DTPOG

(still developing ... )

We propose a framework for Discrete Time Partially Observed (Markov) Game, where gamestate can only be partially observed.

Modeling

The game can be modeled as an automaton with probability, or a chain of Markov stochastic process. $${\text{Game}} = {\boldsymbol{S},\tau\in\mathbb{N+},\eta:I\times\boldsymbol{S}\mapsto\boldsymbol{S},P_{|\boldsymbol{S}|\times|\boldsymbol{S}|},\delta:\boldsymbol{S}\times\mathbb{N+}\mapsto{0,1,2}}$$ where $I$ is the player instruction, $\eta$ maps the player instruction with current state to a new state;

$P$ is the transition matrix, or transition function of the game.

$\tau$ is the discrete time, and $\delta$ maps time with game state to the result of game, which is the only part that conserns time, and does not affect other arguments.

What makes the game interesting is, that the game is a stochastic process with hidden state space, which needs to be inferred from observation. We take a step further that to observe itself is an action applied by agent that will affect game. It costs to get information.

From another perspective, the agent who plays the game, along with the game, is considered as a part of an entire system. The agent plays the role of a control unit, which should operate properly to make the system as reliable as possible.

Project Structure

• todo

Framework

Demo Game

FNAF1