Solving Hanabi: Estimating Hands by Opponent's Actions in Cooperative Game with Incomplete Information

A unique behavior of humans is modifying one’s unobservable behavior based on the reaction of others for cooperation. We used a card game called Hanabi as an evaluation task of imitating human reflective intelligence with artificial intelligence. Hanabi is a cooperative card game with incomplete information. A player cooperates with an opponent in building several card sets constructed with the same color and ordered numbers. However, like a blind man's bluff, each player sees the cards of all other players except his/her own. Also, communication between players is restricted to information about the same numbers and colors, and the player is required to read his/his opponent's intention with the opponent's hand, estimate his/her cards with incomplete information, and play one of them for building a set. We compared human play with several simulated strategies. The results indicate that the strategy with feedbacks from simulated opponent's viewpoints achieves more score than other strategies.  The solving process of this social intelligence is one of the interesting challenges for both artificial intelligence (AI) and cognitive science. Bryne et al. hypothesized that the human brain increases mainly due to this type of social requirement as a evolutionary pressure (Byrne & Whiten 1989). One of the most difficult tasks for using social intelligence is estimating one’s own unobservable information from the behavior of others and to modify one's own information. This type of reflective behavior – using other behavior as a looking glass – is both a biological and psychological task. For example, the human voice is informed by others via sound waves through the air, but informed by him/herself through bone conduction (Chen et al. 2007). In this scenario, a person cannot observe his/her own voice directly. For improving social  influence from one's voice, one needs to observe others' reactions and modify his/her voice. Joseph et al. also defined such unobservable information from oneself as a "blind spot" from a psychological viewpoint (Luft & Ingham 1961). In this study, we solved such reflective estimation tasks using a cooperative game involving incomplete information. We used a card game called Hanabi as a challenge task. Hanabi is a cooperative card game. It has three unique features for contributing to AI and multi-agent system (MAS) studies compared with other card games that have been used in AI studies. First, it is a cooperative card game and not a battle card game. Every player is required to cooperate and build a set of five different colored fireworks (Hanabi in Japanese) before the cards run out. This requires the AI program to handle cooperation of multiple agents. Second, every player can observe all other players' cards except his/her own. This does not require a coordinative leader and requires pure coordination between multiple agents. Finally, communication between players is prohibited except for restricted informing actions for a color or a number of opponent's cards. This allows the AI program to avoid handling natural language processing matters directly. Hanabi won the top German game award due to these unique features (Jahres 2013). We created an AI program to play Hanabi with multiple strategies including simulation of opponents' viewpoints with opponents' behavior, and evaluated how this type of reflective simulation contributes to earning a high score in this game. The paper is organized as follows. Section 2 gives background on incomplete information games involving AI and what challenges there are with Hanabi. Section 3 explains the rules of Hanabi and models. We focused on a two-player game in this paper. Section 4 explains several strategies for playing Hanabi. Section 5 evaluates these strategies and the results are discussed in Section 6. Section 7 explains the contribution of our research, limitations, and future work, and Section 8 concludes our paper. 37 Computer Poker and Imperfect Information: Papers from the 2015 AAAI Workshop