Positional Games and Randomness

on YouTube ↗01h 02m

" summary

Focuses on positional games played on graphs and hypergraphs, exploring how randomness and deterministic structure affect players’ ability to achieve goals in games like Maker-Breaker, Avoider-Enforcer, and strong games. Describes methods linking probabilistic tools (random graph properties) with game-theoretic strategies to determine thresholds, winning tactics, and typical outcomes in these combinatorial games.

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" chapters (23)

1. 0:00Start
2. 1:01Main goal
3. 2:20Positional games - setting
4. 4:21So what's the connection?
5. 5:23Omnipresent randomness in positional games
6. 9:29Basic setting (cont.)
7. 11:59Unbiased Maker-Breaker games
8. 14:25Maker-Breaker games -examples
9. 17:29Erdos-Selfridge criterion-proof sketch
10. 20:56This looks familiar...
11. 22:16Erdös-Selfridge Criterion - application
12. 24:58Maker-Breaker unbiased sames are frequently boring...
13. 27:55Bias monotonicity, threshold bias
14. 30:59So what is the threshold bias for...?
15. 33:11Probabilistic intuition/Erdos paradigm
16. 38:27Biased Hamiltonicity game-resolution
17. 44:09Biased Hamiltonicity game - Maker's side (cont.)
18. 46:27Large component game
19. 50:12Games on random boards
20. 53:17Unbiased Hamiltonicity game on G(np)
21. 54:02Hamiltonicity game on G(np) - result
22. 55:29Half-random games
23. 57:08Hamiltonicity game with random Maker