CMSC 100 Multi-Agent Game Day Professor Marie desJardins Tuesday, November 20, 2012 Tue 11/20/12 1 Multi-Agent Game Day

2 Game Equilibria: Iterated Prisoner’s Dilemma Voting Strategies: Candy Selection Game Distributed Problem Solving: Map Coloring Tue 11/20/12Multi-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 Tue 11/20/12Multi-Agent Game Day

4 Pareto optimality  S is a Pareto-optimal solution iff   S’ (  x U x (S’) > U x (S) →  y U y (S’) < U y (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) X’s utility Y’s utility Which solutions are Pareto-optimal? Which solutions maximize global utility (social welfare)? Tue 11/20/12Multi-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 S i is locally optimal, given the other agents’ strategies No agent has an incentive to change strategies Hence this set of strategies is locally stable Tue 11/20/12Multi-Agent Game Day

Iterated Prisoner’s Dilemma Tue 11/20/12Multi-Agent Game Day 6

7 Prisoner’s Dilemma CooperateDefect Cooperate3, 30, 5 Defect5, 01, 1 A B Tue 11/20/12Multi-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 CooperateDefect Cooperate3, 30, 5 Defect5, 01, 1  Why? A B Tue 11/20/12 8 Multi-Agent Game Day

Voting Strategies Tue 11/20/12 9 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 Tue 11/20/12Multi-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 Tue 11/20/12Multi-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? Tue 11/20/12Multi-Agent Game Day

13 Let’s Vote... Tue 11/20/12Multi-Agent Game Day

Distributed Problem Solving Tue 11/20/12Multi-Agent Game Day 14

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 Tue 11/20/12Multi-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... Tue 11/20/12Multi-Agent Game Day

Tue 11/20/12Multi-Agent Game Day