6th World Congress · 2021

Which Nash equilibria of a bimatrix game are stable under replicator dynamics?

For a constant ε, we prove a P(N) lower bound on the (randomized) communication complexity of ε-Nash equilibrium in two-player N by N games. For n-player binary-action games we prove an exp(n) lower bound for the (randomized) communication complexity of ε-Nash equilibrium. The implications of these results on the rate of convergence of dynamics to Nash equilibria are discussed.

Welfare Economics, the study of economic well-being, consists of two separate branches, one concerning individual well-being, the other concerning social aggregation. The first branch includes the standard revealed preference paradigm as well as tools from Behavioral Welfare Economics. The second branch subsumes work on social choice and welfare.

Vast literatures study these issues from a normative perspective. They ask, how should we evaluate individual well-being? How should we determine overall social welfare? The normative principles that have emerged from these inquiries have proven useful in innumerable applications.

The objective of this research agenda is to study these issues from a positive perspective. We ask, how do people actually evaluate what is good and bad for other individuals? How do they actually aggregate to reach conclusions about social welfare?

Research in positive welfare economics is valuable because it helps us understand why societies adopt particular policies. With respect to aggregation, it helps us understand how people think their societies ought to balance majority preference against the protection of minorities, judgments which (arguably) their elected representatives ought to respect. It also helps us understand how behavioral considerations, such as cognitive biases, can influence policy formation.

This work departs from most (but not all) of the literature on social preferences by focusing on outcomes for others without implicating selfish concerns.