Editing Openai/693343d7-a38c-8012-a67c-11cbed4c0fd9 (section)

===== - Perception and Action Uncertainty: Perception (P) and action (Act) are inherently noisy due to sensory limitations and environmental uncertainty: - We could model perception noise as a random variable P_t = P̂_t + ε_t, where ε_t is Gaussian or other distribution-based noise. - Actions could have stochastic outcomes, modeled by Bernoulli processes or Poisson distributions: </code>`<code> Act(S_t) ~ Bernoulli(p) (i.e., a probabilistic choice between two actions based on state) <syntaxhighlight>- Bayesian Inference: Agents could use Bayesian updates to refine their internal models based on new observations, allowing them to self-correct and adapt probabilistically: </syntaxhighlight> P(θ | data) ∝ P(data | θ) P(θ)  (Bayesian update) <syntaxhighlight>- Statistics: Agent learning or behavior adaptation could be framed in terms of statistical methods, such as: - Maximum Likelihood Estimation (MLE) to infer hidden parameters of agent states. - Markov Decision Processes (MDPs) and Reinforcement Learning with stochastic rewards: </syntaxhighlight> Q(S_t, A_t) = Q(S_t, A_t) + α [R_t + γ max_a Q(S_{t+1}, a) - Q(S_t, A_t)]   <syntaxhighlight> =====
===== - Probabilistic interactions: In social or environmental interactions, agents may follow probabilistic decision-making models, where each decision (e.g., collaboration, competition) has a probability distribution based on external factors, internal drives, or collective behaviors: </syntaxhighlight> P(Interact | Agent A, Agent B) = f(A, B, W, θ)   </code>`<code> Here, P could be influenced by homophily/heterophily effects, the nature of the agents’ goals (via their Ω), and external social dynamics. =====