Stability and Implementation via Simple Mechanisms in the Complete Information Environments

This paper investigates implementation of social choice functions in the complete information environments. We construct particularly simple mechanisms named local direct mechanisms, which require each agent to make a single announcement about her own and neighbors'utility indices. We assume that each agent is boundedly rational in that she may announce any best reply, including disequilibrium messages, even if the others play a Nash equilibrium. We require that the honest message profile be stable in the global sense that it is reachable from every message profile and no other message profile is reachable from it. It is shown that with a minor restriction, every social choice function is virtually implementable. We provide naive models of adaptive dynamics whose convergence characterizes the static definition of stability. We also investigate several variants of the stability notion such as BR-stability, weak stability, and weak BR-stability