Where Does Game Theory Fit in AI?
Both MDPs and Game Theory deal with decision-making under uncertainty,
but they address different sources of uncertainty. MDP handles uncertainty from the environment,
while Game Theory handles uncertainty from other rational agents.
| Aspect |
MDP (Lecture 12) |
Game Theory (Lecture 13) |
| Source of Uncertainty |
Environment dynamics (stochastic transitions) |
Other agents' strategic choices |
| Number of Agents |
Single agent vs Nature/Environment |
Multiple rational agents (2+ players) |
| Environment Behavior |
Probabilistic but non-strategic |
Strategic and reactive to your actions |
| Solution Concept |
Optimal Policy (maximize expected utility) |
Nash Equilibrium (no unilateral deviation) |
| Key Question |
"What should I do given the world's probabilities?" |
"What should I do given what others will do?" |
PEAS Framework for Game Theory
Recall the PEAS framework: Performance, Environment, Actuators, Sensors
Performance Measure
Payoff/utility function ui(s) — what each player wants to maximize
Environment
Other players + game rules. The "world" includes rational opponents!
Actuators
Strategy selection — choosing an action from strategy set Si
Sensors
Game structure, payoff matrix (common knowledge), possibly opponent history
Environment Classification
How does a strategic game classify under the standard AI environment properties?
Observable
Partially Observable
You know the game structure, but NOT what action opponents will choose (simultaneous games)
Deterministic
Strategic (Non-Deterministic)
Outcome depends on others' choices — uncertainty from rationality, not randomness
Agents
Multi-Agent
Multiple rational decision-makers, each with their own goals (competitive or cooperative)
Static vs Dynamic
Static (Simultaneous Games)
Environment doesn't change while you deliberate (one-shot games)
Discrete vs Continuous
Discrete (Finite Games)
Finite set of strategies and outcomes — can be represented as a matrix
Known vs Unknown
Known (Complete Information)
All players know the game structure and payoffs (common knowledge assumption)
Key Insight: Strategic Uncertainty
In MDP, uncertainty comes from nature (random transitions). In Game Theory, uncertainty
comes from other agents who are also trying to maximize their payoffs. This makes the
problem fundamentally harder — the "environment" is thinking back at you!