The degraded broadcast channel with action-dependent states

In this paper we study the degraded broadcast channel with action dependent states and causal side information at the encoder. Two main models are studied: the case where the actions depend only on the messages, and the case where the actions can depend also on past values of the state. The latter model is referred to as actions with feedback. When the actions depend only on the messages, the full capacity region is derived. We then show that if the channel is physically degraded, then dependence of the actions on past values of the state does not increase its capacity region. We further demonstrate by an example that if the channel is stochastically degraded, action feedback can increase its capacity region. This situation resembles previous results on feedback in regular (state-independent) broadcast channels.