##Dynamic control models for strategic interaction
**_John Pearson_**, Shariq Iqbal, Caroline Drucker, Michael Platt
[pearsonlab.github.io/sfn-talk-2016](https://pearsonlab.github.io/sfn-talk-2016)

Shariq Iqbal

Caroline Drucker

Jean-Francois Gariépy

Michael Platt

Penalty Shot

Complexity tax

each trial a different length

how to average, align?

need to "reduce" dynamics

### Our approach
- borrow from control theory, time series
- structured black box models (pieces make sense)
- neural networks for flexible fitting

Modeling I

Observed positions at each time ($y_t$):
$$
y_t = \begin{bmatrix}
y_{goalie} &
x_{puck} &
y_{puck}
\end{bmatrix}^\top
$$
Control inputs ($u_t$) drive changes in observed positions:
$$y_{t + 1} = y_t + v_{max} \sigma(u_t)$$
Goal: predict control inputs from trial history:
$$u_t = F(y_{1:t})$$

Modeling II

One (of many) assumptions we could make:
$$
u_t = f(y_t, y_{1:t-1}) + \eta_t
$$

###Conclusions
- Dynamic control tasks let us leverage motor behavior to study cognitive and social decisions.
- Structured black-box models allow us to carve behavior into interpretable pieces.
- Control models suggest candidate signals for correlation with neural data.