Activity Rules: An ongoing saga …

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________________________________________________________April 13, 2004April 13, 2004CS-286r Class Project Exchange Day PresentationCS-286r Class Project Exchange Day Presentation

Activity Rules: An ongoing Activity Rules: An ongoing saga…saga…

Adam Kirsch, Alex Kulesza, Loizos MichaelAdam Kirsch, Alex Kulesza, Loizos MichaelExchange / Activity Rules GroupExchange / Activity Rules Group

April 13, 2004April 13, 2004CS-286r Class Project Exchange Day PresentationCS-286r Class Project Exchange Day Presentation22

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Agent’s view of Activity RulesAgent’s view of Activity Rules Provide the options of an agent at each step.Provide the options of an agent at each step.

An agent has the right to choose how to satisfy An agent has the right to choose how to satisfy the activity rules from the given choices.the activity rules from the given choices.

An agent has the obligation to choose something, An agent has the obligation to choose something, or else a or else a default actiondefault action is imposed. is imposed. Not a punishment, but rather an implicitly stated Not a punishment, but rather an implicitly stated

choice.choice.

Activity rules should not discourage participation.Activity rules should not discourage participation.


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Proxy’s view of Activity RulesProxy’s view of Activity Rules Advise agent on possible options for bidding.Advise agent on possible options for bidding.

Suggest options that optimize some criteria.Suggest options that optimize some criteria.

Point out consequences of violating activity Point out consequences of violating activity rules.rules.

Suggest how to minimize impact of Suggest how to minimize impact of consequences.consequences.

Advise on how likely is for the exchange to close.Advise on how likely is for the exchange to close.


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Exchange’s view of Activity Exchange’s view of Activity RulesRules Restrict an agent’s strategic behavior.Restrict an agent’s strategic behavior.

Drive exchange to an efficient outcome Drive exchange to an efficient outcome quickly.quickly.

Plus, an activity rule should be…Plus, an activity rule should be…


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List of DesiderataList of Desiderata IntuitiveIntuitive (not arbitrary, makes sense to people) (not arbitrary, makes sense to people) Easy to understandEasy to understand (use only few rules, or one!) (use only few rules, or one!) Easy to checkEasy to check (verify that bids are valid) (verify that bids are valid) Easy to satisfyEasy to satisfy (truthful bidding always works) (truthful bidding always works) FlexibleFlexible (allows a change in the bid structure) (allows a change in the bid structure) GeneralGeneral (works for any bidding language) (works for any bidding language) Promotes fast convergence of pricesPromotes fast convergence of prices Hard to gameHard to game (improve over truthful bidding) (improve over truthful bidding) Possibly hard to accommodate all these! But…Possibly hard to accommodate all these! But…


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Motivating PrinciplesMotivating Principles ……we are trying!we are trying!

Abstract away from specific bidding languages, Abstract away from specific bidding languages, to see what the essence of a bid is.to see what the essence of a bid is.

Decompose activity rule provisions to smaller Decompose activity rule provisions to smaller parts of the bid, so as it can be applied locally.parts of the bid, so as it can be applied locally.

Do not change current way people think of bids.Do not change current way people think of bids. Make agents commit to their choices / bids.Make agents commit to their choices / bids.


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Bids as Logical Operator TreesBids as Logical Operator Trees Leaves are items and interior nodes are Leaves are items and interior nodes are

logical ops. logical ops. Some vertices have values s.t. there is Some vertices have values s.t. there is

exactly one value within each root to leaf exactly one value within each root to leaf path.path.

For upper/lower bounds, make each value a For upper/lower bounds, make each value a pair.pair.

CHOOSE(2)CHOOSE(2)

XOR / $3-5XOR / $3-5 ORORAND / $8-9AND / $8-9

BB DDAA E / $5-6E / $5-6 F / $2-4F / $2-4CC


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The Interval Choose OperatorThe Interval Choose Operator AND(S), OR(S), XOR(S), CHOOSE(k, S) are special AND(S), OR(S), XOR(S), CHOOSE(k, S) are special

cases of the cases of the interval chooseinterval choose operator IC(x, y, S). operator IC(x, y, S).

Value for any subset S`Value for any subset S`S of items s.t. xS of items s.t. x|S`||S`|yy

AND(S)AND(S) IC(|S|, |S|, S)IC(|S|, |S|, S) OR(S) OR(S) IC(1, |S|, S)IC(1, |S|, S) XOR(S) XOR(S) IC(1, 1, S)IC(1, 1, S) CHOOSE(k, S) CHOOSE(k, S) IC(k, k, S)IC(k, k, S)


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IC-TreesIC-Trees

Definition of an Definition of an IC-tree:IC-tree:

Base Case (leaves):Base Case (leaves): a single item. a single item. Recursive Case (interior nodes):Recursive Case (interior nodes): If S is a If S is a

set of IC-trees, and 1set of IC-trees, and 1 x,y x,y |S|, then IC(x, y, |S|, then IC(x, y, S) is an IC-tree.S) is an IC-tree.


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IC-TreesIC-Trees

DD

FFIC(2,3)IC(2,3)IC(1,1)IC(1,1)

IC(1,2)IC(1,2)

CCBBAA EE


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SatisfactionSatisfaction

An IC-tree T is An IC-tree T is satisfiedsatisfied by allocation A iff: by allocation A iff: Base Case (leaves):Base Case (leaves): T is a single item T is a single item

that belongs in A.that belongs in A. Recursive Case (interior nodes):Recursive Case (interior nodes): T is of T is of

the form IC(x, y, S) and at least x the form IC(x, y, S) and at least x elements of S are satisfied by A.elements of S are satisfied by A.


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SatisfactionSatisfaction

DD

FFIC(2,3)IC(2,3)IC(1,1)IC(1,1)

IC(1,2)IC(1,2)

CCBBAA EE

A = A = {C,D}{C,D}


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Bids - Adding Value to IC-Bids - Adding Value to IC-TreesTrees Definition of an Definition of an atomic bid:atomic bid:

An IC-Tree T paired with low/high bounds on the An IC-Tree T paired with low/high bounds on the price an agent will pay for price an agent will pay for anyany satisfying satisfying allocation of T.allocation of T.

IC(1,1)IC(1,1)

BBAA $3-6$3-6

Abbreviated as:Abbreviated as:$3-6$3-6


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Recursive BidsRecursive Bids Definition of a Definition of a bid:bid:

Base CaseBase Case: An atomic bid.: An atomic bid. Recursive CaseRecursive Case: IC(x, y, S), where S is a set of bids : IC(x, y, S), where S is a set of bids

and 1and 1 x,y x,y |S|.|S|.

IC(2,3)IC(2,3)

IC(1,2)IC(1,2)

$3-6$3-6 $3-3$3-3

$1-4$1-4$2-5$2-5$1-8$1-8


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The Activity Rule (for Buyers)The Activity Rule (for Buyers) The activity rule is based on three objects:The activity rule is based on three objects:

The agent’s previous bid BThe agent’s previous bid Boldold

The previous round’s provisional allocation AThe previous round’s provisional allocation A (based on the L/H outcome)(based on the L/H outcome)

A low/high pair of activity rule price sets (PA low/high pair of activity rule price sets (PL L , , PPHH)) Derived from previous round’s linear pricesDerived from previous round’s linear prices


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The Activity RuleThe Activity Rule A new bid B A new bid B meets the activity rulemeets the activity rule iff: iff:

The structure of B matches that of BThe structure of B matches that of Boldold (for (for now)now)

For every atomic bid b in B, the low (high) For every atomic bid b in B, the low (high) bound is at least (most) the corresponding bound is at least (most) the corresponding bound in Bbound in Boldold

B is consistent with B is consistent with maximal commitmentmaximal commitment given A, Pgiven A, PLL, and P, and PHH..


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Maximal CommitmentMaximal Commitment Maximal Commitment:Maximal Commitment: The agent The agent

demonstrates a continued interest in as many demonstrates a continued interest in as many parts of its bid as possible (given its true parts of its bid as possible (given its true valuation), valuation), up to its original stated interestup to its original stated interest..

Roughly speaking, a bid is Roughly speaking, a bid is consistentconsistent with with maximal commitment if upper bounds are maximal commitment if upper bounds are dropped wherever lower bounds are not dropped wherever lower bounds are not raised: if an agent will not bid the current price raised: if an agent will not bid the current price now, it may never do so in the future.now, it may never do so in the future.


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Full CommitmentFull Commitment

Definition of Definition of full commitment:full commitment:

Base Case:Base Case: For atomic bid (T, L, H), either T For atomic bid (T, L, H), either T is satisfied by A or L is satisfied by A or L m mLL = min P = min PLL(A`) over (A`) over allocations A` satisfying T.allocations A` satisfying T.

Recursive Case:Recursive Case: For a bid of the form IC(x, For a bid of the form IC(x, y, S), at least y bids in S are fully y, S), at least y bids in S are fully committed.committed.


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Full CommitmentFull Commitment

IC(2,3)IC(2,3)

IC(1,2)IC(1,2)

$3-6$3-6-> $4-6-> $4-6

$3-3$3-3

$1-4$1-4$2-5$2-5$1-8$1-8mmLL = $4 = $4

mmLL = $8 = $8mmLL = $2 = $2 mmLL = $3 = $3

mmLL = $2 = $2


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Maximal CommitmentMaximal Commitment If B demonstrates full commitment, then by If B demonstrates full commitment, then by

definition it is maximally committed (has definition it is maximally committed (has matched original interest).matched original interest).

If it does not, then by implication a lesser If it does not, then by implication a lesser commitment is maximal given that agent’s commitment is maximal given that agent’s true valuation.true valuation. Therefore, a default action is applied to keep B Therefore, a default action is applied to keep B

consistent with maximal commitment.consistent with maximal commitment.


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The Default ActionThe Default Action

If B does not reflect full commitment, the If B does not reflect full commitment, the default action default action appliesapplies::

Base Case (T, L, H)Base Case (T, L, H): Let m: Let mHH = min P = min PHH (A`) over (A`) over allocations A` satisfying T. Set H = allocations A` satisfying T. Set H = min(H,max(L,mmin(H,max(L,mHH)).)).

Recursive Case IC(x, y, S):Recursive Case IC(x, y, S): Apply default action Apply default action recursively to every bid in S not demonstrating recursively to every bid in S not demonstrating full commitment.full commitment.


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Agent Adjusts Bounds:Agent Adjusts Bounds:

IC(2,3)IC(2,3)

IC(1,2)IC(1,2)

$3-6$3-6 $3-3$3-3

$1-4$1-4-> $3-3-> $3-3$2-5$2-5$1-8$1-8

-> $2-8-> $2-8mmLL = $4 = $4

mmLL = $8 = $8mmLL = $2 = $2 mmLL = $3 = $3

mmLL = $2 = $2


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Full Commitment Bid Marking:Full Commitment Bid Marking:

IC(2,3)IC(2,3)

IC(1,2)IC(1,2)

$3-6$3-6 $3-3$3-3

$3-3$3-3$2-5$2-5$2-8$2-8mmLL = $4 = $4

mmLL = $8 = $8mmLL = $2 = $2 mmLL = $3 = $3

mmLL = $2 = $2


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Default Action Propagation:Default Action Propagation:

IC(2,3)IC(2,3)

IC(1,2)IC(1,2)

$3-6$3-6 $3-3$3-3

$3-3$3-3$2-5$2-5$2-8$2-8


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Default Action Base Case:Default Action Base Case:

IC(2,3)IC(2,3)

IC(1,2)IC(1,2)

$3-6$3-6-> $3-5-> $3-5

$3-3$3-3

$3-3$3-3$2-5$2-5$2-8$2-8mmHH = $5 = $5

mmHH = $9 = $9


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Final Bid:Final Bid:

IC(2,3)IC(2,3)

IC(1,2)IC(1,2)

$3-5$3-5 $3-3$3-3

$3-3$3-3$2-5$2-5$2-8$2-8


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Closing RuleClosing Rule The exchange closes if the L/H price vector The exchange closes if the L/H price vector

has converged.has converged. Convergence means that the LConvergence means that the L norm of the norm of the

vector has changed by less than epsilon for vector has changed by less than epsilon for each of the past N rounds.each of the past N rounds.

Agents are not notified Agents are not notified a priori a priori of a final of a final round, but epsilon and N are always round, but epsilon and N are always available.available.


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Achieving the DesiderataAchieving the DesiderataIntuitive:Intuitive: Agents must address every provisional Agents must address every provisional

allocation by allocation by being content with it (default action / satisfied bid), being content with it (default action / satisfied bid), or modifying bid to beat “provisional price.”or modifying bid to beat “provisional price.”

Easy to Understand:Easy to Understand: A handful of definitions.A handful of definitions. Based entirely on simple recursive structures.Based entirely on simple recursive structures.


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Justification Cont.Justification Cont.Easy to Check:Easy to Check: Can compute values for m with depth-first Can compute values for m with depth-first

search.search. Then check compliance with simple recursion.Then check compliance with simple recursion.

Easy to Satisfy (Truthfully):Easy to Satisfy (Truthfully): Raise some lower bounds. Implement default Raise some lower bounds. Implement default

action on the rest.action on the rest. If this is too demanding, we can introduce a If this is too demanding, we can introduce a

relaxation.relaxation.


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Justification Cont.Justification Cont.Flexible:Flexible: Can easily add sub-bids anywhere.Can easily add sub-bids anywhere. But no deletions.But no deletions. Apply rule retroactively as if new sub-bid was Apply rule retroactively as if new sub-bid was

always there.always there. Possibly subject to gaming.Possibly subject to gaming. May break convergence.May break convergence.

Will not support this for the first implementation.Will not support this for the first implementation.


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Justification Cont.Justification Cont.General:General: Activity Rules are the same for all bidding Activity Rules are the same for all bidding

languages that we have considered.languages that we have considered. Plus interesting ones that we haven’t.Plus interesting ones that we haven’t.

Convergence:Convergence: Forces agents to address every provisional Forces agents to address every provisional

allocation (significant slack reduction).allocation (significant slack reduction). Can make rules less demanding early on, if Can make rules less demanding early on, if

needed.needed.


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Gaming: Dummy Business Gaming: Dummy Business PlansPlans Naive dummy business plan strategy will not Naive dummy business plan strategy will not

work.work.

The agent must alwaysThe agent must always declare interest in a partially satisfying allocationdeclare interest in a partially satisfying allocation declare non-interest in everything else.declare non-interest in everything else.

More advanced dummy-bid strategies require More advanced dummy-bid strategies require more attention.more attention.


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Information for the ProxyInformation for the Proxy The rules admit many simple proxy The rules admit many simple proxy

computations.computations. Minimal lower bounds for bids to meet the activity Minimal lower bounds for bids to meet the activity

rule.rule. Minimal number of changes.Minimal number of changes. Minimal change in sum of upper/lower bounds.Minimal change in sum of upper/lower bounds. Possibly accommodate agent’s constraints?Possibly accommodate agent’s constraints?

Can imagine a pretty GUI with satisfied vertices Can imagine a pretty GUI with satisfied vertices lighting up as values are tweaked.lighting up as values are tweaked.


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ConclusionsConclusions Introduced simple rules for exchange with Introduced simple rules for exchange with

motivating philosophies and justifications.motivating philosophies and justifications.

Outlined the interactions between the rules and Outlined the interactions between the rules and the groups that are affected by them.the groups that are affected by them.

Addressed some (all?) of the points of the rule-Addressed some (all?) of the points of the rule-related confusion/concern that has arisen so far.related confusion/concern that has arisen so far.

To do: Adding bids (changing the bid structure).To do: Adding bids (changing the bid structure).

Activity Rules: An ongoing saga …

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