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Prisoner X | |||
resist | confess | ||
Prisoner 59640 | resist | 3 3 | 0 4 |
confess | 4 0 | 1 1 |
first notion : dominance
Prisoner X | |||
resist | confess | ||
Prisoner 59640 | resist | 3 3 | 0 4 |
confess | 4 0 | 1 1 |
not all games involve dominance
Gangster X | |||
stay home | attack | ||
Gangster Y | stay home | 2 2 | 1 3 |
attack | 3 1 | 0 0 |
No dominance! What to do?
second notion : nash equilibrium
Gangster X | |||
stay home | attack | ||
Gangster Y | stay home | 2 2 | 1 3 |
attack | 3 1 | 0 0 |
A nash equilibrium for a game
is a set of actions
from which no agent can unilaterally profitably deviate
see Osborne & Rubinstein, 1994 p. 14; Dixit et al, 2014 p. 95
Gangster X | |||
stay home | attack | ||
Gangster Y | stay home | 2 2 | 1 3 |
attack | 3 1 | 0 0 |
Why should the players not expect to settle on a non-Nash equilibrium?
If Gangster X expected this to happen, ...
A nash equilibrium for a game
is a set of actions
from which no agent can unilaterally profitably deviate
see Osborne & Rubinstein, 1994, p. 14; Dixit et al., 2014, p. 95
‘we wish to find the mathematically complete principles which define “rational behavior” for the participants in a social economy, and to derive from them the general characteristics of that behavior’
(Neumann, Morgenstern, Rubinstein, & Kuhn, 1953, p. 31).
An action is rational
in a noncooperative game
if it is a member of a nash equilibrium?
How you should act
is a function of two things:
your preferences
and your beliefs about how others will act.
Your beliefs about how others will act
are a function of your knowledge of two things:
your beliefs about their preferences
and your beliefs about how they believe others will act.
Your beliefs about how they believe others will act ...
How you should act:
short essay question:
What is team reasoning?
Which, if any, social interactions are better modeled by team reasoning than game theory?
plan
1. What is game theory? ✓
2a. What are its applications?
2. What are some limits on its applications? ✓
3. What is team reasoning and how might it overcome the limits? ✓