Consider a three player game where all players simultaneously announce a positive integer of their choosing. The smallest unique positive integer wins. What's the optimal strategy for this game? What strategy is so good that, even if everybody was using it - and everybody knew everybody was using it - nobody would change? Such a strategy gives us what's called a Nash equilibrium, and we'll find several for this game. #gametheory #mathematics #mathpuzzle

extended cut with algebra:    • You'll Never Guess the Optimal Strategy (e...  

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0:00 Intro
2:31 Nash Equilibrium
6:06 Mixed Strategies
8:04 Finding a Trivial Equilibrium
9:41 Symmetric Nash Equilibrium
15:35 The Solution (Part 1)
22:16 The Solution (Part 2)
26:35 Algebra
27:52 Final Details
28:45 Conclusion