Presentazione di PowerPoint

Algorithmic Game Theory
Nicola Gatti and Marcello Restelli
{ngatti, restelli}@elet.polimi.it
DEI, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, 20133, Italy
Scientific Areas
2
The object of the study
Situations in which selfish players interact,
each aiming at maximizing its (expected) revenue
•
•
•
•
•
Game Theory
• It studies strategic situations with rational and fully-informed players
• Given a game protocol, the aim is to find players’ optimal strategies
• Solution concepts: Nash equilibrium and refinements
• No solving method (except for backward induction)
Evolutionary Game Theory
• It studies populations that evolve during time (no hypothesis of rationality and full
information is made), playing repeatedly the game
• Solution concepts: Evolutionary Stable Strategies (ESS)
• Dynamical system analysis
Algorithmic Game Theory
• Algorithms for finding game theoretic solutions, usually based on operative research (e.g.
simplex method, linear complementarity problem, heuristics)
Multiagent Learning
• It studies strategic situations with e–greedy and non-fully-informed players (players learn
by exploring and exploiting)
• Players repeatedly play the game
• Algorithms for learning the optimal strategies
Mechanism Design
• It is the reverse of game theory: given players’ strategies searches for the protocol such that
those strategies are optimal
Nicola Gatti, Marcello Restelli
Intersections between Areas
Game Theory
3
Algorithmic
Game Theory
Mechanism
Design
Evolutionary
Game Theory
Nicola Gatti, Marcello Restelli
Multiagent Learning
Course Organization (1)
• N. Gatti (10 hours)
• Game theory groundings
•
•
•
•
Modeling a game
Game classes
Non-equilibrium solutions
Equilibrium concepts
• Algorithms for basic solutions
•
•
•
•
Solving a zero-sum strategic-form game
Solving a general-sum two-player strategic-form game
Computational issues in solving games
Solving a general-sum two-player extensive-form game
• Illustrations
• Negotiations
• Strategic patrolling
• Selfish routing
• Research directions
Nicola Gatti, Marcello Restelli
4
Course Organization (2)
• M. Restelli (10 hours)
• Multi-agent learning
• Reinforcement learning
• Differences with single-agent learning
• Differences with game-theoretical approaches
• Equilibrium learning
• Zero-sum games
• Coordination games
• General-sum games
• Best response learning
• Fictitious play
• Independent learning
• No regret learning
• Learning to coordinate
• Optimistic approaches
• Collective intelligence
• Evolutionary game theory
• Evolutionary stable strategies
• Replicator dynamics
Nicola Gatti, Marcello Restelli
5
Examples of Strategic Settings: Bilateral Negotiations
6
• eCommerce settings: electronic marketplace (e.g., eBay) with
• A software entity (agent) that sells items (e.g., food)
• A software agent that buys items
• The items have some cost for the seller, say RPs
• The buyer have a maximum budget, say RPb
• The difference between (RPb – RPb) is a surplus produced by the
transaction
• What is the split of the surplus that is optimal for agents
Nicola Gatti, Marcello Restelli
Examples of Strategic Settings: Web-Service Pricing
7
• eCommerce settings: electronic marketplace (e.g., eBay) with
• A provider that sells services
• Some customers that buy services
• Services are characterized by price p and response time r
• Customers are in competition with respect to the purchase of the
services with the minimal response time
• Agreements are pairs (p, r)
• Extensions:
• More providers are in competition with respect to the sale of
services
Nicola Gatti, Marcello Restelli
Examples of Strategic Settings: Strategic Patrolling
Nicola Gatti, Marcello Restelli
8
Examples of Strategic Settings: Selfish Routing
Sink
Source
Nicola Gatti, Marcello Restelli
9
10
And now,
we can start!
Nicola Gatti, Marcello Restelli

Download Report