Competitive Strategy Lecture Notes

Games Without Dominant Strategies

  • Many games lack dominant strategies.
  • Choices are often not discrete.
  • Even with discrete choices, a player’s best response can depend on the other player’s strategy.
  • Example: Football

Football Strategy

  • Neither offense nor defense possesses a dominant strategy.
  • If the offense chooses "Run," the defense's best response is "Counter Run."
  • If the offense chooses "Pass," the defense's best response is "Counter Pass."
  • The offense benefits most from playing "Pass" except when facing a blitz.

Dominated Strategies

  • "Blitz" is a dominated strategy for the defense, as it's never optimal.
  • Dominated strategies can be eliminated when seeking solutions, as the opponent won't use them.

Solving Games by Eliminating Dominated Strategies

  • With "Blitz" removed, "Pass" becomes a dominant strategy for the offense.
  • For the defense, "Counter Pass" is the best response to "Pass."
  • Finding the Nash equilibrium becomes straightforward.

Coordination Games

  • Scenario: Fred and Barney, living in the Stone Age, typically hunt rabbits individually.
  • They realize pooling efforts could yield bigger game like stag or bison, increasing their food supply.
  • They plan to hunt big game together but fail to specify which type.

Coordination - Big Game Hunting

  • Stag and bison hunting grounds are distant and in opposite directions.
  • The question is, which game do Fred and Barney choose to hunt?

Coordination – Nash Equilibrium

  • There are no dominant or dominated strategies in this scenario.
  • There exist three pure strategy Nash equilibria.

Achieving Equilibrium

  • Without communication, each player must predict the other's action.
  • The question arises: Are any choices more prominent?
  • If a choice is notably more prominent to both, it can act as a focal point and become the outcome.

Nash Equilibrium and Focal Points

  • Fred and Barney show a strong preference for Bison.
  • Bison appears to be the more obvious choice, but the three equilibria remain.

Additional Information

  • The original "stag hunt game" was formulated by J-J Rousseau.
  • A modification is attributed to Dixit and Nalebuff's "The Art of Strategy."
  • Thomas Schelling, a Nobel laureate, contributed significantly to the understanding of focal points.

Mystery Game

  • A coordination game.
  • Prize: Class participation points.

Other Examples of Coordination Games

  • Research joint ventures.
  • Chicken (brinkmanship): The war of attrition.
  • Standards: DVD or DIVX?

DVD vs. DIVX

  • DVD was introduced in early 1997 by a consortium, including Toshiba, Sony, Matsushita, Philips, and others.
  • DVD offered superior quality compared to VCR.
  • By spring 1997, several studios released movies in DVD format. Summer hardware sales were promising, and the consortium hoped Christmas 1997 would be DVD's breakthrough.
  • In fall 1997, Circuit City launched DIVX, which was partially incompatible with DVD, aiming to dominate the market.
  • Consumers were uncertain which format would win, resulting in a disappointing Christmas 1997 season for both DVD and DIVX (a short-term coordination failure eventually led to DVD's dominance).
  • This situation also serves as an entry story.

Sequential-Move Games - Boulton & Watt

  • James Watt significantly improved the steam engine in 1765 with the separate condenser.
  • Watt secured a 14-year patent for the separate condenser in 1769, extended by 17 years in 1775, lasting until 1800.
  • Watt’s patent also claimed coverage for devices using steam's forcing power, though these claims were weaker.
  • Boulton & Watt faced entrants imitating the separate condenser during the 1780s and 1790s, including Edward Bull and the Hornblower brothers.
  • Richard Trevithick also entered in the 1790s, using the forcing pressure of steam but not imitating the separate condenser.

Boulton & Watt Facing Entry by Low-Pressure Engines

  • If you're a potential entrant, consider whether to enter.
  • If you're Boulton & Watt, consider whether to litigate if entry occurs.

Solving Sequential-Move Games

  • Think forward, reason backward.
  • Begin with Boulton & Watt’s decision to litigate if entry occurs to find their best response.
  • Then, considering that best response, analyze Bull’s decision on whether to enter.
  • This leads to a sequentially rational, or subgame perfect, equilibrium.
  • The Dixit-Skeath book refers to this as a rollback equilibrium.

Boulton & Watt’s Decision

  • Boulton & Watt benefit from litigating, as not doing so would encourage firms to stop paying royalties.

Bull’s Decision

  • Bull earns a positive payoff even expecting litigation, so entry is his best response.
  • The equilibrium is entry followed by litigation.

Boulton & Watt Facing Entry by High-Pressure Engines

  • High-pressure technology (using the forcing pressure of steam) was not mature and less of a threat to business.

Trevithick’s Decision

  • If Boulton & Watt were to sue, Trevithick’s payoff would be worse than if he refrains from entering.
  • However, it is not in Boulton & Watt’s interest to sue, so Trevithick can enter without legal repercussions.

Could Boulton & Watt Prevent Entry By Bluffing?

  • They attempted to do so.
  • In 1782, Boulton & Watt advertised in the Bristol newspaper, threatening to sue all entrants, including those using high-pressure steam.
  • Can such bluffs prevent entry? Is it an equilibrium for Boulton and Watt to "sue if entry occurs" and for Trevithick to stay out?
  • This can be a Nash equilibrium but not a subgame perfect equilibrium. If Trevithick believes Boulton & Watt will sue, it is in his best interest not to enter. Since he never enters, Boulton & Watt never make an irrational decision.

Subgame Perfection

  • However, this Nash equilibrium (Don’t Enter, Litigate if Entry) requires Trevithick to expect irrational behavior from Boulton & Watt.
  • Subgame perfection is the benchmark solution criterion in sequential games and seems highly predictive and appropriate for the Boulton & Watt case study. However, strategists should be alert to a possible role for human passion and psychology; they may be important in some circumstances.
  • When games are repeated, it is possible to build a reputation for aggression and to thereby preclude entry…more on this later.
  • Boulton & Watt filed (and eventually won) lawsuits against Bull and Jabez Hornblower for imitation of the separate condenser. They never sued Trevithick. High-pressure steam came to dominate steam technology several decades later.