Escape Rooms and Shapley Values in Game Theory
Explore the fascinating intersection of game theory, escape rooms, and Shapley values with Elan Roth under the guidance of mentor Ryan Brill. Discover how games relate to math and the various characterizations of games in both cooperative and non-cooperative settings. Uncover the fun and intrigue behind resource allocation, tactics, code-breaking, and more.
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Presentation Transcript
Game Theory: Escape Rooms and Shapley Values Elan Roth Mentor: Ryan Brill
What to Expect 01 Motivation 02 Formal Games 03 Shapley Values Giving credit where credit is due My favorite part of mathematics Games are fun! Math is fun! Do they relate ?
Motivation 01 Games are fun! Math is fun! Do they relate ?
Games are Everywhere Chess Economy War Board games, card games, party games, ... Stock market, rational herding, betting, ... Resource allocation, tactics, code breaking,
Games are Everywhere Chess Economy War What is the best move? What s the best move? What s the best move?
Mathematics loves to generalize
Formal Games 02 A non-cooperative, zero-sum, complete information game: Tag
Characterizations of Games Cooperative Non-Cooperative Simultaneous Sequential Zero-Sum Non-Zero-Sum Perfect Information Imperfect Information
Characterizations of Games Cooperative Non-Cooperative Simultaneous Sequential Zero-Sum Non-Zero-Sum Perfect Information Imperfect Information
Characterizations of Games Cooperative Non-Cooperative Simultaneous Sequential Zero-Sum Non-Zero-Sum Perfect Information Imperfect Information
Characterizations of Games Cooperative Non-Cooperative Simultaneous Sequential Zero-Sum Non-Zero-Sum Perfect Information Imperfect Information
Characterizations of Games Cooperative Non-Cooperative Simultaneous Sequential Zero-Sum Non-Zero-Sum Perfect Information Imperfect Information
Shapley Values 03 Giving credit where credit is due
Escape Rooms Objective: Escape the room Players: Alice, Bob, and Charlemagne Simple Game Binary output (success/failure) Need at least one person to succeed
Example 1 Empty Alice Bob Charlemagne A B A C B C A B C
Example 2 Empty Alice Bob Charlemagne A B A C B C A B C
Example 3 Empty Alice Bob Charlemagne A B A C B C A B C
Example 4 Empty Alice Bob Charlemagne A B A C B C A B C
Escape Rooms Objective: Escape the room Players: Alice, Bob, and Charlemagne Simple Game Binary output (success/failure) Need at least one person to succeed
Desirable Features Symmetry Linearity Efficiency Null Player
Example 1 Alice: 0 Bob: 0 Charlemagne: 1 Empty Alice Bob Charlemagne A B A C B C A B C
Example 2 Alice: Bob: Charlemagne: Empty Alice Bob Charlemagne A B A C B C A B C
Example 3 Alice: Bob: Charlemagne: - Empty Alice Bob Charlemagne A B A C B C A B C
Example 4 Alice: Bob: Charlemagne: Empty Alice Bob Charlemagne A B A C B C A B C
Thank you! Questions? Elan Roth Mentor: Ryan Brill
