Re:Machine Money and People Money
by antisthenes on Monday July 11, 2016 @07:26PM
(#12075586)
If both actors have the options of the first 2 outcomes you described then where does the (-0.5, -0.5) come from?
That outcome cannot be NE by your own given inputs, since both actors can improve their outcomes by switching to a different strategy.
The outcomes of the individual decisions are added, so (-0.5, -0.5) comes from each agent picking options a, resulting in +1 for themselves and -1.5 to the other. The outcome for each agent in this case is +1-1.5=0.5
The payout matrix is:
(-0.5, -0.5) (+1, -1)
(-1, +1) (+0.5, +0.5)
As you can see, from the [a,a] option, no agent can improve their situation by UNILATERALLY changing. In the case of [a,b], [b,a] and [b,b], one (or both) of the agents can always improve their own payout by switching from b to a.
So there's only one Nash equilibrium, at [a,a].
a) Use more resources: +1 for them, -1.5 for everyone else b) Use same resources: +0.5 for them, +0 for everyone else
There is only one Nash equilibrium: (a,a) with payout (-0.5,-0.5).
Repeat it again and again without cooperation and you have the tragedy of the commons.
Nash equilibrium isn't about a repeating game reaching equilibrium over time, but about the decisions multiple agents face in one specific round.