Introduction to the Strategy of Game Theory
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Game theory is a strategic approach to understanding interactive situations. It examines how individuals make decisions in contexts where outcomes depend on the decisions of others. Key components of game theory include players, rules, strategies, and payoffs. Static games analyze single-shot interactions, while repeated games consider how cooperation can emerge over multiple iterations if players use strategies like tit-for-tat that punish non-cooperation but also forgive. Sequential games incorporate timing of moves, and concepts like backward induction help analyze them. Real-world applications of game theory include how to establish cooperation between parties and the value of commitment devices for changing strategic incentives.
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Introduction to the Strategy of Game Theory
- 1. Introduction to the Strategy of Game Theory Jonathon Flegg Manager
- 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
- 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 Card Why would the CEO of Australia’s biggest coal miner support a carbon tax? ANSWER: GAME THEORY
- 8. Paper, scissors, rock SCISSORS PAPER ROCK ROCK ● Is it strategic? NO ● Is it interactive? NO
- 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
- 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 cooperation Typically 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
Notas del editor
- We’ve all played Risk before.What is the goal of risk: world domination.How do you (hopefully) get there? By strategically deciding on when and with whom to cooperate and when and with whom to bring on conflict.
- The Government preferred ETS TAX NOTHING (Rudd and Gillard promising “no tax”) then it switched to TAXETSNOTHING. NOTHING was least likely. BHP preferred TAX NOTHING ETS (if it was without uranium it might have been NOTHING TAX ETS)A broad-based carbon tax, he said, would affect BHP's business if there was "no rebating for trade-exposed industries".A BHP spokesman confirmed that Mr Kloppers believed there should be "some form of treatment" to recognise export sector industries under the carbon tax, echoing growing calls for special deals across the economy, including from the steel industry, cement manufacturers, food and groceries, oil, gas and aluminium.
- What would happen if the depositors held personal accounts in the fund? What would change?
- EXAMPLES: arms race, global climate change agreements, fall in trade union membershipMany other examples. Can you think of some?
- Player A and Player B. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails) Player A keeps both pennies, so wins one from Player B (+1 for A, -1 for B). If the pennies do not match (one heads and one tails) Player B keeps both pennies, so receives one from Player A (-1 for A, +1 for B). This is an example of a zero-sum game, where one player's gain is exactly equal to the other player's loss.This game has no pure strategyNash equilibrium since there is no pure strategy (heads or tails) that is a best response to a best response. EXAMPLE: paper, scissors, rock
- two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts a stag, he must have the cooperation of his partner in order to succeed. An individual can get a hare by himself, but a hare is worth less than a stag. This is taken to be an important analogy for social cooperation.
- Imagine a couple that agreed to meet this evening, but cannot recall if they will be attending the opera or a football match. The husband would most of all like to go to the football game. The wife would like to go to the opera. Both would prefer to go to the same place rather than different ones. If they cannot communicate, where should they go?This game has two pure strategyNash equilibria, one where both go to the opera and another where both go to the football game.
- The game of chicken models two drivers, both headed for a single lane bridge from opposite directions. The first to swerve away yields the bridge to the other. If neither player swerves, the result is a potentially fatal head-on collision. It is presumed that the best thing for each driver is to stay straight while the other swerves (since the other is the "chicken" while a crash is avoided). Additionally, a crash is presumed to be the worst outcome for both players. This yields a situation where each player, in attempting to secure his best outcome, risks the worst.http://www.youtube.com/watch?v=rExm2FbY-BE&NR=1
- Coercion and punishment – tax evasion punishmentPre-commitment devices – coal purchase orders and airport/airlinesSelective incentives – Growcom Reputation – selling a lemon on ebay or a car (use reputation reporting highly effective - if the word gets out his business will dry up)Establishing trust – small communities
- Compare the risks in a one-off sale of a lemon car compared with a fruit wholesaler who sells to a restaurant every day?
- In 1980, Robert Axelrod, professor of political science at the University of Michigan, held a tournament of various strategies for the prisoner's dilemma. He invited a number of well-known game theorists to submit strategies to be run by computers. In the tournament, programs played games against each other and themselves repeatedly. Each strategy specified whether to cooperate or defect based on the previous moves of both the strategy and its opponent.
- Consider two players: Alice and Bob. Alice moves first. At the start of the game, Alice has two piles of coins in front of her: one pile contains 4 coins and the other pile contains 1 coin. Each player has two moves available: either "take" the larger pile of coins and give the smaller pile to the other player or "push" both piles across the table to the other player. Each time the piles of coins pass across the table, the quantity of coins in each pile doubles. For example, assume that Alice chooses to "push" the piles on her first move, handing the piles of 1 and 4 coins over to Bob, doubling them to 2 and 8. Bob could now use his first move to either "take" the pile of 8 coins and give 2 coins to Alice, or he can "push" the two piles back across the table again to Alice, again increasing the size of the piles to 4 and 16 coins. The game continues for a fixed number of rounds or until a player decides to end the game by pocketing a pile of coins.
- Why do you think is going to happen?
- What do you think is going to happen?Now you can see why the US Congressional committees are so incredibly powerful!
- What do you think is going to happen?Now you can see why the US Congressional committees are so incredibly powerful!
- What do you think is going to happen?Now you can see why the US Congressional committees are so incredibly powerful!