Whose dice is it anyway?
K. S. Thejaswini
Randomness is a strange resource. One player with a die can use the randomness in strategies to reduce memory, evade an adversary who knows its strategy and hide its intentions. With more than one agent, there are other questions. Whose dice is it? Do the agents roll the dice together or does each agent roll alone? Consider a four-player game of matching pennies, where three players form a team against the Devil and all four simultaneously say “Heads” or “Tails”. The team wins only if all four calls agree. Randomising independently, they win with probability 1/8, sharing a single coin, 1/2. Now assuming every pair of teammates share a coin that only those two see (and no other source of randomness). With what probability does the team win? Starting from this puzzle, we will survey some questions about teams of agents and the randomness available to them and argue that modelling randomness significant. Whose die it is, who sees it, and how the players feel about it can each changes the outcome.
This talk is based on some joint works with Ali Asadi, Guy Avni, Léonard Brice, Krishnendu Chatterjee, Thomas A. Henzinger, Kaushik Mallik, Alipasha Montaseri, Suman Sadhukhan, and Ali Shaifee.