Policy “Games”
description
Transcript of Policy “Games”
Policy “Games”
Strategic Decisions Strategic Decisions & Game Theory& Game Theory
2
Outline Defining strategic gamesDefining strategic games Considering some common examples of strategic games in Considering some common examples of strategic games in
policy settingspolicy settings Working through solution concepts and mechanicsWorking through solution concepts and mechanics
Simultaneous gamesSimultaneous games Sequential gamesSequential games
Understanding and countering strategic movesUnderstanding and countering strategic moves Advantages and disadvantages of going firstAdvantages and disadvantages of going first Bargaining games & experimental outcomesBargaining games & experimental outcomes
3
Defining “Strategic Decisions” In narrow sense used here, strategic decisions (games) In narrow sense used here, strategic decisions (games)
meanmean Decisions where optimal strategies of 2 (or more) Decisions where optimal strategies of 2 (or more)
players are actively interdependentplayers are actively interdependent Optimal strategy depends on predictions of other Optimal strategy depends on predictions of other
participant(s) best strategyparticipant(s) best strategy Not just “playing against nature or world” with Not just “playing against nature or world” with
fixed prices, probabilities, behaviorfixed prices, probabilities, behavior Think chess, poker, or rock-paper-scissors, not Think chess, poker, or rock-paper-scissors, not
roulletteroullette
Some Policy-related Games
Prisoner’s dilemmaPrisoner’s dilemma Hostage’s dilemmaHostage’s dilemma Samaritan’s dilemmaSamaritan’s dilemma Agenda ControlAgenda Control Fed Time ConsistencyFed Time Consistency Median Voter Model (Location Game)Median Voter Model (Location Game) BargainingBargaining Terms limits & unravelingTerms limits & unraveling
Prisoner’s Dilemma 2 criminals arrested for crime2 criminals arrested for crime
Interrogated separately Interrogated separately Choices: Confess/Don’t confessChoices: Confess/Don’t confess
Confession by one leads to low/high Confession by one leads to low/high sentencessentences
Confession by both leads to moderate Confession by both leads to moderate sentencessentences
Confession by neither leads to acquittalConfession by neither leads to acquittal Not Confess = “cooperative”, positive sum (for Not Confess = “cooperative”, positive sum (for
participants) solutionparticipants) solution Confess = competitive solutionConfess = competitive solution
5
Prisoner’s Dilemma-like Games
Hostage’s DilemmaHostage’s Dilemma Multi-person version of PDMulti-person version of PD Positive sum through cooperationPositive sum through cooperation Non-cooperative solution often Non-cooperative solution often
dominatesdominates Oligopoly Games (pricing, ads, entry, …)Oligopoly Games (pricing, ads, entry, …)
Cooperation (maybe implicit) leads to Cooperation (maybe implicit) leads to higher profits than competitionhigher profits than competition
6
Samaritan’s Dilemma
Giver-RecipientGiver-Recipient Giver: I’ll give you $X, when that’s gone, you Giver: I’ll give you $X, when that’s gone, you
are on your own (or if you do Y, the money are on your own (or if you do Y, the money stops)stops)
Recipient: knows giver’s preferences -- Recipient: knows giver’s preferences -- recipient “starvation” is “worst case”recipient “starvation” is “worst case”
Equilibrium: recipient abuses gift, gets moreEquilibrium: recipient abuses gift, gets more Ex: Parent-child; gov’t-recipient; moral Ex: Parent-child; gov’t-recipient; moral
hazard & catastropheshazard & catastrophes
7
Fed Money Game Strategic setupStrategic setup
Fed money-inflation policyFed money-inflation policy Citizens form inflation expectationsCitizens form inflation expectations Sequence of actions/reactions/anticipationsSequence of actions/reactions/anticipations
If citizens think Fed is keeping inflation low, Fed can spur If citizens think Fed is keeping inflation low, Fed can spur sluggish economy with more money; citizens treat as more sluggish economy with more money; citizens treat as more income/output rather than as lower dollar valueincome/output rather than as lower dollar value
Citizens adjust expectations, expect higher inflationCitizens adjust expectations, expect higher inflation Less money creation to slow inflation now leads to slower Less money creation to slow inflation now leads to slower
income/output but inflation doesn’t respond quicklyincome/output but inflation doesn’t respond quickly Fed must rebuild reputation for low inflation policyFed must rebuild reputation for low inflation policy
“Location” Games Where to setup shop if consumer/voters positioned along a Where to setup shop if consumer/voters positioned along a
road or distributed about a point uniformly or normal road or distributed about a point uniformly or normal distribution, given that competitor is trying to setup shop distribution, given that competitor is trying to setup shop in best location also?in best location also?
Simple Solution: Move to the middle (median), otherwise, Simple Solution: Move to the middle (median), otherwise, competitor can locate just to the “busier” side and capture competitor can locate just to the “busier” side and capture everyone on that sideeveryone on that side
Examples: Median voter model and evidence such as Examples: Median voter model and evidence such as primary & general election races; retail shopsprimary & general election races; retail shops
Complications: multiple dimensions to choiceComplications: multiple dimensions to choice
9
Political Chess
Tom Hanks directed a 12 part HBO series-- Tom Hanks directed a 12 part HBO series-- From the Earth to the From the Earth to the MoonMoon– dramatizing the U.S. space program from Mercury through – dramatizing the U.S. space program from Mercury through the Apollo moon landings. One segment depicts the events of Apollo the Apollo moon landings. One segment depicts the events of Apollo 1 in which three astronauts died in a capsule fire during a routine test. 1 in which three astronauts died in a capsule fire during a routine test. The fire resulted from a spark in wiring causing the highly The fire resulted from a spark in wiring causing the highly pressurized, pure oxygen air in the capsule to ignite and reach pressurized, pure oxygen air in the capsule to ignite and reach temperatures over 1000 degrees 15 seconds. The capsule contractor -- temperatures over 1000 degrees 15 seconds. The capsule contractor -- North American and its executive in charge of the Apollo – learned North American and its executive in charge of the Apollo – learned that NASA would likely lay substantial blame on North American. that NASA would likely lay substantial blame on North American. The NA executive, a hardworking and upstanding person, is outraged The NA executive, a hardworking and upstanding person, is outraged and explains to his boss how NA should expose NASA by providing and explains to his boss how NA should expose NASA by providing Congress with documentation of the written warnings to NASA about Congress with documentation of the written warnings to NASA about the dangers of a pure oxygen gas system as well as pressurized tests at the dangers of a pure oxygen gas system as well as pressurized tests at sea level. His boss says , no,we’re not and goes on to respond. Can sea level. His boss says , no,we’re not and goes on to respond. Can you make sense of the boss’ decision?you make sense of the boss’ decision?
The boss looked ahead to the Congress/NASA relationship should The boss looked ahead to the Congress/NASA relationship should NASA be exposed or not, and worked backward to the effect on NANASA be exposed or not, and worked backward to the effect on NA
10
Changing the game: Fight or Die
Upon arriving in Mexico, Cortez burned his Upon arriving in Mexico, Cortez burned his shipsships
His crew now had strongest possible His crew now had strongest possible incentive to fight as hard as possibleincentive to fight as hard as possible
Example of changing the nature of the game Example of changing the nature of the game by changing player optionsby changing player options
Ex: Limiting rival options through big, Ex: Limiting rival options through big, irreversible investmentsirreversible investments
11
12
A Sampler of Strategic Decisions
Strategic SituationsStrategic Situations Bidding-Negotiation; Auctions; Bidding-Negotiation; Auctions;
(homes, cars, yard sales, …) (homes, cars, yard sales, …) Employment: Job Market; Employment: Job Market;
Board-Management; Board-Management; Management-Labor; Management-Labor;
Politics/Group DynamicsPolitics/Group Dynamics Pricing, Ad, … CompetitionPricing, Ad, … Competition Dating, MarriageDating, Marriage Families: Parent-Child, Families: Parent-Child,
Spouses, SiblingsSpouses, Siblings Games: Poker, … Games: Poker, …
Strategic-Related Strategic-Related BehaviorBehavior
Signaling & Filtering Signaling & Filtering InformationInformation
Altering Perceptions-BeliefsAltering Perceptions-Beliefs Promises/ThreatsPromises/Threats Changing “Rules” (nature of Changing “Rules” (nature of
game)game) Repeated IDsRepeated IDs Mixing ActionsMixing Actions Incentives for CooperationIncentives for Cooperation Cooperation-Compete Cooperation-Compete
DilemmasDilemmas Free-RidingFree-Riding
13
Six Essentials Questions of SDs Who are Key Decision makers (units)? Who are Key Decision makers (units)?
Who are the decision entities?Who are the decision entities? What is the Timing of DecisionsWhat is the Timing of Decisions??
Sequences or simultaneous? Sequences or simultaneous? One-shot or repeated?One-shot or repeated?
What Information is Available?What Information is Available? What do players know/believe?What do players know/believe?
What Actions are Possible?What Actions are Possible? Aggressive/passive; high/low; fold/bluff; …Aggressive/passive; high/low; fold/bluff; … CooperationCooperation
Payoffs to decisions?Payoffs to decisions? Fixed sum, positive sum, or negative sum?Fixed sum, positive sum, or negative sum? Quantitative & qualitativeQuantitative & qualitative
Manipulation Possibilities? Manipulation Possibilities? Can players alter rules or beliefs of others? Can players alter rules or beliefs of others?
Practicing Essentials: PD Decision Makers?Decision Makers? Timing?Timing? Info?Info? Actions?Actions? Payoffs?Payoffs? Manipulation?Manipulation?
Decision Makers: 2 Accused (police in background)Decision Makers: 2 Accused (police in background) Timing: Effectively simultaneous because of lack of info even if Timing: Effectively simultaneous because of lack of info even if
sequential in real timesequential in real time Info: Not aware of other’s choice until no return/police info not Info: Not aware of other’s choice until no return/police info not
reliable reliable Actions: Confess or not (highly simplified)Actions: Confess or not (highly simplified) Payoffs: Variable sum, higher if cooperationPayoffs: Variable sum, higher if cooperation Manipulation: Not in simple versionManipulation: Not in simple version
Solution Concepts ““Nash Equilibrium”: outcome where Nash Equilibrium”: outcome where
opponent doing best possible opponent doing best possible Sequential Sequential
““Rollback”: Look ahead to last period Rollback”: Look ahead to last period and work backand work back
Simultaneous Simultaneous Iterative: step-by-step analysis of best Iterative: step-by-step analysis of best
choice given a decision by otherchoice given a decision by other Repeated SimultaneousRepeated Simultaneous
Rollback + IterativeRollback + Iterative 15
Solution Mechanics: “Classic PD” Example• Payoffs = (jail time for #1, jail time for #2)
Prisoner 2Prisoner 2CC NCNC
Prisoner 1Prisoner 1CC 1010,10,10 11,,2020NCNC 2020,,11 33,,33
Solution Mechanics: “Classic PD” Example
• Iterative: prisoner 1 considers best choice if #2 confesses (column 1) & chooses C (time = 10); #1 considers best choice if #2 not confess & chooses C (payoff = 1); NC is dominant strategy for #1
Prisoner 2Prisoner 2CC
Prisoner 1Prisoner 1CC 1010,10,10 NCNC 2020,,11
Best outcome for #1, if # 2 Confesses
Solution Mechanics: “Classic PD” Example
• #1 considers best choice if #2 not confess & chooses C (payoff = 1);
• C is dominant strategy for #1; always better than NC
Prisoner 2Prisoner 2NCNC
Prisoner 1Prisoner 1CC 11,,2020NCNC 33,,33
Best outcome for #1, if#2 no confess
Samaritan’s Dilemma • Recipient Chooses High Effort (HE) or Low Effort (LE);
Giver Chooses Pay or No Pay; Payoffs (Recipient; Giver)
• Can you find the typical solution: consider Giver’s payoffs in view of recipient’s choices
GiverGiverPayPay No PayNo Pay
RecipientRecipientHEHE 1010,100,100 00,,2020LELE 100100,,1010 2020,,00
Samaritan’s Dilemma • Iterative solution: If Recipient HE, Giver Pay; If Recipient
LE, Giver Pay – Pay dominant for Giver (the dilemma); recipient exploits this information and chooses LE
GiverGiverPayPay No PayNo Pay
RecipientRecipientHEHE 1010,100,100 00,,2020LELE 100100,,1010 2020,,00
Dominant outcome
Sequential Mechanics: Agenda Control byLooking Ahead and Working Back Rules of order may seem trivial, but where they are strictly Rules of order may seem trivial, but where they are strictly
followed, they empower strategic decision makersfollowed, they empower strategic decision makers Suppose a committee made up of members who favor Suppose a committee made up of members who favor
proposal s (E), (M), and (R). They must decide on a single proposal s (E), (M), and (R). They must decide on a single proposal and the mix of members creates the following likely proposal and the mix of members creates the following likely voting outcomes:voting outcomes: E prefers: E > M > RE prefers: E > M > R M prefers: M > R > EM prefers: M > R > E R prefers: R > E > MR prefers: R > E > M So, E beats M, M beat R, and R beats ESo, E beats M, M beat R, and R beats E
How should chairperson structure the vote if wants M to How should chairperson structure the vote if wants M to win? win?
Voting Possibilities: Game Tree
Vote 1 Vote 2Vote 1 Vote 2 WinnerWinner R v. MR v. M M v. EM v. E E E
M v. EM v. E E v. RE v. R R R
E v. R E v. R R v. MR v. M M M
22
Sequential Solutions: Looking Ahead
Vote 2Vote 2 WinnerWinnerM v. EM v. E E E
E v. RE v. R R R
R v. MR v. M M M For M to win in the second vote, the matchup must be For M to win in the second vote, the matchup must be
R v. M, so eliminate other options R v. M, so eliminate other options 23
Sequential Solutions: Looking Ahead and Working Back Vote 1 Vote 2Vote 1 Vote 2 WinnerWinner R v. MR v. M
M v. EM v. E
E v. R E v. R R v. MR v. M M M
With options in vote 2 paired down, the choice for vote 1 becomes clearWith options in vote 2 paired down, the choice for vote 1 becomes clear
24
25
Strategic Moves: Manipulating the Game Changing order of movesChanging order of moves
Agenda control exampleAgenda control example Changing information or beliefs Changing information or beliefs
Threats, promises, credibility Threats, promises, credibility Poker examples (info sending & receiving)Poker examples (info sending & receiving) nuclear deterrencenuclear deterrence
Changing available strategiesChanging available strategies CortezCortez
Changing payoffs or beliefs about themChanging payoffs or beliefs about them Negotiation & “salami tactics” Negotiation & “salami tactics” Use of agents, e.g. retailUse of agents, e.g. retail
26
Countering Strategic Moves:Manipulating Manipulators Order counter-measuresOrder counter-measures
Amendments, coalitions, …Amendments, coalitions, … Information-Extraction countermeasuresInformation-Extraction countermeasures
Signal-Jamming, e.g. vaguenessSignal-Jamming, e.g. vagueness Threat/promise countermeasuresThreat/promise countermeasures
Brinksmanship; salamiBrinksmanship; salami Option/payoff-limiting countermeasuresOption/payoff-limiting countermeasures
Expand Options, e.g., Exclude Agents-Non-Expand Options, e.g., Exclude Agents-Non-decision makersdecision makers
Salami (more increments/consistency in Salami (more increments/consistency in payoffs, e.g. Hawken research)payoffs, e.g. Hawken research)
27
Misc. SD Observations:First or Second Mover Advantage? First Mover Advantage if manipulation of game First Mover Advantage if manipulation of game
possible through changing game or beliefs of rivalpossible through changing game or beliefs of rival – – Princess BridePrincess Bride
Second Mover Advantage if information becomes Second Mover Advantage if information becomes available by rival’s move available by rival’s move
Sailing; NCAA Football Overtime; Sailing; NCAA Football Overtime; What about “Hold-em” Poker?What about “Hold-em” Poker?
Tradeoff: manipulation v. info gatheringTradeoff: manipulation v. info gathering
28
Misc. SD Observations:Bargaining Ultimatum Game (and related) theory and experimentationUltimatum Game (and related) theory and experimentation
UG = split of pot if 2 parties agree on split; 1 makes offer-UG = split of pot if 2 parties agree on split; 1 makes offer-1 accepts or declines offer; 1 accepts or declines offer;
Variations: size of pot; depreciation of pot; anonymity; Variations: size of pot; depreciation of pot; anonymity; repetitionrepetition
Money matters but not all that mattersMoney matters but not all that matters Typical outcomes: bigger than 99:1, less than 50:50Typical outcomes: bigger than 99:1, less than 50:50
Time Values Time Values Patience is a virtue Patience is a virtue Patience is the best signal of patiencePatience is the best signal of patience
29
Misc SD Observations:Bargaining Tradeoffs Custom Home ProjectCustom Home Project
Builder-HomeownerBuilder-HomeownerBuilder info advantageBuilder info advantage
Options: Options: Flex Price w/fixed percentageFlex Price w/fixed percentageFixed-Price w/negotiated changesFixed-Price w/negotiated changes
Info/Incentive TradeoffsInfo/Incentive TradeoffsFlex: flexibility of changes; no “hold-out Flex: flexibility of changes; no “hold-out
problem”; wrong incentive for info problemproblem”; wrong incentive for info problemFixed: Incentive to monitor & control expenses; Fixed: Incentive to monitor & control expenses;
“hold-out” problem on changes; incentive to cut “hold-out” problem on changes; incentive to cut cornerscorners