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- 1. Introduction to the Strategy ofGame TheoryJonathon FleggManager
- 2. Outline Concept of game theory Static games Repeated games Sequential games Game theory in the real world
- 3. What is Game Theory? ○ it is not another useless theory ○ it is not just useful for trivial games ○ it is not just for mathematical egg heads ○ . “Game theory is a tool for exploring and understanding situations laced with strategic reasoning” - Joe Harrington (Johns Hopkins University) KEY DEFINING WORDS: STRATEGIC AND INTERACTION
- 4. Cooperate or conflict?
- 5. You probably know some intuitively ... good result, given the ... let’s shift the circumstances. goalposts.... they had no ... I’m keeping other option. ... the result was inevitable. my powder dry. ... gaming the ... launched a ... they burned pre-emptive system ... they’re own strike. bridge. ... need to ... swimming ... tit-for-tat manage against the strategy. expectations. school.
- 6. Questions for game theory● Why does the Westminster system of parliamentary democracy generate conflict?● Why did Neville Chamberlain sign the Munich Agreement with Adolf Hitler?● How hard should you work on a team project at university?● In a penalty kick situation in soccer, is there any advantage from kicking the ball to the right or to the left?
- 7. A Game Theorist Plays Trump CardWhy would the CEO of Australia’sbiggest coal miner support acarbon tax?ANSWER: GAME THEORY
- 8. Paper, scissors, rock SCISSORS PAPER ROCK ROCK ● Is it strategic? NO ● Is it interactive? NO
- 9. Paper, scissors, rock
- 10. A simple example● Did you develop a strategy?● Did it work or not work?● How was this different to the first game with the tape recorder?
- 11. A few assumptions● Each player is rational● Each player knows the full extent to which each other player is rational● Each player knows the potential pay-offs for themselves and others● Each player knows the rules of the game Rational actors are those that construct the most efficient or cost- effective means to achieve their specific goal.
- 12. Key components Players individuals, firms, organisations and governments Rules contracts, laws, regulations and customary agreements Strategies bidding in an auction, running for election, filing a lawsuit, paying a bribe Pay-offs winning an auction, losing a job, going to jail, receiving compensation
- 13. Outline Concept of game theory Static games Repeated games Sequential games Game theory in the real world
- 14. M&M Challenge● You have saved up your whole life a delicious nest egg of 50 M&Ms● Government wants to incentivise M&M saving so it offers individuals the opportunity of depositing your M&Ms in a joint super M&M fund● Government will top-up the joint account with 3 times the M&Ms in the fund and distribute them the same amount to all who contributed● How many M&Ms will you put in the fund?
- 15. Prisoner’s dilemma● Two thieves are caught and interrogated separately● If both thieves stay quiet they will avoid any charges● If both thieves confess they will each get 8 years● If one dobs in the other he walks free while his partner gets 10 years● What do you think is going to happen? http://www.youtube.com/watch?v=ED9gaAb2BEw
- 16. Prisoner’s Dilemma
- 17. Matching Pennies
- 18. The Stag Hunt
- 19. Battle of the Sexes
- 20. The Chicken Game
- 21. Two very important concepts A dominated strategy is a move that always bears outcomes inferior to another, no matter what the other player does.
- 22. Two very important concepts A Nash Equilibrium is a strategy profile with the property that no player can do better by choosing a different strategy.
- 23. Gaining cooperationTypically techniques for promoting coordination fall into two categories:altering the pay-offs or changing the rules of the game. ○ Coercion and punishment ○ Pre-commitment devices and contracts ○ Selective incentives ○ Positive reputation ○ Establishing trust ○ Repeating the game ○ Players move sequentially
- 24. Outline Concept of game theory Static games Repeated games Sequential games Game theory in the real world
- 25. Repeated games● In reality, games are rarely one-off events● In general cooperation can be sustained over time if● Can you think of some examples where this would be the case?● What do you think could happen when the relation starts to come to an end?
- 26. Tit-for-tat strategy● An academic tournament was held in 1980 to test which strategy performs the best over repeated Prisoner’s Dilemmas● The outstanding strategy was Robert Axelrod’s tit-for-tat strategy that follows some simple rules: ○ Unless provoked, a player will always cooperate ○ If provoked, a player will retaliate ○ The agent is quick to forgive● Whilst defecting is the optimal solution in a one-off Prisoner’s Dilemma, the tit- for-tat strategy has a ‘disciplining’ effect on any other mindful player that encourages cooperation
- 27. Outline Concept of game theory Static games Repeated games Sequential games Game theory in the real world
- 28. Centipede Game● There are two bowls of M&Ms – one with one M&M and one with four● Your team can choose to take the bigger pile (leaving the other team with the smaller pile) or passing● Passing the piles causes them to double
- 29. United States example● In the United States, the Congress needs to decide on a new carbon tax to applied to large energy producers. The current rate is $15 per tonne of carbon emitted.● The Senate Committee on Energy and Natural Resource’s preferred tax is $18 per tonne. Once Committee proposes a bill, the legislature is free to amend it before taking a final vote. ○ What will the Committee do if the Senate’s preferred policy is $25 per tonne? ○ What about $14 per tonne?
- 30. Backward induction in the Senate Senate $25 $18 C’tee $15 $15
- 31. Backward induction in the Senate Senate $14 $18 C’tee $15 $15
- 32. Commitment devices "a means with which to lock yourself into a course of action that you might not otherwise choose but that produces a desired result" (Dubner and Levitt 2007)
- 33. Military example● Norway’s army must decide whether to attack Sweden’s, which is occupying an island between the two countries.● In the event of an attack, Sweden may fight, or retreat over a bridge to its mainland. Each army prefers to occupy the island than not to occupy it; a fight is the worst outcome for both armies.● What changes if Sweden’s army burns the bridge back to its mainland, cutting off its only method of retreat?
- 34. Without a commitment device Sweden Fight Norway Attack Retreat Retreat
- 35. Using a commitment device Sweden Fight Norway Attack Retreat Retreat
- 36. Outline Concept of game theory Static games Repeated games Sequential games Game theory in the real world
- 37. Into the real world● Small pay-offs● Uncertain future outcomes● Long-term and repeated games● Behavioural and mental limits
- 38. Fleggie’s final tips● Consider others’ strategies before considering your own● History means very little. Always be forward-looking and anticipatory● Always consider how much actual ability you have to influence a final outcome● Timing is everything, and it’s not always better to move second● Change the rules, changes the outcome
- 39. Final tips on strategy● Never forget the status quo is itself a strategy● Look for dominated strategies that you can take off the table early● Also look for inevitable outcomes. If you can embrace an inevitable outcome, albeit negative, you might be in a position to minimise its impact● Be wary of other players’ publicly released comments. Often they have strong incentives to misrepresent their preferences● Don’t be afraid to use a firm yet forgiving tit-for-tat strategy. It is a proven strategy for cooperation in a broad range of contexts
- 40. Discussion

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