An exercise in selfish stabilization

Abstract

Stabilizing distributed systems expect all the component processes to run predefined programs that are externally mandated. In Internet scale systems, this is unrealistic, since each process may have selfish interests and motives related to maximizing its own payoff. This article formulates the problem of selfish stabilization to show how competition blends with cooperation in a stabilizing environment.

Nash Equilibria in Stabilizing Systems

“…There are, however, substantial differences between the problems addressed in the current paper and those addressed in [3] and [4].…”

“…The notion that each process in a stabilizing distributed system may have a distinct gain function (that the process seeks to maximize during the system execution) has appeared in the pioneering work of [3] and [4]. There are, however, substantial differences between the problems addressed in the current paper and those addressed in [3] and [4].…”

“…In [3] and [4], the gain function of each process in a stabilizing distributed system is defined at each state (whether stable or not) of the system. By contrast, in the current paper, the gain function of each process in the system is defined only at the (stable) fixed points of the system.…”

“…2. In [3] and [4], the actions of each process in the system are intended to increase the value of the gain function of that process. In the current paper, the actions of each process are only intended to force the system into a fixed point.…”

“…3. In [3] and [4], once the system reaches a fixed point, no process can perturb its local state. In the current paper, once the system reaches a fixed point, any process can perturb its local state in order to push the system towards another fixed point, provided that the gain function of the process has a higher value at this new fixed point.…”