Limited-Information Game

A Limited-Information Game is a game in which some player information is private information (to game opponents).

• AKA: Imperfect Information Game.
• Context:
  • It can (typically) be a Sequential Limited-Information Game.
  • It can range from being a Deterministic Limited-Information Game to being a Stochastic Limited-Information Game.
  • It can be studied by Games Research.
• Example(s):
  • a Solitaire Game.
  • a Poker Game, such as Fixed-Limit Texas Holdem.
  • …
• Counter-Example(s):
  • a Perfect Information Game, such as a chess game or a Go game.
• See: Prisoners Dilemma.

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References

2017

• (Silver, 2017) ⇒ David Silver. (2017). “Technical Perspective: Solving Imperfect Information Games.” In: Communications of the ACM Journal, 60(11). doi:10.1145/3131286
  • QUOTE: Most of this research focused on perfect information games, in which all events are observed by all players, … However, many applications in the real world have imperfect information: each agent observes different events. This leads to the possibility of deception and a wealth of social strategies. Imperfect information games provide a microcosm of these social interactions, while abstracting away the messiness of the real world.

    Among imperfect information games, Poker is the most widely studied — the latest drosophila—due to its enormous popularity and strategic depth. The smallest competitively played variant by humans, and the most widely played by computers, is the two-player game known as Heads-Up Limit Hold'Em (HULHE), in which each player holds two private cards in addition to five public cards. Two decades of research in this game has led to powerful methods, such as counterfactual regret minimization (CFR), for approximating a Nash equilibrium. Several years ago, a program called Polaris — created by many of the authors of the following paper —defeated for the first time a human professional poker player in HULHE.

2016

• (Heinrich & Silver, 2016) ⇒ Johannes Heinrich, and David Silver. (2016). “Deep Reinforcement Learning from Self-play in Imperfect-information Games.” In: Proceedings of NIPS Deep Reinforcement Learning Workshop.
  • QUOTE: Many real-world applications can be described as large-scale games of imperfect information. To deal with these challenging domains, prior work has focused on computing Nash equilibria in a handcrafted abstraction of the domain. In this paper we introduce the first scalable end-to-end approach to learning approximate Nash equilibria without prior domain knowledge. Our method combines fictitious self-play with deep reinforcement learning. When applied to Leduc poker, Neural Fictitious Self-Play (NFSP) approached a Nash equilibrium, whereas common reinforcement learning methods diverged. In Limit Texas Holdem, a poker game of real-world scale, NFSP learnt a strategy that approached the performance of state-of-the-art, superhuman algorithms based on significant domain expertise.

2014

• http://en.wikipedia.org/wiki/Game_theory#Perfect_information_and_imperfect_information
  • … Many card games are games of imperfect information, such as poker or contract bridge.

    Perfect information is often confused with complete information, which is a similar concept. Complete information requires that every player know the strategies and payoffs available to the other players but not necessarily the actions taken. Games of incomplete information can be reduced, however, to games of imperfect information by introducing “moves by nature” Template:Leyton-Brown.

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