<p>Countably infinite is easy to extend to, no obstacles. You can use results by <a href="http://www.sciencedirect.com/science/article/pii/S089054010500204X" rel="nofollow">Moss and Viglizzo (2006)</a>. I will also shamelessly promote my own work <a href="http://sanderheinsalu.com/papers/Universal%20type%20structures%20with%20unawareness.pdf" rel="nofollow">Universal type structures with unawareness</a> that mathematically treats each of (possibly countably infinitely many) awareness levels as a player.</p>

CC BY-SA 3.0
2015-04-15T06:55:05.170Z
Wow, thank you for your answer. I tried to figure out myself, but only to see that it's true for the case when each of the countably infinite players has a compact metrizable strategy space. I have to confess that I have no prior exposure to category theory. Could you please provide some reference to understand the stuffs in the works you recommended?
Metta World Peace
CC BY-SA 3.0
2015-04-15T07:40:23.577Z
Assumptions on strategy spaces are of course needed. There are two basic approaches to universal type spaces - the Mertens and Zamir topological one (compact metrizable etc strategies is a generalization) and the Heifetz and Samet purely measurable one (generalized by Moss and Viglizzo). I don't have a good reference for category theory, sorry.
Sander Heinsalu
CC BY-SA 3.0
2015-04-15T07:49:46.673Z
Thank you for your information. I should have expected there's no short-cut for this stuff.
Metta World Peace
CC BY-SA 3.0
2015-04-15T04:53:51.287Z
2015-04-15T04:53:51.287Z
Sander Heinsalu
<p>Having just dabbled in <a href="https://books.google.com.hk/books?id=HkAwexYQww4C&amp;printsec=frontcover&amp;hl=zh-CN#v=onepage&amp;q&amp;f=false" rel="nofollow">7.1</a>of rationality in extensive games by Andres Perea, I got an impression all constructions of universal type space are restricted to finite players. What's the obstacle to extend it to countably infinite players? For example, is it trivial to extend them to cover OLG games in which each stage game is only played by finite players?</p>

<mathematical-economics><game-theory><reference-request>
Is there a universal type space involving infinite players?
Metta World Peace
# Is there a universal type space involving infinite players?

(Asked by: username_0 on 2015-03-25)

Having just dabbled in [7.1](https://books.google.com.hk/books?id=HkAwexYQww4C&printsec=frontcover&hl=zh-CN#v=onepage&q&f=false)of rationality in extensive games by Andres Perea, I got an impression all constructions of universal type space are restricted to finite players. What's the obstacle to extend it to countably infinite players? For example, is it trivial to extend them to cover OLG games in which each stage game is only played by finite players?

**Tags:** mathematical-economics, game-theory, reference-request

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## 1 answers

### Answer by username_1 on 2015-04-15. Score: 2 | Accepted answer

Countably infinite is easy to extend to, no obstacles. You can use results by [Moss and Viglizzo (2006)](http://www.sciencedirect.com/science/article/pii/S089054010500204X). I will also shamelessly promote my own work [Universal type structures with unawareness](http://sanderheinsalu.com/papers/Universal%20type%20structures%20with%20unawareness.pdf) that mathematically treats each of (possibly countably infinitely many) awareness levels as a player.

> **Comments:**
> **username_0**: Wow, thank you for your answer. I tried to figure out myself, but only to see that it's true for the case when each of the countably infinite players has a compact metrizable strategy space. I have to confess that I have no prior exposure to category theory. Could you please provide some reference to understand the stuffs in the works you recommended?  
> **username_1**: Assumptions on strategy spaces are of course needed. There are two basic approaches to universal type spaces - the Mertens and Zamir topological one (compact metrizable etc strategies is a generalization) and the Heifetz and Samet purely measurable one (generalized by Moss and Viglizzo). I don't have a good reference for category theory, sorry.  
> **username_0**: Thank you for your information. I should have expected there's no short-cut for this stuff.  

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