Discover Data Analytics with Dr. Emrick

Game Theory & Leadership

Kelly Emrick DHSc, PhD, MBA
1–2 minutes

Leadership Game‑Theory Interactive Lab

Make assumptions. Run scenarios. See the strategic implications.

How to use this lab

No external libraries • Local only

This page converts the core ideas from Game Theory and Leadership into practical levers. Pick a module, tune assumptions, and generate predictions to inform policy and leadership choices. You can export or save your inputs, print a brief report, and share screenshots of the results.

  • Game Builder helps you craft a 2×2 payoff matrix, find pure‑strategy Nash equilibria, and inspect dominated strategies.
  • Repeated Game Lab explores cooperation dynamics under strategies such as Tit‑for‑Tat, Grim Trigger, Win‑Stay Lose‑Shift, with noise and discounting.
  • Bargaining Lab computes a Nash bargaining split with optional power weights and BATNAs.
  • Signaling/Screening tests whether honest signals separate high‑ and low‑types, or whether pooling arises.
  • Coalitions allocates value with Shapley values (up to 3 players).
  • Competition contrasts Cournot quantity competition and Bertrand price competition.
  • Incentives sketches a principal‑agent model that links incentive intensity to expected effort and surplus.

All calculations are deterministic toy models to support leadership conversations, not forecasts. Pair these with judgment and context.

Quick presets

Presets populate multiple modules at once. Tweak as needed, then Save or Export.

2×2 Payoff Matrix

Find Nash Equilibria
Col: CooperateCol: Defect
Row: Cooperate
Row payoff
Col payoff
Row payoff
Col payoff
Row: Defect
Row payoff
Col payoff
Row payoff
Col payoff

Findings

Best responses are highlighted with ★. Cells with both players best‑responding are pure‑strategy Nash equilibria.

Strategies & Environment

Repeated PD with noise
Rounds (N)
Continuation prob (δ)
Noise: mis‑execution ε
Random p (if RAND)
Payoffs (T,R,P,S)
T (temptation)
R (reward)
P (punishment)
S (sucker)

Results

—

Nash Bargaining with Weights

BATNAs + Power Weights
Total surplus (S)
Leader BATNA (A)
Counterparty BATNA (B)
Leader weight (wL)
Counterparty weight (wC)
Enforce non‑negative shares

Split & Guidance

Solution uses uL=A + wL/(wL+wC)·(S−A−B) and uC=B + wC/(wL+wC)·(S−A−B), provided S≥A+B.

Signals, Types, and Incentive Constraints

Simple two‑type model
High‑type benefit if trusted (BH)
Low‑type benefit if trusted (BL)
Signal cost, high‑type (cH)
Signal cost, low‑type (cL)
Prior probability high (θ)
Receiver payoff when trusting

Outcome

We report whether the incentive constraints allow separating (only high sends the costly signal), pooling (no one signals or both signal), or semi‑separating regions.

Coalition Values

Three‑player Shapley
v({1})
v({2})
v({3})
v({1,2})
v({1,3})
v({2,3})
v({1,2,3})

Allocation

Shapley value averages each player’s marginal contribution across coalition orders.

Market Model

Linear demand
a (intercept)
b (slope)
c1 (MC firm 1)
c2 (MC firm 2)

Results

Incentive Intensity and Effort

Principal‑Agent sketch
Bonus intensity (s)
Effort cost parameter (k)
Fixed salary (f)
Revenue per unit output (v)
Noise variance proxy
Team externality (τ)

Outcomes

Toy model: agent best‑response effort e=s/k. Expected output ≈ e. Expected principal surplus ≈ (v−s)·e − f, with a penalty for noise and externalities.

Methods in brief

  1. Game Builder computes best responses by comparing payoffs row‑wise and column‑wise; pure‑strategy Nash equilibria appear where both players best‑respond.
  2. Repeated Game Lab implements stateful strategies (TFT, Grim, WSLS, etc.) with mis‑execution ε and a continuation probability δ. Cooperation share and average payoffs summarize trajectories.
  3. Bargaining reports the weighted Nash bargaining solution with BATNAs.
  4. Signaling checks simple incentive constraints for a costly signal across two types and classifies the equilibrium region.
  5. Shapley uses the closed‑form for three players to average marginal contributions across all coalition orders.
  6. Cournot/Bertrand uses linear demand P=a−b(q1+q2) and constant marginal costs to compute the Cournot NE; Bertrand sets price to marginal cost if products are homogeneous and costs identical.
  7. Principal‑Agent is a sketch to connect incentive intensity with effort in a way leaders can reason with before detailed modeling.

This lab is a leadership teaching aid inspired by topics such as Nash equilibrium, repeated games, signaling and screening, bargaining, coalition values, competition, and incentive design.

Shortcode: [leadership_lab] • Local‑first • Export/Import JSON • Print to PDF