1 / 17

CMSC 100 Multi-Agent Game Day

CMSC 100 Multi-Agent Game Day. Professor Marie desJardins Tuesday, November 20, 2012. Multi-Agent Game Day. Game Equilibria: Iterated Prisoner’s Dilemma Voting Strategies: Candy Selection Game Distributed Problem Solving: Map Coloring. Distributed Rationality.

floydm
Download Presentation

CMSC 100 Multi-Agent Game Day

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CMSC 100Multi-Agent Game Day Professor Marie desJardinsTuesday, November 20, 2012 Multi-Agent Game Day

  2. Multi-Agent Game Day • Game Equilibria: Iterated Prisoner’s Dilemma • Voting Strategies: Candy Selection Game • Distributed Problem Solving: Map Coloring Multi-Agent Game Day

  3. Distributed Rationality • Techniques to encourage/coax/force self-interested agents to play fairly in the sandbox • Voting: Everybody’s opinion counts (but how much?) • Auctions: Everybody gets a chance to earn value (but how to do it fairly?) • Issues: • Global utility • Fairness • Stability • Cheating and lying Multi-Agent Game Day

  4. Pareto optimality • S is a Pareto-optimal solution iff • S’ (x Ux(S’) > Ux(S) → y Uy(S’) < Uy(S)) • i.e., if X is better off in S’, then some Y must be worse off • Social welfare, or global utility, is the sum of all agents’ utility • If S maximizes social welfare, it is also Pareto-optimal (but not vice versa) Which solutions are Pareto-optimal? Y’s utility Which solutions maximize global utility (social welfare)? X’s utility Multi-Agent Game Day

  5. Stability • If an agent can always maximize its utility with a particular strategy (regardless of other agents’ behavior) then that strategy is dominant • A set of agent strategies is in Nash equilibrium if each agent’s strategy Si is locally optimal, given the other agents’ strategies • No agent has an incentive to change strategies • Hence this set of strategies is locally stable Multi-Agent Game Day

  6. Iterated Prisoner’s Dilemma Multi-Agent Game Day

  7. Prisoner’s Dilemma Let's play! B A Multi-Agent Game Day

  8. Prisoner’s Dilemma: Analysis • Pareto-optimal and social welfare maximizing solution: Both agents cooperate • Dominant strategy and Nash equilibrium: Both agents defect B A • Why? Multi-Agent Game Day

  9. Voting Strategies Multi-Agent Game Day

  10. Voting • How should we rank the possible outcomes, given individual agents’ preferences (votes)? • Six desirable properties (which can’t all simultaneously be satisfied): • Every combination of votes should lead to a ranking • Every pair of outcomes should have a relative ranking • The ranking should be asymmetric and transitive • The ranking should be Pareto-optimal • Irrelevant alternatives shouldn’t influence the outcome • Share the wealth: No agent should always get their way  Multi-Agent Game Day

  11. Voting Protocols • Plurality voting: the outcome with the highest number of votes wins • Irrelevant alternatives can change the outcome: The Ross Perot factor • Borda voting: Agents’ rankings are used as weights, which are summed across all agents • Agents can “spend” high rankings on losing choices, making their remaining votes less influential • Range voting: Agents score each choice • Binary voting: Agents rank sequential pairs of choices (“elimination voting”) • Irrelevant alternatives can still change the outcome • Very order-dependent Multi-Agent Game Day

  12. Voting Game • Why do you care? The winners may appear at the final exam... • The first two rounds will use plurality (1/0) voting: • The naive strategy is to vote for your top choice. But is it the best strategy? • The next two rounds will use Borda (1..k) voting: • Your top choice receives k votes; your second choice, k-1, etc. • The next two rounds will use range (0..10) voting • Discuss... did we achieve global social welfare? Fairness? Were there interesting dynamics? Multi-Agent Game Day

  13. Let’s Vote... Multi-Agent Game Day

  14. Distributed Problem Solving Multi-Agent Game Day

  15. Distributed Problem Solving • Many problems can be represented as a set of constraints that have to be satisfied • Routing problem (GPS navigation) • Logistics problem (FedEx trucks) • VLSI circuit layout optimization • Factory job-shop scheduling (making widgets) • Academic scheduling (from student and classroom perspectives) • Distributed constraint satisfaction: • Individual agents have “responsibility” for different aspects of the constraints • Advantage: Parallel solving, local knowledge reduces bandwidth • Disadvantage: Communication failures can lead to thrashing Multi-Agent Game Day

  16. Distributed Map Game • You’ll have to stand up now... • Two sets of cards – congregate with your shared color • Each card has an “agent number” that identifies you • Each card also has a list of “neighbors” that you have to coordinate with • You have to choose one of four colors: red, yellow, green, blue • Your color has to be different from any of your neighbors’ colors • You can only exchange agent numbers and colors – no other information or discussion is permitted! • You can change your color (but remember this may cause problems for your neighbors...) • In five minutes, we’ll reconvene and see which group is the most internally consistent... Multi-Agent Game Day

  17. 5 6 2 3 1 4 9 10 8 7 15 14 12 11 13 20 16 19 18 17 Multi-Agent Game Day

More Related