ACHIEVEMENT DESCRIPTION Utility

STATUS QUO

IMPACT

State of device i

State of other devices

Action of device i

NEXT-PHASE GOALS

NEW INSIGHTS

Oblivious equilibrium for stochastic games with concave utilityS. Adlakha, R. Johari, G. Weintraub, A. Goldsmith MAIN RESULT:

Consider stochastic games per-period utility and state dynamics that are increasing, concave, submodular.

Then in a large system, each node can find approximately optimal policies by treating the state of other nodes as constant.

HOW IT WORKS:

Under our assumptions, no single node is overly influential )we can replace other nodes’ states by their mean.So the optimal policies decouple between nodes.

ASSUMPTIONS AND LIMITATIONS:

This result holds under much more general technical assumptions than our early results on the problem.

A key modeling limitation, however, is that the limit requires all nodes to interact with each other.Thus the results apply only to densenetworks.

- Our results provide a general framework to study the interaction of multiple devices.
- Further, our results:
- unify existing models for which such limits were known
- and provide simple exogenous conditions that can be checked to ensure the main result holds

Next state

Utility

Current state orcurrent action

Current state orcurrent action

Many cognitive radio models do notaccount for reaction of other devicesto a single device’s action.

In prior work, we developed a generalstochastic game model to tractably capture interactions of many devices.

# of other devices withgiven state

In principle, tracking state of other devices is complex.

We approximate state of other devices via a mean field limit.

State

We will apply our results to a modelof interfering transmissions among energy-constrained devices.

Our main goal is to develop arelated model that applies when a single node interacts with a small number of other nodes each period.

Real environments are reactive and non-stationary;this requires new game-theoretic models of interaction