Available games

green circle: thoroughly-tested. In many cases, we verified against known values and/or reproduced results from papers.

~: implemented but lightly tested.

X: known issues (see code for details).

Status Game
Backgammon
~ Battleship
~ Blackjack
Breakthrough
Bridge
(Uncontested) Bridge bidding
~ Catch
~ Cliff Walking
~ Clobber
~ Coin Game
Connect Four
~ Cooperative Box-Pushing
Chess
~ Dark Hex
~ Deep Sea
First-price Sealed-Bid Auction
Gin Rummy
Go
Goofspiel
Hanabi
Havannah
~ Hearts
~ Hex
~ Kriegspiel
Kuhn poker
~ Laser Tag
Leduc poker
~ Lewis Signaling
Liar's Dice
~ Markov Soccer
Matching Pennies (Three-player)
Mean Field Game : garnet
Mean Field Game : crowd modelling
Mean Field Game : crowd modelling 2d
Mean Field Game : predator prey
Mean Field Game : routing
Negotiation
X Oh Hell
Oshi-Zumo
Oware
Pentago
~ Phantom Tic-Tac-Toe
Pig
~ Poker (Hold 'em)
Quoridor
~ Reconnaissance Blind Chess
Routing game
~ Sheriff
~ Slovenian Tarok
~ Skat (simplified bidding)
~ Solitaire (K+)
Tic-Tac-Toe
Tiny Bridge
Tiny Hanabi
Trade Comm
Y

Details

Backgammon

  • Players move their pieces through the board based on the rolls of dice.

  • Idiosyncratic format.

  • Traditional game.

  • Non-deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Battleship

Blackjack

  • Simplified version of blackjack, with only HIT/STAND moves.

  • Traditional game.

  • Non-deterministic.

  • Imperfect information.

  • 1 player.

  • Wikipedia

Breakthrough

  • Simplified chess using only pawns.

  • Pieces on a grid.

  • Modern game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Bridge

  • A card game where players compete in pairs.

  • Card game.

  • Traditional game.

  • Non-deterministic.

  • Imperfect information.

  • 4 players.

  • Wikipedia

(Uncontested) Bridge bidding

  • Players score points by forming specific sets with the cards in their hands.

  • Card game.

  • Research game.

  • Non-deterministic.

  • Imperfect information.

  • 2 players.

  • Wikipedia

Catch

Cliff Walking

  • Agent must find goal without falling off a cliff. Designed to demonstrate exploration-with-danger.

  • Agent on a grid.

  • Research game.

  • Deterministic.

  • Perfect information.

  • 1 players.

  • Sutton et al. ‘18, page 132

Clobber

  • Simplified checkers, where tokens can capture neighbouring tokens. Designed to be amenable to combinatorial analysis.

  • Pieces on a grid.

  • Research game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Coin Game

Connect Four

  • Players drop tokens into columns to try and form a pattern.

  • Tokens on a grid.

  • Traditional game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Cooperative Box-Pushing

Chess

  • Players move pieces around the board with the goal of eliminating the opposing pieces.

  • Pieces on a grid.

  • Traditional game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Dark Hex

  • Hex, except the opponent’s tokens are hidden. (Imperfect-information version)

  • Uses tokens on a hex grid.

  • Research game.

  • Deterministic.

  • Imperfect information.

  • 2 players.

Deep Sea

First-price Sealed-Bid Auction

  • Agents submit bids simultaneously; highest bid wins, and that’s the price paid.

  • Idiosyncratic format.

  • Research game.

  • Non-deterministic.

  • Imperfect, incomplete information.

  • 2-10 players.

  • Wikipedia

Gin Rummy

  • Players score points by forming specific sets with the cards in their hands.

  • Card game.

  • Traditional game.

  • Non-deterministic.

  • Imperfect information.

  • 2 players.

  • Wikipedia

Go

  • Players place tokens on the board with the goal of encircling territory.

  • Tokens on a grid.

  • Traditional game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Goofspiel

  • Players bid with their cards to win other cards.

  • Card game.

  • Traditional game.

  • Non-deterministic.

  • Imperfect information.

  • 2-10 players.

  • Wikipedia

Hanabi

Havannah

  • Players add tokens to a hex grid to try and form a winning structure.

  • Tokens on a hex grid.

  • Modern game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Hearts

  • A card game where players try to avoid playing the highest card in each round.

  • Card game.

  • Traditional game.

  • Non-deterministic.

  • Imperfect information.

  • 3-6 players.

  • Wikipedia

Hex

Kriegspiel

Kuhn poker

  • Simplified poker amenable to game-theoretic analysis.

  • Cards with bidding.

  • Research game.

  • Non-deterministic.

  • Imperfect information.

  • 2 players.

  • Wikipedia

Laser Tag

  • Agents see a local part of the grid, and attempt to tag each other with beams.

  • Agents on a grid.

  • Research game.

  • Non-deterministic.

  • Imperfect information.

  • 2 players.

  • Leibo et al. ‘17, Lanctot et al. ‘17

Leduc poker

Lewis Signaling

  • Receiver must choose an action dependent on the sender’s hidden state. Designed to demonstrate the use of conventions.

  • Idiosyncratic format.

  • Research game.

  • Non-deterministic.

  • Imperfect information.

  • 2 players.

  • Wikipedia

Liar’s Dice

  • Players bid and bluff on the state of all the dice together, given only the state of their dice.

  • Dice with bidding.

  • Traditional game.

  • Non-deterministic.

  • Imperfect information.

  • 2 players.

  • Wikipedia

Markov Soccer

Matching Pennies (Three-player)

  • Players must predict and match/oppose another player. Designed to have an unstable Nash equilibrium.

  • Idiosyncratic format.

  • Research game.

  • Deterministic.

  • Imperfect information.

  • 3 players.

  • “Three problems in learning mixed-strategy Nash equilibria”

Mean Field Game : routing

  • Representative player chooses at each nodes where they go. They has an origin, a destination and a departure time and choose their route to minimize their travel time. Time spent on each link is a function of the distribution of players on the link when the player reaches the link.

  • Network with choice of route.

  • Research game.

  • Mean-field (with a unique player).

  • Explicit stochastic game (only for initial node).

  • Perfect information.

  • Cabannes et. al. ‘21, Solving N-player dynamic routing games with congestion: a mean field approach.

Negotiation

  • Agents with different utilities must negotiate an allocation of resources.

  • Idiosyncratic format.

  • Research game.

  • Non-deterministic.

  • Imperfect information.

  • 2 players.

  • Lewis et al. ‘17, Cao et al. ‘18

Oh Hell

  • A card game where players try to win exactly a declared number of tricks.

  • Card game.

  • Traditional game.

  • Non-deterministic.

  • Imperfect information.

  • 3-7 players.

  • Wikipedia

Oshi-Zumo

Oware

  • Players redistribute tokens from their half of the board to capture tokens in the opponent’s part of the board.

  • Idiosyncratic format.

  • Traditional game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Pentago

  • Players place tokens on the board, then rotate part of the board to a new orientation.

  • Uses tokens on a grid.

  • Modern game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Phantom Tic-Tac-Toe

Pig

  • Each player rolls a dice until they get a 1 or they ‘hold’; the rolled total is added to their score.

  • Dice game.

  • Traditional game.

  • Non-deterministic.

  • Perfect information.

  • 2-10 players.

  • Wikipedia

Poker (Hold ‘em)

  • Players bet on whether their hand of cards plus some communal cards will form a special set.

  • Cards with bidding.

  • Traditional game.

  • Non-deterministic.

  • Imperfect information.

  • 2-10 players.

  • Wikipedia

  • Implemented via ACPC.

Quoridor

  • Each turn, players can either move their agent or add a small wall to the board.

  • Idiosyncratic format.

  • Modern game.

  • Deterministic.

  • Perfect information.

  • 2-4 players.

  • Wikipedia

Reconnaissance Blind Chess

Routing game

Sheriff

Slovenian Tarok

Skat (simplified bidding)

  • Each turn, players bid to compete against the other two players.

  • Cards with bidding.

  • Traditional game.

  • Non-deterministic.

  • Imperfect information.

  • 3 players.

  • Wikipedia

Solitaire (K+)

Tic-Tac-Toe

  • Players place tokens to try and form a pattern.

  • Uses tokens on a grid.

  • Traditional game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia

Tiny Bridge

  • Simplified Bridge with fewer cards and tricks.

  • Cards with bidding.

  • Research game.

  • Non-deterministic.

  • Imperfect information.

  • 2, 4 players.

  • See implementation for details.

Tiny Hanabi

Trade Comm

  • Players with different utilities and items communicate and then trade.

  • Idiosyncratic format.

  • Research game.

  • Non-deterministic.

  • Imperfect information.

  • 2 players.

  • A simple emergent communication game based on trading.

Y

  • Players place tokens to try and connect sides of a triangular board.

  • Tokens on hex grid.

  • Modern game.

  • Deterministic.

  • Perfect information.

  • 2 players.

  • Wikipedia