Algorithmic Game Theory Nicola Gatti and Marcello Restelli {ngatti, restelli}@elet.polimi.it

1. 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

2. Scientific Areas 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

3. Intersections between Areas Game Theory Algorithmic Game Theory Mechanism Design Evolutionary Game Theory Multiagent Learning

4. 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

5. 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

6. Examples of Strategic Settings: Bilateral Negotiations • 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

7. Examples of Strategic Settings: Web-Service Pricing • 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

8. Examples of Strategic Settings: Strategic Patrolling

9. Examples of Strategic Settings: Selfish Routing Sink Source

10. And now, we can start!