4 ms·
> there are mathematical proofs that at least one stable Nash equilibrium must exist in any game That's actually not true. E.g. the game "you get the amount of
by singron 6y ago
> there are mathematical proofs that at least one stable Nash equilibrium must exist in any game
That's actually not true. E.g. the game "you get the amount of money you ask for" has no equilibrium because you can always ask for a larger number. The proof on wikipedia doesn't apply to this game because the strategy space isn't compact. In real life, this doesn't come up much because usually your strategy is bounded somehow (e.g. you are limited by available cash+credit). I'm not as familiar with the other conditions listed and how they might relate to game strategies, but it would be interesting to hear an example game for each.
- tomrod 6y agoDoes your example classify as a game? Who are you playing against? Usually nature isn't consider a "player" per say, but rather just defines an environment. Otherwise, a game consists of three structures[0]: • a collection of participants, or players. • Each player has a set of choices, or strategies, for how to play/behave. • Combined behavior results in payoffs (satisfaction level) for each player Macroeconomic theory handwaves and says assets are generally bounded above by some non-binding constraint to rule out this behavior you've pointed out, for the record. [0] Lazy google search result scribbed liberally from https://www.cs.cmu.edu/~avrim/598/lect0504GameTheory.pdf https://www.cs.cmu.edu/~avrim/598/lect0504GameTheory.pdf