game theory

game theory

the science of making good decisions involving strategic interaction

strategic interaction

when your best choice may depend on what others choose, and their best choice may depend on what you choose

• underlying idea comes from the interdependence principle → our decisions are intertwined with those of others

• relate to both competition and collaboration

examples of strategic interaction

• games → boxing, football, basketball, chess

• business → your decision about whether to enter a market depends on how other businesses in the market may respond

• politics → payoff from voting on a bill depends on whether others vote for it too

• friends & family → you will go to a party only if your friends also go

steps for making strategic decisions

1. consider all possible outcomes

2. think about the “what ifs” separately

3. play your best response

4. put yourself in other player’s shoes

best responses

your best response is the choice that gives you the highest payoff given what the other player is doing

• to find best responses:

  • fix the other player’s choice

  • compare your possible payoffs

  • choose the option with the highest payoff

Nash equilibrium

each player makes their best response based on the other player’s choice

• no one can do better by changing their choice alone

• each makes their best choice given the choice of others

socially optimal decision

• they are jointly better off if they cooperate

• why would one of them defect?

  • they believe the other has a strong incentive to defect

  • if one defects and the other doesn’t, one group gets nothing

• thus the best response is usually to defect

  • temptation to defect undermines cooperation, sometimes agreements are not credible

• ie. prisoner’s dilemma

dominant strategy

a choice that gives you a higher payoff than any other option, no matter what the other player does

dominated strategy

always gives a lower payoff than some other option, no matter what the other player does

dominant strategy equilibrium

when each player is choosing a dominant strategy

• both coke-pepsi and prisoner’s dilemma have the same game structure

  • each firm has an incentive to defeat, even though both would be better off cooperating

coordination games

players benefit from matching choices

• difficult because there may be multiple equilibria

• failure to coordinate can lead to an inferior outcome

• ex. choosing a company’s business hours

anti-coordination games

players benefit from making different choices

• can also have multiple equilibria

• ex. choosing different routes to avoid traffic

solutions to coordination issues

1. communication → works when incentives are aligned

2. focal points, culture, and norms → ex. shaking hands vs bowing depends on ^, they can help select a particular equilibrium

3. laws and regulations → choosing which side of the road to drive on

sequential games

you observe a rival’s action before choosing yours

• vs simultaneous games: you choose without seeing the other player’s choice

• order matters → may create first-mover or second-mover advantages

first mover advantage

• gaining strategically by committing early

  • airline scheduling example → if WestJet chooses to be aggressive, Air Canada is forced to respond less aggressively

• moving late or early depends on commitment vs flexibility

second mover advantage

adapting to the first mover’s choice

• examples:

  • pricing: undercut after observing prices

  • product positioning: fill underserved niches

  • cake-cutting: they cut, you pick

game trees

shows how a game plays out overtime

• the first move forming the trunk, each subsequent choice branching out, final leaves show all possible outcomes

• how to solve game trees:

  • look forward → anticipate consequences of choices

  • reason backward → begin at final decision and work to the start

  • backwards induction reveals optimal choices today