| Original Formulation | Baker Skis | Baker goes to Festval |
| Abel Skis |
1
|
0
|
| Abel goes to Festival |
-1
|
2
|
A point on the graph is a Nash Equilibrium point if neither player can
unilaterally improve his or her utility. All pure strategies are nash equilibria
except the onw where each goes, alone, where the other wanted to
go.
Although a Nash equilibrium, the failure point is not pareto optimal
aince, by co-operating, they can mive to a point that is better for both,
either skiing together or going to the music festival together.
Any mixed strategy in which they both will go to the same place,
determined at random, is also Pareto optimal. These mixed strategies arde
also Nash equilibria sonce if one player cheats yjey just replace the probability
of going together to the other's preferred site with the same probability
of going alone to his or her own.
The key question is how to determine which ofthe pareto optimal points
to choose;
that is. what will be the probability of skiing.
Nash proposed the following utility gormula for the utility of a specific
point:
Nasj utility = (Abel's EU-Abels failure point)*(Baker's EU-Baker's
failure point)
Now, usppose Abel has the option to ski with Charlie. It's not
as much fun for him
as skiing with Baker, but it has a utility to Abel of .5.
Click here to see the effect
on negotiations between Abel & baker