DOC: Update docstrings in lqnash.jl to follow style guide

[Copilot]

This PR updates the docstring for the nnash function in src/lqnash.jl to follow the conventions specified in .github/copilot-instructions.md.

Changes Made

1. Added function signature - The docstring now starts with a four-space indented function signature showing the function name and all parameters with their default values:

   nnash(A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2; beta=1.0, tol=1e-8, max_iter=1000)

2. Updated section headers - Changed from ##### to single # for "Arguments" and "Returns" sections to match the standard style used throughout the codebase

3. Improved consistency - All parameter and return value descriptions now end with periods for consistency

4. Fixed typos - Corrected spelling errors:

   • "ticcati" → "Riccati"
   • "riccati" → "Riccati"

5. Capitalized variable names - All variable names in the function signature and mathematical equations now use uppercase to match the argument descriptions:

   • Function signature: A, B1, B2, R1, R2, Q1, Q2, S1, S2, W1, W2, M1, M2
   • Mathematical equations: R_i, W_i, Q_i, S_i, M_i, B_1, B_2

6. Added missing discount term - Added the missing \beta^{t-1} discount factor in the minimization equation

7. Preserved mathematical notation - Maintained the @doc doc""" syntax for proper LaTeX rendering in the documentation

The updated docstring provides clearer documentation and follows the established conventions used in other files like compute_fp.jl and arma.jl.

Verification

• Documentation builds successfully without parsing errors
• Package loads correctly
• Docstring renders properly with mathematical notation intact

[!WARNING]

Original prompt

---

This section details on the original issue you should resolve

<filter_complete></filter_complete>

<issue_title>DOC: Update docstrings in lqnash.jl</issue_title>
<issue_description>Follow the instruction in .github/copilot-instructions.md.

Scope: Only edit docstrings in lqnash.jl</issue_description>

Comments on the Issue (you are @copilot in this section)

Fixes #344

Original prompt

---

This section details on the original issue you should resolve

<issue_title>DOC: Update docstrings in lqnash.jl</issue_title>
<issue_description>Follow the instruction in .github/copilot-instructions.md.

Scope: Only edit docstrings in lqnash.jl</issue_description>

Comments on the Issue (you are @copilot in this section)

Fixes #344

---

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[oyamad]

@copilot Capitalize the variables b_1, ..., m_i in the equations accordingly:

QuantEcon.jl/src/lqnash.jl

Lines 19 to 23 in 441d042

	```math
	\sum_{t=1}^{\infty}(x_t' r_i x_t + 2 x_t' w_i
	u_{it} +u_{it}' q_i u_{it} + u_{jt}' s_i u_{jt} + 2 u_{jt}'
	m_i u_{it})
	```

QuantEcon.jl/src/lqnash.jl

Lines 27 to 29 in 441d042

	```math
	x_{t+1} = A x_t + b_1 u_{1t} + b_2 u_{2t}
	```

• Also add a missing \beta^{t-1} in the first equation just after \sum_{t=1}^{\infty}.

[oyamad]

@copilot
Capitalize the variable names a, ..., m2, consistent with those in the descriptions.

[Copilot]

Capitalized all variable names in the function signature to match the argument descriptions in commit 88b3dd6.

[Copilot]

@copilot Capitalize the variables b_1, ..., m_i in the equations accordingly:

QuantEcon.jl/src/lqnash.jl

Lines 19 to 23 in 441d042

	```math
	\sum_{t=1}^{\infty}(x_t' r_i x_t + 2 x_t' w_i
	u_{it} +u_{it}' q_i u_{it} + u_{jt}' s_i u_{jt} + 2 u_{jt}'
	m_i u_{it})
	```

https://...

Capitalized the variables in the equations (R_i, W_i, Q_i, S_i, M_i, B_1, B_2) and added the missing β^{t-1} discount term in commit 88b3dd6.

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