with this:. The bank cannot (and should not) predict future revenue. That should be the players job. And I am not sure how this takes into account that shares may be dilluted over time by other players.  
> **username_2**: @username_0 I'm not saying that the bank should predict the revenue, just that it should use the "real" expected revenue stream to set the price.  If the bank sets the prices according to the expected return of the income stream, then the expected "profits" of the bank are in fact zero, so you can think of this as a perfectly competitive banking sector with zero profits. I don't understand what you mean by "shares are diluted over time by other players"  
> **username_0**: The income stream isn't set by the bank, its determined by player actions (otherwise they would be impossible to predict). So the bank has no idea what the income is going to be. The bank is also not a player so it can't predict it either. I don't know what you mean by "real expected revenue stream". Buying portions of the income stream must be possible at any time. So this means more shares are created, meaning the share pool gets "diluted" over time (100 shares may be 30% of the income stream at some point but turn into 20% as players create more shares by buying them).  

---

