Policy “Games”

1. Policy “Games” Strategic Decisions & Game Theory

2. Outline • Defining strategic games • Considering some common examples of strategic games in policy settings • Working through solution concepts and mechanics • Simultaneous games • Sequential games • Understanding and countering strategic moves • Advantages and disadvantages of going first • Bargaining games & experimental outcomes

3. Defining “Strategic Decisions” • In narrow sense used here, strategic decisions (games) mean • Decisions where optimal strategies of 2 (or more) players are actively interdependent • Optimal strategy depends on predictions of other participant(s) best strategy • Not just “playing against nature or world” with fixed prices, probabilities, behavior • Think chess, poker, or rock-paper-scissors, not roullette

4. Some Policy-related Games Prisoner’s dilemma Hostage’s dilemma Samaritan’s dilemma Agenda Control Fed Time Consistency Median Voter Model (Location Game) Bargaining Terms limits & unraveling

5. Prisoner’s Dilemma • 2 criminals arrested for crime • Interrogated separately • Choices: Confess/Don’t confess • Confession by one leads to low/high sentences • Confession by both leads to moderate sentences • Confession by neither leads to acquittal • Not Confess = “cooperative”, positive sum (for participants) solution • Confess = competitive solution

6. Prisoner’s Dilemma-like Games • Hostage’s Dilemma • Multi-person version of PD • Positive sum through cooperation • Non-cooperative solution often dominates • Oligopoly Games (pricing, ads, entry, …) • Cooperation (maybe implicit) leads to higher profits than competition

7. Samaritan’s Dilemma • Giver-Recipient • Giver: I’ll give you $X, when that’s gone, you are on your own (or if you do Y, the money stops) • Recipient: knows giver’s preferences -- recipient “starvation” is “worst case” • Equilibrium: recipient abuses gift, gets more • Ex: Parent-child; gov’t-recipient; moral hazard & catastrophes

8. Fed Money Game • Strategic setup • Fed money-inflation policy • Citizens form inflation expectations • Sequence of actions/reactions/anticipations • If citizens think Fed is keeping inflation low, Fed can spur sluggish economy with more money; citizens treat as more income/output rather than as lower dollar value • Citizens adjust expectations, expect higher inflation • Less money creation to slow inflation now leads to slower income/output but inflation doesn’t respond quickly • Fed must rebuild reputation for low inflation policy

9. “Location” Games Where to setup shop if consumer/voters positioned along a road or distributed about a point uniformly or normal distribution, given that competitor is trying to setup shop in best location also? Simple Solution: Move to the middle (median), otherwise, competitor can locate just to the “busier” side and capture everyone on that side Examples: Median voter model and evidence such as primary & general election races; retail shops Complications: multiple dimensions to choice

10. Political Chess Tom Hanks directed a 12 part HBO series-- From the Earth to the Moon– dramatizing the U.S. space program from Mercury through 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. The fire resulted from a spark in wiring causing the highly pressurized, pure oxygen air in the capsule to ignite and reach temperatures over 1000 degrees 15 seconds. The capsule contractor -- North American and its executive in charge of the Apollo – learned that NASA would likely lay substantial blame on North American.  The NA executive, a hardworking and upstanding person, is outraged and explains to his boss how NA should expose NASA by providing Congress with documentation of the written warnings to NASA about 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 you make sense of the boss’ decision? The boss looked ahead to the Congress/NASA relationship should NASA be exposed or not, and worked backward to the effect on NA

11. Changing the game: Fight or Die Upon arriving in Mexico, Cortez burned his ships His crew now had strongest possible incentive to fight as hard as possible Example of changing the nature of the game by changing player options Ex: Limiting rival options through big, irreversible investments

12. Strategic Situations Bidding-Negotiation; Auctions; (homes, cars, yard sales, …) Employment: Job Market; Board-Management; Management-Labor; Politics/Group Dynamics Pricing, Ad, … Competition Dating, Marriage Families: Parent-Child, Spouses, Siblings Games: Poker, … Strategic-Related Behavior Signaling & Filtering Information Altering Perceptions-Beliefs Promises/Threats Changing “Rules” (nature of game) Repeated IDs Mixing Actions Incentives for Cooperation Cooperation-Compete Dilemmas Free-Riding A Sampler of Strategic Decisions

13. Six Essentials Questions of SDs • Who are Key Decision makers (units)? • Who are the decision entities? • What is the Timing of Decisions? • Sequences or simultaneous? • One-shot or repeated? • What Information is Available? • What do players know/believe? • What Actions are Possible? • Aggressive/passive; high/low; fold/bluff; … • Cooperation • Payoffs to decisions? • Fixed sum, positive sum, or negative sum? • Quantitative & qualitative • Manipulation Possibilities? • Can players alter rules or beliefs of others?

14. Practicing Essentials: PD • Decision Makers? • Timing? • Info? • Actions? • Payoffs? • Manipulation? • Decision Makers: 2 Accused (police in background) • Timing: Effectively simultaneous because of lack of info even if sequential in real time • Info: Not aware of other’s choice until no return/police info not reliable • Actions: Confess or not (highly simplified) • Payoffs: Variable sum, higher if cooperation • Manipulation: Not in simple version

15. Solution Concepts • “Nash Equilibrium”: outcome where opponent doing best possible • Sequential • “Rollback”: Look ahead to last period and work back • Simultaneous • Iterative: step-by-step analysis of best choice given a decision by other • Repeated Simultaneous • Rollback + Iterative

16. Solution Mechanics: “Classic PD” Example • Payoffs = (jail time for #1, jail time for #2)

17. 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 Best outcome for #1, if # 2 Confesses

18. 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 Best outcome for #1, if #2 no confess

19. 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

20. 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 Dominant outcome

21. Sequential Mechanics: Agenda Control byLooking Ahead and Working Back • Rules of order may seem trivial, but where they are strictly followed, they empower strategic decision makers • Suppose a committee made up of members who favor proposal s (E), (M), and (R). They must decide on a single proposal and the mix of members creates the following likely voting outcomes: • E prefers: E > M > R • M prefers: M > R > E • R prefers: R > E > M • So, E beats M, M beat R, and R beats E • How should chairperson structure the vote if wants M to win?

22. Voting Possibilities: Game Tree Vote 1 Vote 2 Winner R v. M M v. E E M v. E E v. R R E v. R R v. M M

23. Sequential Solutions: Looking Ahead Vote 2 Winner M v. E E E v. R R R v. M M • For M to win in the second vote, the matchup must be R v. M, so eliminate other options

24. Sequential Solutions: Looking Ahead and Working Back Vote 1 Vote 2 Winner R v. M M v. E E v. R R v. M M With options in vote 2 paired down, the choice for vote 1 becomes clear

25. Strategic Moves: Manipulating the Game • Changing order of moves • Agenda control example • Changing information or beliefs • Threats, promises, credibility • Poker examples (info sending & receiving) • nuclear deterrence • Changing available strategies • Cortez • Changing payoffs or beliefs about them • Negotiation & “salami tactics” • Use of agents, e.g. retail

26. Countering Strategic Moves:Manipulating Manipulators • Order counter-measures • Amendments, coalitions, … • Information-Extraction countermeasures • Signal-Jamming, e.g. vagueness • Threat/promise countermeasures • Brinksmanship; salami • Option/payoff-limiting countermeasures • Expand Options, e.g., Exclude Agents-Non-decision makers • Salami (more increments/consistency in payoffs, e.g. Hawken research)

27. Misc. SD Observations:First or Second Mover Advantage? • First Mover Advantage if manipulation of game possible through changing game or beliefs of rival • – Princess Bride • Second Mover Advantage if information becomes available by rival’s move • Sailing; NCAA Football Overtime; • What about “Hold-em” Poker? • Tradeoff: manipulation v. info gathering

28. Misc. SD Observations:Bargaining • Ultimatum Game (and related) theory and experimentation • UG = split of pot if 2 parties agree on split; 1 makes offer-1 accepts or declines offer; • Variations: size of pot; depreciation of pot; anonymity; repetition • Money matters but not all that matters • Typical outcomes: bigger than 99:1, less than 50:50 • Time Values • Patience is a virtue • Patience is the best signal of patience

29. Misc SD Observations:Bargaining Tradeoffs • Custom Home Project • Builder-Homeowner • Builder info advantage • Options: • Flex Price w/fixed percentage • Fixed-Price w/negotiated changes • Info/Incentive Tradeoffs • Flex: flexibility of changes; no “hold-out problem”; wrong incentive for info problem • Fixed: Incentive to monitor & control expenses; “hold-out” problem on changes; incentive to cut corners