Back to Master EncyclopediaGAME THEORY LOGIC
Game Theory & Mathematical Logic
Formal Bayesian probability equations and information asymmetry principles governing hidden-role deduction.
1. Information Asymmetry Principle
I_{\text{civilian}} = \{W, C\}, \quad I_{\text{imposter}} = \{C\}
Information asymmetry is defined by sets of known variables. Civilians know both the secret word W and the category C, whereas the Imposter knows only the category C.
2. Bayesian Belief Updating Equation
P(\text{Imposter}_i \mid \text{Clue}_k) = \frac{P(\text{Clue}_k \mid \text{Imposter}_i) \cdot P(\text{Imposter}_i)}{P(\text{Clue}_k)}
Civilians update their posterior probability estimate of player i being the Imposter based on the likelihood of their spoken clue k given the category C versus the secret word W.
3. Nash Equilibrium in Clue Selection
q^* = \frac{1}{|W_C| + 1}
The optimal Imposter strategy balances clue vagueness and specificity to match the expected distribution of civilian clues within the word category domain W_C.
Citing Stanford Encyclopedia of Philosophy & MIT Game Lab ResearchRead Stanford Game Theory Entry