Missile vs. Laser: The Game of Terminal Maneuvers
29 points by EthanHeilman
29 points by EthanHeilman
Delightful reading, thanks for posting!
Very cool! I find it very fascinating how game theory has a lot of applications outside of game design. It feels like game design is actually the field where game theory is least useful sometimes!
Very cool!
This is very interesting, and I’m thinking of using “Missile vs Laser” as a toy example for some technologies I want to learn.
(I might even, crediting the author, as part of didactic examples when teaching programming topics: there are some core topics, e.g., generator coroutines, that this might motivate nicely. It’s actually surprisingly hard to find games that are extremely simple while still being interesting.)
I wonder why the author fixed the missile fuel to 7 units, if that means that the laser wins 75% of the time. Since fuel level is such a small discrete space, why not search for the value that gives even odds? Would this make the game more sensitive to “strategy”?
Presumably the author could not derive (nor prove) an “optimum strategy,” despite having some background in game theory. How would one go about proving whether such an optimum strategy does or does not exist? (Does the author’s intuition suggest that such a strategy must or must not exist?)
Finally, in the absence of an optimum strategy, has the author published any comparisons of strategies? I see from the code that there are a few choices for AI-strategy (though they are largely random). Would this tell us anything interesting about the “structure” of the game?
Thanks for reading it. I really enjoyed your questions
I wonder why the author fixed the missile fuel to 7 units, if that means that the laser wins 75% of the time
Because it makes the missile players moves less interesting in my opinion. 6 is too unfair, 7 forces really tough decisions on the missile. Who knows maybe 8 is the sweet spot, play around with it and let me know what you find out.
Since fuel level is such a small discrete space, why not search for the value that gives even odds?
That’s an question I’ve pondered but haven’t found an exact answer. There is a strategy with 15 fuel where the missile always has slightly better than even chance. Pay 14 fuel to stay safe for rounds 1 to 4 and then randomly choose 0 or 1 for the last round. It is almost certainly the case there are better strategies for the missile at 14 fuel. My guess is that it shifts in the missiles favor around 8, 9 or 10.
Presumably the author could not derive (nor prove) an “optimum strategy,” despite having some background in game theory. How would one go about proving whether such an optimum strategy does or does not exist? (Does the author’s intuition suggest that such a strategy must or must not exist?)
A friend of mine found nash equilibria for the last three rounds of game but they sadly did not publish their results. Finding equilibria is a convex optimization problem and the solvers you can find online didn’t support the number of variables needed for all 5 rounds. It is likely doable, but requires more work that I was willing to put in. Would be a great Math masters thesis project if you know anyone who is interested.
Finally, in the absence of an optimum strategy, has the author published any comparisons of strategies? I see from the code that there are a few choices for AI-strategy (though they are largely random). Would this tell us anything interesting about the “structure” of the game?
I don’t know. It would be fun to have a tournament like that famous Prison’s Dilemma tournament and see which strategy wins. I suspect some elements of the game are like rock paper scissors where random play is best.