# Game Theory Applications Worksheet

## Overview
Game Theory provides a framework for understanding strategic interactions where the outcome for each participant depends on the actions of all involved. This worksheet helps analyze competitive situations, predict behaviors, and develop optimal strategies in business contexts.

## Pre-Analysis Setup

**Strategic Situation:** _________________________________
**Date:** _____________
**Analysis Team:** _________________________________
**Key Decision:** _________________________________
**Time Horizon:** _________________________________

## Game Definition

### Players Identification
**Player 1 (Us):** _________________________________
- Objectives: _________________________________
- Constraints: _________________________________
- Information available: _________________________________

**Player 2:** _________________________________
- Objectives: _________________________________
- Constraints: _________________________________
- Information available: _________________________________

**Player 3 (if applicable):** _________________________________
- Objectives: _________________________________
- Constraints: _________________________________
- Information available: _________________________________

**Additional Players:** _________________________________

### Game Characteristics
**Game Type:**
- [ ] Simultaneous move
- [ ] Sequential move
- [ ] Repeated game
- [ ] One-shot game

**Information Structure:**
- [ ] Perfect information
- [ ] Imperfect information
- [ ] Complete information
- [ ] Incomplete information

**Sum Type:**
- [ ] Zero-sum (one's gain is another's loss)
- [ ] Non-zero-sum (mutual gains possible)

## Strategic Options

### Our Strategic Options
1. **Strategy A:** _________________________________
   - Description: _________________________________
   - Resources required: _________________________________
   - Risk level: High / Medium / Low

2. **Strategy B:** _________________________________
   - Description: _________________________________
   - Resources required: _________________________________
   - Risk level: High / Medium / Low

3. **Strategy C:** _________________________________
   - Description: _________________________________
   - Resources required: _________________________________
   - Risk level: High / Medium / Low

### Competitor Strategic Options
**Player 2 Options:**
1. _________________________________
2. _________________________________
3. _________________________________

**Player 3 Options (if applicable):**
1. _________________________________
2. _________________________________
3. _________________________________

## Payoff Matrix

### Two-Player Game
|  | Competitor Strategy 1 | Competitor Strategy 2 | Competitor Strategy 3 |
|---|---|---|---|
| **Our Strategy A** | Us: _____ <br> Them: _____ | Us: _____ <br> Them: _____ | Us: _____ <br> Them: _____ |
| **Our Strategy B** | Us: _____ <br> Them: _____ | Us: _____ <br> Them: _____ | Us: _____ <br> Them: _____ |
| **Our Strategy C** | Us: _____ <br> Them: _____ | Us: _____ <br> Them: _____ | Us: _____ <br> Them: _____ |

*Payoffs can be: profit, market share, utility scores, or ranked preferences*

### Multi-Player Considerations
**Three-way interactions:**
_________________________________________________________________
_________________________________________________________________

## Equilibrium Analysis

### Nash Equilibrium
*Where no player can improve by unilaterally changing strategy*

**Identified Equilibria:**
1. Strategies: (Our: _______, Their: _______)
   - Stability: Strong / Moderate / Weak
   - Desirability for us: High / Medium / Low

2. Strategies: (Our: _______, Their: _______)
   - Stability: Strong / Moderate / Weak
   - Desirability for us: High / Medium / Low

### Dominant Strategies
**Our Dominant Strategy (if exists):** _________________________________
**Their Dominant Strategy (if exists):** _________________________________

### Pareto Optimal Outcomes
*Outcomes where no one can be better off without making someone worse off*
1. _________________________________________________________________
2. _________________________________________________________________

## Sequential Game Analysis

### Game Tree (if sequential)
```
Start
  |
  Our Move
  |----Strategy A
  |     |----Their Response 1 → Outcome: _______
  |     |----Their Response 2 → Outcome: _______
  |
  |----Strategy B
        |----Their Response 1 → Outcome: _______
        |----Their Response 2 → Outcome: _______
```

### Backward Induction Analysis
**Optimal Path:** _________________________________
**Expected Outcome:** _________________________________

## Common Game Theory Scenarios

### Prisoner's Dilemma Elements
- [ ] Individual rationality leads to collective irrationality
- [ ] Mutual cooperation would be better
- [ ] Trust and communication issues

**Cooperation Mechanisms:**
1. _________________________________
2. _________________________________
3. _________________________________

### Chicken Game Elements
- [ ] Mutual aggression is worst outcome
- [ ] First to back down loses face
- [ ] Commitment strategies important

**Commitment Devices:**
1. _________________________________
2. _________________________________

### Coordination Game Elements
- [ ] Multiple equilibria exist
- [ ] Players prefer same outcome
- [ ] Communication helps

**Coordination Mechanisms:**
1. _________________________________
2. _________________________________

## Strategic Moves

### Commitment Strategies
*Actions that limit future options to gain advantage*
1. [ ] _________________________________________________________________
2. [ ] _________________________________________________________________
3. [ ] _________________________________________________________________

### Threat Strategies
*Conditional statements to influence behavior*
| Threat | Credibility (H/M/L) | Impact (H/M/L) | Counter-threat |
|--------|-------------------|----------------|----------------|
| | | | |
| | | | |

### Promise Strategies
*Positive inducements for desired behavior*
1. _________________________________________________________________
2. _________________________________________________________________

## Information Strategies

### Signaling Opportunities
*How can we credibly communicate our intentions?*
1. _________________________________________________________________
2. _________________________________________________________________
3. _________________________________________________________________

### Information Asymmetry Exploitation
**What we know that they don't:**
1. _________________________________________________________________
2. _________________________________________________________________

**What they might know that we don't:**
1. _________________________________________________________________
2. _________________________________________________________________

## Repeated Game Considerations

### Reputation Effects
**Reputation Value:** High / Medium / Low
**Reputation Factors:**
- [ ] Reliability in commitments
- [ ] Competitive behavior patterns
- [ ] Market position
- [ ] Financial strength

### Learning Dynamics
**What we can learn over time:**
1. _________________________________________________________________
2. _________________________________________________________________

**Adaptive Strategies:**
1. _________________________________________________________________
2. _________________________________________________________________

## Coalition Analysis

### Potential Alliances
| Coalition | Members | Combined Strength | Stability | Our Role |
|-----------|---------|-------------------|-----------|----------|
| | | | H/M/L | |
| | | | H/M/L | |

### Coalition-Breaking Strategies
1. _________________________________________________________________
2. _________________________________________________________________

## Implementation Strategy

### Chosen Strategy
**Selected Approach:** _________________________________
**Rationale:** _________________________________

### Contingency Planning
**If they choose Strategy 1:**
- Our response: _________________________________

**If they choose Strategy 2:**
- Our response: _________________________________

**If they choose Strategy 3:**
- Our response: _________________________________

### Communication Plan
**What to signal:** _________________________________
**How to signal:** _________________________________
**When to signal:** _________________________________

## Monitoring and Adaptation

### Key Indicators to Watch
1. **Indicator:** _________________ **Threshold:** _________________
2. **Indicator:** _________________ **Threshold:** _________________
3. **Indicator:** _________________ **Threshold:** _________________

### Decision Points
**Reassessment triggers:**
- [ ] Competitor action: _________________________________
- [ ] Market change: _________________________________
- [ ] Time-based: _________________________________

## Risk Analysis

### Strategy Risks
| Risk | Probability | Impact | Mitigation |
|------|-------------|--------|------------|
| Misread competitor | H/M/L | H/M/L | |
| Market shifts | H/M/L | H/M/L | |
| Coalition forms against us | H/M/L | H/M/L | |
| Information leakage | H/M/L | H/M/L | |

## Example: Airline Pricing Game

**Players:** Airline A (us) vs Airline B (competitor)
**Game:** Price competition on popular route

**Payoff Matrix (Daily Profit in $000s):**
|  | B: High Price | B: Low Price |
|---|---|---|
| **A: High Price** | A: 100<br>B: 100 | A: 20<br>B: 140 |
| **A: Low Price** | A: 140<br>B: 20 | A: 50<br>B: 50 |

**Analysis:**
- Nash Equilibrium: Both choose low price (50, 50)
- Prisoner's Dilemma structure
- Better outcome if both maintain high prices

**Strategic Solutions:**
- Price matching guarantee (commitment device)
- Capacity management signals
- Frequent flyer programs (switching costs)

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*Completed by:* _____________
*Date:* _____________
*Next Review:* _____________