Update (10/7)
Finding Unexploitable Strategies
Finding maximally exploitative strategy with static opponent
Converging to unexploitable strategy via self-play
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2
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\(N\)
Ability to solve arbitrarily sized matrix games efficiently
\(\mathcal{A} = \mathbb{R}^{N\times N}\)
U(\vec{\sigma}) = \begin{bmatrix}
(10,-10) & (-1,1) & \dots & (-1,1)\\
(-1,1) & (10,-10) & & \vdots\\
\vdots & & \ddots & & \\
(-1,1) & \dots & \dots & (10,-10) \\
\end{bmatrix}
U(\vec{\sigma}) = \begin{bmatrix}
(10,-10) & (-1,1) & \dots & (-1,1)\\
(-1,1) & (10,-10) & & \vdots\\
\vdots & & \ddots & & \\
(-1,1) & \dots & \dots & (10,-10) \\
\end{bmatrix}
Static Opponent Strategy
U(\vec{\sigma}) = \begin{bmatrix}
(10,-10) & (-1,1) & \dots & (-1,1)\\
(-10,10) & (10,-10) & & \vdots\\
\vdots & & \ddots & & \\
(-10,10) & \dots & \dots & (10,-10) \\
\end{bmatrix}
Non-uniform Equilibria
Extensive Form Games
- Reasoning about action histories
R
P
S
Player 1
Player 2
\sigma : H \rightarrow \mathcal{A}
Extensive Form Games
- Reasoning about action histories
R
P
S
R
P
S
R
P
S
R
P
S
Player 1
Player 2
(0,0)
(0,0)
(0,0)
(-1,1)
(-1,1)
(-1,1)
(1,-1)
(1,-1)
(1,-1)
\sigma : H \rightarrow \mathcal{A}
Imperfect Information Extensive Form Games
- Reasoning about information sets
R
P
S
R
P
S
R
P
S
R
P
S
Player 1
Player 2
(0,0)
(0,0)
(0,0)
(-1,1)
(-1,1)
(-1,1)
(1,-1)
(1,-1)
(1,-1)
I_1
I_2
\sigma : \mathcal{I} \rightarrow \mathcal{A}
Develop framework for finding difficult to exploit sensor strategies
Matrix Games
Imperfect Info Extended Games
Continuous \(\mathcal{A}\)
Custody Maintenance
Cislunar Orbital Dynamics
Copy of SDA Stuff
By Zachary Sunberg
