You solve games by having solution criteria . Unfortunately, for any reasonable list of solution criteria you will always be able to find games where the result doesn’t seem to make sense. Also, there is no set of obviously correct and complete solution concepts. Consider the following game:
Two rational people simultaneously and secretly write down a real number [0,100]. The person who writes down the highest number gets a payoff of zero, and the person who writes down the lowest number gets that as his payoff. If there is a tie they each get zero. What happens?
The only “Nash equilibrium” (the most important solution concept in all of game theory) is for both players to write down 0, but this is a crazy result because picking 0 is weakly dominated by picking any other number (expect 100).
Game theory also has trouble solving many games where (a) Player Two only gets to move if Player One does a certain thing, (b) Player One’s strategy is determined by what he expects Player Two would do if Player Two gets to move, and (c) in equilibrium Player Two never moves.
Are you agreeing or disagreeing with “the things you describe in this post seem to be the kind of maths a smart alien race might discover just like we did”?
It depends on what you mean by “might” and “discover” (as opposed to invent). I predict that smart aliens’ theories of physics, chemistry, and evolution would be much more similar to ours than their theories of how rational people play games would be.
Can you explain this? I always thought of game theory as being like calculus, and not about human values (like this comment says).
You solve games by having solution criteria . Unfortunately, for any reasonable list of solution criteria you will always be able to find games where the result doesn’t seem to make sense. Also, there is no set of obviously correct and complete solution concepts. Consider the following game:
Two rational people simultaneously and secretly write down a real number [0,100]. The person who writes down the highest number gets a payoff of zero, and the person who writes down the lowest number gets that as his payoff. If there is a tie they each get zero. What happens?
The only “Nash equilibrium” (the most important solution concept in all of game theory) is for both players to write down 0, but this is a crazy result because picking 0 is weakly dominated by picking any other number (expect 100).
Game theory also has trouble solving many games where (a) Player Two only gets to move if Player One does a certain thing, (b) Player One’s strategy is determined by what he expects Player Two would do if Player Two gets to move, and (c) in equilibrium Player Two never moves.
I’m not understanding you, the things you describe in this post seem to be the kind of maths a smart alien race might discover just like we did.
Many games don’t have solutions, or the solutions depend on arbitrary criteria.
… and?
Are you agreeing or disagreeing with “the things you describe in this post seem to be the kind of maths a smart alien race might discover just like we did”?
It depends on what you mean by “might” and “discover” (as opposed to invent). I predict that smart aliens’ theories of physics, chemistry, and evolution would be much more similar to ours than their theories of how rational people play games would be.