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Consider a typical organization whose worker agents seek to collectivelycooperate for its general betterment. However, each individual agentsimultaneously seeks to act to secure a larger chunk than its co-workers of theannual increment in compensation, which usually comes from a {\em fixed} pot.As such, the individual agent in the organization must cooperate and compete.Another feature of many organizations is that a worker receives a bonus, whichis often a fraction of previous year's total profit. As such, the agent derivesa reward that is also partly dependent on historical performance. How shouldthe individual agent decide to act in this context? Few methods for the mixedcooperative-competitive setting have been presented in recent years, but theseare challenged by problem domains whose reward functions do not depend on thecurrent state and action only. Recent deep multi-agent reinforcement learning(MARL) methods using long short-term memory (LSTM) may be used, but these adopta joint perspective to the interaction or require explicit exchange ofinformation among the agents to promote cooperation, which may not be possibleunder competition. In this paper, we first show that the agent'sdecision-making problem can be modeled as an interactive partially observableMarkov decision process (I-POMDP) that captures the dynamic of ahistory-dependent reward. We present an interactive advantage actor-criticmethod (IA2C$^+$), which combines the independent advantage actor-criticnetwork with a belief filter that maintains a belief distribution over otheragents' models. Empirical results show that IA2C$^+$ learns the optimal policyfaster and more robustly than several other baselines including one that uses aLSTM, even when attributed models are incorrect.

Cooperative-Competitive Reinforcement Learning with History-Dependent Rewards