CMSC 100 Multi-Agent Game Day

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

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