Bayesian agents

Let’s try to define a KR framework for a Bayesian agent.

A starting point is that instead of using large monolithic context frames which are difficult to handle, and inefficient to process we use a notion of context splitting to put together smaller, more flexible units. Embeddings that are good representation would be easier to easier to acquire on short context. And hopefully if with a little luck we could put them together into a package that feeds different attention heads allowing few-shot learning to proceed.

erDiagram    
    Thematic-Role-Frame {
    verb move-object
    agent Alice
    object wedge
    destination block
    }    
    Thematic-Role-Frame ||--|| State-Change-Frame : induces     
    State-Change-Frame {
    object alice
    destination happy
    }

So this is splits cause action from its outcome.

Bayesian Games and Sub

In a Bayesian game there are a number of constructs, lets put them into a pro-ontology

• state of the world:
  • information
    • what moves have been made.
    • what types each player is.
    • other information.
  • information sets:
    • set of agent who are privy to a bit of info.
  • contrafactuals:
    • competing hypothesis regarding the state of the world.
  • incomplete information:
    • players may be unaware of other player’s type,moves and strategy.
  • uncertainty knowledge is modeled using distribution.
• agents:
  • type which determines a strategy
  • information
• a strategy profile:
  • for each type their full strategy
  • simple strategy
  • complex strategy
  • utility (payoffs driving an agent’s preference)
• population dynamics
  • the number of a agent at a given type (based on their score at the previous round)

erDiagram    
    Action-Frame {
    verb move-object
    agent Alice
    object bullet
    destination Bob
    tool gun
    visibility universe
    }
    Action-Frame ||--|| State-Change-Frame : induces
    Action-Frame ||--|| Agent-Frame_1 : participates
    Action-Frame ||--|| Agent-Frame_2 : participates
    Action-Frame ||--|| Information-Set-Frame : visibility
    State-Change-Frame {
    object alice
    destination angry
    info-set universe
    payoffs Alice_1__Bob_0
    }
    Information-Set-Frame{
    name universe
    members Alice_Bob
    }
    Agent-Frame_1 {
    name Alice
    type robber
    info json_data1
    }
    Agent-Frame_2 {
    name Alice
    type sherif
    info json_data1
    }
    Info-Frame_0 {
    Alice-Type any
    Bob-Type any
    }
    Info-Frame_1 {
    Alice-Type robber
    }
    Info-Frame_2 {
    Bob-Type sheriff
    }

    State-Change-Frame ||--|| Information-Set-Frame : visibility

How many information sets for k players?

There are 2^k and they form the power set of \{a \space ... \space k\}.

A Bayesian game usually start with a move by nature which assigns types to players m_n: p \to \tau.

Extensive form game

The most important TikZ command used to draw game trees is:

...node(coordinate label)[drawing/style options] at(coordinate) {node texts}...;

The command child{} is used to specify a successor of a (parent) node. Note that if the style of a particular branch needs to be modified, such as adding texts to the branch or changing its color, edge from parent must be put after node{} and all of its children.

Complete pooling

info sets

info-sets

info-sets-extended