Question 1: Short answer
hardAI-checkedMulti-Agent SystemsIn a two-player game, player 1 has these payoffs (player 2 always gets 0):
| left | right | |
|---|---|---|
| top | 6 | 0 |
| middle | 0 | 6 |
| bottom | 2 | 8 |
A joint distribution puts probability on (top, left) and on (middle, right), so player 1 earns 6 on average. If player 1 instead commits in advance to one fixed action while player 2 keeps following , what is the best expected payoff player 1 can get?