On: Machine Money and People Money

[antisthenes]

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.

[_jgvg → antisthenes]

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].