<p>If I understand the question correctly, I believe the neatest way to put it is to simply call you solution concept "individual rationality". </p>

<p>Individual rationality can easily be seen as a cooperative game theory solution concept in its own right. I am not aware of any other name for a solution concept consisting only of an individual rationality requirement.</p>

CC BY-SA 3.0
2014-12-01T16:38:03.357Z
2014-12-01T17:12:37.860Z
2014-12-01T17:12:37.860Z
Martin Van der Linden
<p>I suppose it would look something like</p>

<p>$\Pi^m$ is the profit of a monopolist.
$\Pi^c$ is the profit under collusion.
$\Pi^c=\frac{\Pi^m}{n}$
$\Pi^{comp}$</p>

<p>suppose $\Pi^m&gt; \Pi^c&gt; \Pi^{comp} $.
The profit a firm gets for deviating through 1 period is $\Pi^d=\Pi^m-\epsilon=\Pi^m$</p>

<p>The condition to sustain collusion is $\Pi^d +\delta \Pi^{comp} +\delta ^2 \Pi^{comp}+...&gt; \Pi^c+ \delta \Pi^c+ ... $</p>

<p>for collusion to be sustained, time needs to be infinite and discount factor $\delta$ needs to be sufficiently high.</p>

CC BY-SA 3.0
2014-11-20T00:53:43.773Z
2014-11-20T00:53:43.773Z
Jamzy
<p>In the core of cooperative games, the total cost of forming a coalition is shared by all members in a coalition (efficiency). However for my problem I only require that all members are individually rational in the coalition - that is, if the utility of at least one member of the coalition is less than the utility he would gain by being alone, then he will break away from the coalition.</p>

<p>In other words, what is the solution concept that only requires stability and does not carry the notion of efficiency? </p>

CC BY-SA 3.0
2014-11-19T14:01:12.203Z
To me it is not quite clear if you are talking about a concept in cooperative GT (e.g. in NTU games) or if you are talking about non-cooperative GT.
The Almighty Bob
CC BY-SA 3.0
2014-11-19T18:12:11.873Z
@TheAlmightyBob: Cooperative GT. Is there a concept of coalition in non-coop GT as well?
Bravo
CC BY-SA 3.0
2014-11-19T18:33:29.970Z
Do you mean rational self-interest?
Jason Nichols
CC BY-SA 3.0
2014-11-19T18:59:24.420Z
In non-coop GT, there is a solution concept called **coalition-proof Nash equilibrium**, proposed by Bernheim, Peleg, Whinston (1987, *JET*). But existence of such an equilibrium is not guaranteed in general.
Herr K.
<game-theory><cooperative-game-theory>
Modified core for cooperative games
Bravo
# Modified core for cooperative games

(Asked by: username_0 on 2014-11-19)

In the core of cooperative games, the total cost of forming a coalition is shared by all members in a coalition (efficiency). However for my problem I only require that all members are individually rational in the coalition - that is, if the utility of at least one member of the coalition is less than the utility he would gain by being alone, then he will break away from the coalition.

In other words, what is the solution concept that only requires stability and does not carry the notion of efficiency?

**Tags:** game-theory, cooperative-game-theory
> **Comments:**
> **username_1**: To me it is not quite clear if you are talking about a concept in cooperative GT (e.g. in NTU games) or if you are talking about non-cooperative GT.  
> **username_0**: @TheAlmightyBob: Cooperative GT. Is there a concept of coalition in non-coop GT as well?  
> **username_2**: Do you mean rational self-interest?  
> **username_3**: In non-coop GT, there is a solution concept called **coalition-proof Nash equilibrium**, proposed by Bernheim, Peleg, Whinston (1987, *JET*). But existence of such an equilibrium is not guaranteed in general.  

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## 2 answers

### Answer by username_4 on 2014-12-01. Score: 2

If I understand the question correctly, I believe the neatest way to put it is to simply call you solution concept "individual rationality".

Individual rationality can easily be seen as a cooperative game theory solution concept in its own right. I am not aware of any other name for a solution concept consisting only of an individual rationality requirement.


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### Answer by username_5 on 2014-11-20. Score: 1

I suppose it would look something like

$\Pi^m$ is the profit of a monopolist.
$\Pi^c$ is the profit under collusion.
$\Pi^c=\frac{\Pi^m}{n}$
$\Pi^{comp}$

suppose $\Pi^m> \Pi^c> \Pi^{comp} $.
The profit a firm gets for deviating through 1 period is $\Pi^d=\Pi^m-\epsilon=\Pi^m$

The condition to sustain collusion is $\Pi^d +\delta \Pi^{comp} +\delta ^2 \Pi^{comp}+...> \Pi^c+ \delta \Pi^c+ ... $

for collusion to be sustained, time needs to be infinite and discount factor $\delta$ needs to be sufficiently high.


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