\section{Related work}

\paragraph{Games} Among the long history of early works that model language evolution between agents \cite[e.g.][]{Steels:2003b,Brighton:etal:2003}, \newcite{Reitter:Lebiere:2011} simulate human language evolution with a Pictionary type task. Most recently, with the advent of neural network architectures, literature focuses on simple
referential games with a sender sending a single message to a
receiver, and reward depending directly on communication success
\cite[e.g.,][]{Lazaridou:etal:2017,Havrylov:Titov:2017,Lazaridou:etal:2018}. \newcite{Evtimova:etal:2018}
extend the referential game presenting the sender and receiver with
referent views in different modalities, and allowing multiple
message rounds. Still, reward is given directly for referential
success, and the roles and turns of the agents are
fixed. \newcite{Das:etal:2017b} generalize Lewis' signaling game \citep{Lewis:1969} and propose a cooperative image guessing game between two agents, a question bot and an answer bot. They find that grounded language emerges without supervision. \newcite{Cao:etal:2018} \citep[expanding on][]{Lewis:etal:2017}
propose a setup where two agents see the same set of items, and each
is provided with arbitrary, episode-specific utility functions for the
object. The agents must converge in multi-turn conversation to a
decision about how to split the items. The fundamental novelty of our
game with respect to theirs is that our rewards depend on consistent,
realistic commonsense knowledge that is stable across episodes
(hammers are good to break hard-shell fruits,
etc.). \citet{Mordatch:Abbeel:2018} \citep[see also][]{Lowe:etal:2017}
study emergent communication among multiple ($>2$) agents pursuing
their respective goals in a maze. In their setup, fully symmetric
agents are encouraged to use flexible, multi-turn communication as a
problem-solving tool. However, the independent complexities of
navigation make the environment somewhat cumbersome if the aim is to study
emergent communication.

\paragraph{Communication analysis} Relatively few papers have focused
specifically on the analysis of the emergent communication
protocol. Among the ones more closely related to our line of inquiry,
\newcite{Kottur:etal:2017} analyze a multi-turn signaling game. One
important result is that, in their game, the agents only develop a sensible code if the sender is deprived of memory across
turns. \newcite{Evtimova:etal:2018} study the dynamics of agent
confidence and informativeness as a conversation progresses. \newcite{Cao:etal:2018} train probe classifiers to predict, from the messages, each agent utility function and the decided split of items. Most directly related to our pragmatic analysis, \newcite{Lowe:etal:2019},
who focus on simple matrix communication games, introduce the notions
of positive signaling (an agent sends messages that are related to its
state) and positive listening (an agent's behaviour is influenced by
the message it receives). They show that positive signaling does not
entail positive listening, and commonly used metrics might not
necessarily detect the presence of one or the other. We build on their
work, by focusing on the importance of mutual positive listening in
communication (our ``bilateral communication'' measure). We
further refine the causal approach to measuring influence they
introduce. \citet{Jaques:etal:2018} also use the notion of causal
influence, both directly as a term in the agent cost function, and to
analyze their behaviour.
