# Reception Capacity: Definitions, Game Theory and Hardness

## TL;DR

This paper introduces a new reception capacity concept for wireless networks, models it through a novel optimization problem, and analyzes its bounds under game-theoretic and distributed algorithm frameworks.

## Contribution

It defines reception capacity based on omnidirectional antennas, relates it to the MaxPDS problem, and provides tight bounds under game-theoretic equilibrium conditions.

## Key findings

- Tight bounds on reception capacity approximation.
- Relation between reception capacity and MaxPDS problem.
- Analysis of capacity under Nash and correlated equilibria.

## Abstract

The capacity of wireless networks is a classic and important topic of study. Informally, the capacity of a network is simply the total amount of information which it can transfer. In the context of models of wireless radio networks, this has usually meant the total number of point-to-point messages which can be sent or received in one time step. This definition has seen intensive study in recent years, particularly with respect to more accurate models of radio networks such as the SINR model. This paper is motivated by an obvious fact: radio antennae are (at least traditionally) omnidirectional, and hence point-to-point connections are not necessarily the best definition of the true capacity of a wireless network. To fix this, we introduce a new definition of reception capacity as the maximum number of messages which can be received in one round, and show that this is related to a new optimization problem we call the Maximum Perfect Dominated Set (MaxPDS) problem. Using this relationship we give a tight lower bound for approximating this capacity which essentially matches a known upper bound. As our main result, we analyze this notion of capacity under game-theoretic constraints, giving tight bounds on the average quality achieved at any coarse correlated equilibrium (and thus at any Nash). This immediately gives bounds on the average behavior of the natural distributed algorithm in which every transmitter uses online learning algorithms to learn whether to transmit.