Symbolab is a new search engine that allows one to search for equations. A great idea for those of us who, for example, forgot how the model of “stochastic game” is called, but remember that in stochastic games one is interested in the discounted sum of payoffs. The search engine presumably searches through articles to look for the equation that you look for.

Excited about the prospect that forgetting words is no longer devastating, I immediately searched for the formula of the discounted sum of payoffs:

$\sum _{t=1}^{\infty }\left(\lambda \left(1-\lambda \right)^{t-1}r\left(s_t,a_t\right)\right)$

Unfortunately 0 results were found. I did not give up and change the payoff function from “r” to “c” and then to “u”. Maybe the engine prefers costs or utilities. When I searched for the equation with costs, I got one result; a sum related to convex sets which is not related whatsoever to discounted sum. When I searched for the equation with utilities the engine gave up. I got 174 results! but they were of various sums, none of them (at least, not the 30 top ones which I looked at) involved discounted sums. There were references to statistics, ergodic theory, and various other topics, but no economics or game theory.

Maybe stochastic games are not that common on the net. Let’s look for something simpler:

$u_i\left(\sigma \right)\ge \:u_i\left(\sigma _{-i},\sigma ‘_i\right)$

which is the condition that defines Nash equilibrium. 0 results again. I gave up.

Unfortunately, it seems that we will have to continue remembering names of concepts, and will have to consult with colleagues when we need results in topics we are not familiar with. Magic has not been found yet.