Аn application of algebraic topology and graph theory in microeconomics

One of the important questions in mechanism design is the implementability of allocation rules. An allocation rule is called implementable if for any agent, benefit from revealing its true type is better than benefit from lying. I’ll show some illustrative examples. Obviously, some allocation rules are not implementable. Rochet’s theorem states that an allocation rule is implementable iff it is cyclically monotone. During the talk, I’ll present a new convenient topological condition that guarantees that cyclic monotonicity is equivalent to ordinary monotonicity. The last one is easy to check (in contrary to cyclic one). Graph theory and algebraic topology appear to be very useful here.