Slides on Self Interested MAS - Distributed Software Develop | CS 682, Study notes of Software Engineering

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Distributed Software Development^ Self-interested MAS^ Chris BrooksDepartment of Computer ScienceUniversity of San Francisco

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Engineering systems vs Engineering

agents

-^ Recall that at the end of Thursday’s class, we weretalking about ant algorithms.^ •^ By specifying a simple set of rules, we can achieveinteresting large-scale behavior. •^ Ant-type approaches lead us to think about how wecan build systems that produce the effects we want. •^ “Given that agents will act in a particular way, howcan we constrain the environment to achieve adesirable outcome?” •^ This method of problem solving is best applied toproblems involving self-interested agents.

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Rationality and protocol design

-^ By treating participants as rational agents, we canexploit techniques from game theory and economics. •^ Assume everyone will act to maximize their ownpayoff •^ How do we structure the rules of the game so thatthis behavior leads to a desired outcome? •^ This approach is called

mechanism design.^ Department of Computer Science — University of San Francisco – p. 4/

Example: Clarke tax

-^ Assume that we want to find the shortest paththrough a graph. •^ Each edge is associated with an agent. •^ Each edge has a privately known transmission cost.^ •^ Agents might choose to lie about theirtransmission cost. •^ How can we find the shortest path?

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Example

start^

finish 3 (g) 5 (f) 4 (d) 7 (h) 4 (e) 2 (a)^2 (b)

2(c)

-^ Assume each agent bids truthfully. •^ Agents A, B, and C are each paid 8 - (6 - 2) = 4^ •^ This is their contribution to the ’best solution’ •^ Other agents are paid nothing.

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Example

-^ Why is truth-telling a dominant strategy?^ •^ What if a underbids?^ •^ A bids 1: paid 8 - (5 - 1) = 4. No benefit.^ •^ What if A overbids?^ •^ A bids 3: paid 8 - (7 - 3) = 4. No benefit.^ •^ A bids 5. No longer on the shortest path, so Agets 0.^ •^ What if d underbids?^ •^ D bids 3: no change.^ •^ D bids 1: paid 6 - (5 - 1) = 2. But his cost is 4.^ •^ D overbids: no change.

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Solution concepts

-^ There are a number of potential solution concepts wecan use:^ •^ Social welfare - sum of all agent utility.^ •^ Pareto efficiency^ •^ Is there a solution that makes one agent betteroff without making anyone worse off?^ •^ Individual rationality^ •^ An agent who participates in the solution shouldbe better off than if it hadn’t participated.^ •^ Stability^ •^ The mechanism should not be able to bemanipulated by one or more agents. •^ It’s not usually possible to optimize all of these at thesame time.^

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Stability

-^ Ideally, we can design mechanisms with

dominant strategies^ •^ A dominant strategy is the best thing to do nomatter what any other agent does.^ •^ In the previous example, truth-telling was adominant strategy.^ •^ We would say that the mechanism isnon-manipulable. (lying can’t break it.) • Unfortunately, many problems don’t have a dominantstrategy. • Instead, the best thing for agent 1 to do depends onwhat agents 2,3,4,... do.

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Nash equilibrium

-^ If BM climbs the tree^ •^ BM gets 6 C, LM gets 4 C^ •^ LM eats some before BM gets down •^ If LM climbs the tree^ •^ BM gets 9 C, LM gets 1 C^ •^ BM eats almost all before LM gets down •^ If both climb the tree^ •^ BM gets 7 C, LM gets 3 C^ •^ BM hogs coconut •^ How should the monkeys each act so as to maximizetheir own calorie gain?

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Nash equilibrium

-^ Assume BM decides first^ •^ Two choices: wait or climb •^ LM has four choices:^ •^ Always wait, always climb, same as BM, oppositeof BM.

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Nash equilibrium

-^ Nash eqilibria are nice in systems with rationalagents. •^ If I assume other agents are rational, then I canassume they’ll play a best response. •^ I only need to consider Nash equilibria. •^ They are^ efficient^ (in the Pareto sense). •^ Problems:^ •^ There can be many Nash equilibria. (thecake-cutting problem has an infinite number ofNash equilibria)^ •^ Some games have no Nash equilibrium.^ •^ There may be ways for groups of agents to cheat.

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Selecting between equilibria

-^ Given that there are lots of possible Nash equilibria ina problem, how does an agent choose a strategy? •^ In some cases, external forces are used to make oneequilibrium more attractive.^ •^ Government regulation, taxes or penalties •^ In other cases a natural

focal point^ exists.

-^ There is a solution that is attractive or sensible^ outside the scope of the game .^ Department of Computer Science — University of San Francisco – p. 17/

Auctions

-^ An auction is a negotiation mechanism where:^ •^ The mechanism is well-specified (it runs accordingto explicit rules)^ •^ The negotiation is mediated by an intermediary^ •^ Exchanges are market/currency-based •^ Agents place bids on items or collections of items. •^ An auctioneer determines how goods are allocated. •^ Requirements: the auction should be fair, efficient,easy to use, and computationally efficient. •^ We’ll need to trade these against each other.

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Auctions

-^ Private-value auctions are easier to think about atfirst. •^ In this case, the value agent A places on a job hasnothing to do with the value that agent B places onthe object.^ •^ For example, an hour of computing time. •^ In common-value auctions, the value an agent placeson an item depends on how much others value it.^ •^ Example: art, collectibles, precious metals.

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