I have this problem:
- We dispose of some resources, say $\{f_1, f_2, \dotsc, f_m\}$;
- We have some agents or players, say $\{\mathrm{p}_1, \mathrm{p}_2, \dotsc, \mathrm{p}_n\}$;
- Every player has some utility $u_i$;
- If two player or more $(u_i, u_i^{'}, \dotsc)$ choose the same resource $f_j$, the payoff will decrease;
- The problem is to maximize the sum of the utility, $\sum\limits_{i}u_i$;
- When a resource $f_j$ is selected by a player $\mathrm{p}_i$, she get a payoff of, say, $u_i(f_j)$;
Now the idea to solve the problem is something like this:
- Every player $\mathrm{p}_i$ chooses randomly with some probability distribution, say uniform distribution, a resource $f_j$.
- Now, every player calculates its payoff: If the payoff is acceptable then the player keeps that resource with probability $1$. Else the player change to other resource with some probability, say $p$.
My question is: Could you please give me some good reference that tackle this kind of problem? What is the kinds of algorithms used to solve it? Is it learning algorithms? Is it distributed algorithms? Is it stochastic programming? What is it$\dotsc$? I looked for these words on google but I cannot find a good references.
Any suggestions, books, references would be appreciated.
Thanks.
I think it is best known as the fair division problem. Here's wikipedia to get started http://en.wikipedia.org/wiki/Fair_division However, I haven't seen the exact protocol you specify. It seems similar to the economic concept of directed search. http://www.nber.org/papers/w17746