Chapter 9: Game Theory and Strategic Thinking

1© 2014 by McGraw‐Hill Education 1 Chapter 9 Game Theory and Strategic Thinking © 2014 by McGraw‐Hill Education 2 What will you learn in this chapter? • What strategic behavior is and what the  components of a strategic game are. • Why noncooperation is a dominant strategy in the  prisoners’ dilemma. • How repeated play can enable cooperation. • How backward induction can be used to make  decisions. • How first‐movers have an advantage. • How patient players have more bargaining power. • How a commitment strategy can allow players to  achieve their goals by limiting their options. © 2014 by McGraw‐Hill Education 3 Games and strategic behavior • People behave rationally when they look at the  trade‐offs they face and pursue their goals in the  most effective way possible. • Game theory studies how people behave  strategically under different circumstances. – A game refers to any situation involving at least two  people that requires those involved to think  strategically. – Behaving strategically involves acting to achieve a goal  by anticipating the interplay between your own and  others’ decisions. 2© 2014 by McGraw‐Hill Education 4 Rules, strategies, and payoffs • All games share three features: rules,  strategies, and payoffs. – Rules define the actions that are allowed in a  game. – Strategies are the plans of action that players  follow to achieve their goals.  – Payoffs are the rewards that come from particular  actions. © 2014 by McGraw‐Hill Education 5 The prisoners’ dilemma You Confess Don’t confess Yo ur a cc om pl ic e C on fe ss 10 years 3rd choice 10 years 3rd choice 20 years 4th choice 1 year 1st choice D on ’t c on fe ss 1 year 1st choice 20 years 4th choice 2 years 2nd choice 2 years 2nd choice • Payoff depends on actions of  both players: – Both confess. – One player confesses. – Neither player confesses. • Solve game by finding what the  other player would do if you  choose a specific action and  vice‐versa. • Because of strategic behavior,  the realized outcome is not the  best possible outcome available. The prisoners’ dilemma is a one‐time game of strategy in  which two people in isolation make the choice to  ‘confess’ or ‘don’t confess’ that together they committed  a crime. © 2014 by McGraw‐Hill Education 6 The prisoners’ dilemma Kerry Go negative Stay positive B us h G o ne ga tiv e Tight race Bad reputation 3rd choiceTight race Bad reputation 3rd choice Lose 4th choice Win 1st choice St ay p os iti ve Win 1st choice Lose 4th choice Tight race Good reputation 2nd choice Tight race Good reputation 2nd choice • Does either player have a dominant strategy – an action  that they always choose?  – Kerry: Go negative. – Bush: Go negative. • The dominant strategies solve  the game. • The realized outcome is not  the best possible outcome  available. – This is due to an inability to  cooperate. The prisoners’ dilemma can be extended to other  applications, such as the Bush‐Kerry presidential election  and the choice to use negative or positive advertising. 3© 2014 by McGraw‐Hill Education 7 The prisoners’ dilemma You Don’t litter Yo ur ne ig hb or Li tte r -10 3rd choice -10 3rd choice -15 4th choice 0 1st choice 0 1st choice -15 4th choice -5 2nd choice -5 2nd choice Litter D on ’t lit te r • Sometimes all players lose,  but want to contain their  losses. • The dominant strategies solve  the game. • The solution to the game is  called a Nash equilibrium – when all players choose the  best strategy they can given  the choices of all other  players. The prisoners’ dilemma can also be extended to whether  you should or should not litter. © 2014 by McGraw‐Hill Education 8 Dominant strategies Player B Rock Paper Scissors Pl ay er A R oc k P ap er S ci ss or s Tie A wins B wins B wins B wins A wins A wins Tie Tie • The game of rock,  paper, scissors has no  Nash equilibrium. • There is no stable  outcome where you  or your opponent  would wish to change  your strategy once  you find out what the  other player is doing. While dominant strategies can sometimes solve for the  Nash equilibrium, sometimes games do not have an  equilibrium. © 2014 by McGraw‐Hill Education 9 Reaching equilibrium • The Nash equilibrium is sometimes referred to  as the non‐cooperative equilibrium. – This is because players act independently, only  pursuing their individual interests. • Sometimes players may collude (or cooperate)  to obtain a better outcome for both. – In the case of the prisoners’ dilemma, the  cooperative equilibrium would make both players  better off. 4© 2014 by McGraw‐Hill Education 10 Active Learning: Finding equilibrium Suppose Greg and Renee must choose whether or not to  offer a lunch special at their respective restaurants. • Find the Nash equilibrium. Greg’s Pizzeria Don’t offer lunch special R en ee ’s G re ek S al ad B ar O ffe r l un ch sp ec ia l -10 -5 -15 20 30 -10 35 25 Offer lunch special D on ’t of fe r lu nc h sp ec ia l © 2014 by McGraw‐Hill Education 11 Avoiding competition through commitment • Sustaining collusion to obtain the cooperative  equilibrium is extremely difficult, as one player  can typically be made better off by defecting. • It may require a punishment for defecting that  is larger than the payoff for defecting. – An agreement to submit to a penalty for defecting  to obtain a certain outcome is an example of a  commitment strategy. • Often the commitment is non‐binding and  individuals break their agreement. © 2014 by McGraw‐Hill Education 12 Promoting competition in the public interest Collusion Exxon Low prices High prices Co no co Lo w p ric es Low profits 3rd choice Low profits 3rd choice No profit 4th choice High profits 1st choice H ig h pr ic es High profits 1st choice No profit 4th choice Moderate profits 2nd choice Moderate profits 2nd choice Competition • Suppose a small town has  two gas stations, each  setting their price. – If they collude, they will  earn moderate profits. – If they compete, they will  earn low profits. • The non‐cooperative  Nash equilibrium is the  competitive equilibrium. While cooperation may serve the best interests of the  players directly involved, it may have societal  consequences. 5© 2014 by McGraw‐Hill Education 13 Repeat play in the prisoners’ dilemma • Repeated games are not one‐time, but are  played more than once. • The cooperative equilibrium is more likely to  occur because simple commitment  mechanisms exist. – Tit‐for‐tat: One player does the same action as the  other did in the previous game. © 2014 by McGraw‐Hill Education 14 Sequential games • In all of the previously discussed games, both  players moved simultaneously. • In many instances, an individual or company must  move prior to other participants choosing an  action. – Typically the player who chooses first gets a higher  payoff, a first‐mover advantage. • The optimal strategies are determined by using  backward induction, in which the optimal strategy  of the last player to choose is determined,  followed by the second‐to‐last player, and so on. © 2014 by McGraw‐Hill Education 15 Sequential games Q. What do you have to do to win the Pulitzer prize? A. You have to work for a top newspaper. Q. What do you have to do to get a job at a top newspaper? A. You have to have a graduate degree in journalism. Q. What do you have to do to get a graduate degree in journalism? A. You have to have an undergraduate degree in English. Q. What do you have to do to get that degree? A. You have to take the prerequisite courses in nonfiction writing. Therefore, you should take introductory nonfiction writing next semester. • Suppose you aspire to win the Pulitzer Prize. • Start with the outcome and work backwards to  determine your sequence of choices. 6© 2014 by McGraw‐Hill Education 16 Deterring market entry: a sequential game Burger King: Should we enter? If so, where? Bu ger King: Shoul we e ter? If so whe e? Center of town Outskirts of town No Outskirts Outskirts Center Center No Profits BK: 2% McD: 12% BK: 4% McD: 4% BK: 10% McD: 12% BK: 8% McD: 8% BK: 12% McD: 2% BK: 10% McD: 20% McDonalds:  Where should we  build? Burger King:  Should we enter?  If so, where? Burger King:  Should we  nter?  If so, where? • If McD enters in the center of  town: – BK will not enter and earns a  10% return. – McD earns 12% return. • If McD enters in outskirts of  town: – BK will enter at center and  earns a 12% return. – McD earns 2% return. • McD chooses between 12%  return or 2% return. • McD chooses to locate at the  center of town and BK does not  enter. • A decision tree visualizes sequential games. For example,  McDonald’s is considering a new store in a small town. • Profits (the payoffs) are affected by what location is built in  and by how many burger joints enter. © 2014 by McGraw‐Hill Education 17 Sequential games Company:What shouldwepay employees? Company: 0% Union: 0% 1% surplus Yes Share of surplus No Labor Union: Should we accept the new offer? Company: 99% Union: 1% Company: t should we pay employees? • If this was a one‐round game and the company moved first, it could offer just 1 percent of the  surplus and the union would have to make a choice: – Accept the offer. – Reject it by going on strike and shutting down production. • The union chooses between a 1% pay raise and 0%. – The union will accept the offer. • This is an example of an ultimatum game: One player makes an offer and the other player has  the simple choice of whether to accept or reject. • First‐mover advantage can be extremely important in one‐round sequential  games. • Consider a bargaining game, in which a company is negotiating with its  employees’ labor union over wages. © 2014 by McGraw‐Hill Education 18 Commitment in sequential games Aztecs: Advance or retreat? Cortés: Advance or retreat? Cortés: fight to death Aztecs: fight to death Cortés: lives Aztecs: keep land Cortés: wins land Aztecs: live Cortés: lives Aztecs: keep land Advance Retreat Advance Retreat Retreat Advance Result Cortés: Advance or retreat? • Both prefer land, lives,  and then a fight to the  death. • If all strategies are  available: – If Aztecs advance, Cortes  will retreat. – If Aztecs retreat, Cortes will  advance. • Given these strategies,  Aztecs will advance and  Cortes will retreat. • Commitment in sequential games can affect the realized  outcome. • Suppose that the Aztecs and Cortes’ men have the choice to  either advance or retreat. 7© 2014 by McGraw‐Hill Education 19 Commitment in sequential games Cortés: fight to death Aztecs: fight to death Cortés: wins land Aztecs: live Advance Retreat Advance Retreat Retreat Advance Result Eliminated Aztecs: Advance or retreat? Cortés: Advance or retreat? Cortés: Advance or retreat? Eliminated • Consider the same game, but now assume that Cortes commits  to advancing by burning his ships. • Burning his ships  eliminates the choice to  retreat. • Given this limited choice  set, Aztecs choose  between: – Advancing, and fighting to  the death. – Retreating, and living. • Given these strategies,  Aztecs will retreat and  Cortes will advance. © 2014 by McGraw‐Hill Education 20 Active Learning: Commitment in sequential  games Burger King: Should we enter? If so, where? Bu ger King: Shoul we e ter? If so whe e? Center of town Outskirts of town No Outskirts Outskirts Center Center No Profits BK: 2% McD: 12% BK: 4% McD: 4% BK: 10% McD: 12% BK: 8% McD: 8% BK: 12% McD: 2% BK: 10% McD: 20% McDonalds:  Where should we  build? Burger King:  Should we enter?  If so, where? Burger King:  Should we  nter?  If so, where? In an effort to not lose market share, suppose Burger King commits  to build in every new town that McDonalds does. • How does this affect the outcome? © 2014 by McGraw‐Hill Education 21 Summary • The concept of strategic games was  introduced. • Many real‐life decisions can be analyzed as if a  strategic game is being played. • Game theory can explain choices that may  seem unintuitive, such as why people in  custody confess to their crimes. • Simultaneous move games were examined as  well as sequential move games. – Commitment can affect the outcome of both.