Find an equilibrium and the corresponding payoff. In Problems 1 and 2, the bet is $1.
1. Nim. Last move wins. 2,5, or 9 stones in a move. Initial position: 1 pile, 1000 stones.
2. Blackjack. Players has 10 and 6. Dealer shows 10. Cards left: 5, 5, 6, 7.
3. Matrix game.
| 3 | 4 | 3 | 0 | 3 |
| 5 | 7 | 5 | 5 | 0 |
| 5 | 4 | 4 | 6 | 3 |
| 7 | 5 | 5 | 6 | 5 |
4. Matrix game.
| 3 | -1 | 2 | 0 | 2 |
| 3 | 0 | 2 | 1 | 4 |
| 0 | 3 | 2 | 1 | -1 |
5. Matrix game.
| 2 | 1 | 2 | 0 | 3 |
| 2 | 2 | 0 | 2 | 2 |
| 3 | 2 | 1 | 1 | 1 |
| 4 | 5 | 1 | 1 | 1 |