Competitive Strategy: Game Theory Basics

Why Game Theory?

  • Peter Thiel in "Zero to One" emphasizes finding new ways to deliver value and monopolize them as key to entrepreneurship.
  • Pure, long-lived legal monopolies are rare; successful firms usually face a few rivals.
  • Porter (1996) suggests good business strategy involves:
    • Differentiation from competitors.
    • Difficulty to imitate.
  • Good strategy aims for closer-to-monopoly positioning with few rivals.

Strategists and Game Theory

  • Good strategists:
    • Anticipate rivals' moves.
    • Create difficult positions for rivals.
    • Respond effectively to rivals' moves.
  • Strategists view business situations as "games," choosing which to play/avoid and aiming to win.
  • Bad strategy leads to commoditization with easy imitation/entry, making profitable moves scarce.
  • Example: PC computers in the 1980s (dramatized in "Halt and Catch Fire").

Game Theory Defined

  • Game Theory: a framework for understanding behavior in settings of strategic interdependence.
  • Players: Self-interested individuals/firms.
  • Strategy: An action or set of actions chosen by a player.
  • Interdependence: Actions have cross-effects on outcomes.
    • Without interdependence, there is no game.
  • Mutual Awareness: Players consider cross-effects in their decisions.
    • Price-taking behavior is inconsistent with mutual awareness.

Businesses That Play Games

  • Markets with market power:
    • Monopolistic or oligopolistic horizontal rivals.
    • Monopolistic or oligopolistic input suppliers.
    • Monopolistic or oligopolistic customers (e.g., powerful retailers).
  • Environment where players are aware of each other's presence/intentions.
    • Companies reference rivals in ads.
    • Companies benchmark products against rivals.

Defining a Game

  • Opening a coffee shop: Is it a game?
    • If you will be the only coffee shop (monopoly), then no, not a game. It's just a decision.
    • If coffe shops are owned by large national chains that don't consider local competition (perfect competition), then no, not a game. It's just a decision.
    • If another firm is dominant in that location, likely a game.

Coffee at the Athens Farmers Market

  • For years, 1000 Faces Coffee was the sole vendor.
  • Jittery Joe’s application to serve was denied in 2009.
  • Reason: The current vendor was a long-time member, sponsor, and board member.

Examples of Games Businesses Play

  • Many markets have a small number of players, where game theory is effective.
  • Examples:
    • Large Concentrated Industries: tech (Google, Amazon, Apple, Facebook), media/wireless/cable (AT&T, Verizon, Comcast), health care (hospitals, insurers, pharma), airlines (Delta, American, Ryanair), package delivery (FedEx, UPS), soft drinks (Coke, Pepsi), mattresses (Sealy, Simmons).
    • Your Hometown…

The Theory: Rules

  • Timing of moves.
  • Nature of actions and cross-effects on payoffs.
  • Information.
  • Enforceability of contracts (is the game non-cooperative?).

Timing: Simultaneous-Move Games

  • Players act "at the same time."
  • Examples: Rock, paper, scissors, sealed-bid auctions.
  • Simultaneity can be assumed for analytical purposes even if not literally simultaneous.
  • Examples:
    • Do I confess in a Prisoner’s Dilemma game?
    • How many heirloom tomatoes do I bring to the farmer’s market this week?
    • How deeply do I discount prices on Black Friday?

Timing: Sequential-Move Games

  • Players act asynchronously (one after the other).
  • Examples: Chess, checkers, alternating offers in bargaining.
  • Sequential moves can be assumed for analytical purposes even if not literally sequential.
  • Examples:
    • How do I decide how much manufacturing capacity to build in my new plant?
    • How do I design the next generation smartphone?
  • Irreversible actions, observed by other players, define sequential-move games.
  • Prices are not costly to change.
  • A venture-specific investment—going “all in”—is costly to change.

Sequential-Move Games: Player Influence

  • In sequential-move games, a player can influence:
    • Their own set of possible future moves.
    • A rival’s subsequent moves.
    • The nexus of competition (i.e., the type of game) for future interactions.
  • Bold, aggressive moves are often best.
  • "Never mind maneuvers, always go at them." - Admiral Nelson.
  • Rupert Murdoch (newspapers in Australia, network TV in the US, satellite TV in the UK) exemplifies this.

Timing: Repeated Simultaneous Games

  • Players act simultaneously in each period of a multi-period game.
  • Examples: Rock, paper, scissors (best 2 out of 3), repeat interaction in auctions.
  • Useful for understanding dynamic rivalry when key strategic actions are easily changed often.
  • Examples:
    • Price wars.
    • Collusion.
    • Signaling.

An Action

  • A single choice in a single stage of a game.
  • The “Pawn to King Four” opening move in chess.
  • Continuous choices like price or output.
  • Discrete choices like “enter the market” or “don’t enter the market.”

A Strategy: A Set of Actions

  • Single action in a non-repeated simultaneous-move game like "rock" in rock-paper-scissors.
    • Action and (pure) strategy are synonymous in such cases.
  • A set of conditional actions in a sequential-move or repeated-simultaneous game.
    • “Enter if the other firm doesn’t enter” and “Don’t enter if the other firm does enter.”
    • Very specific—must account for all contingencies. Much more specific than “counter the Ruy Lopez (pawn to king four opening plus standard subsequent moves) with the Schliemann defense.”
    • Making a split-the-difference offer in the third round of alternating-offer bargaining.
  • Game theory allows for strategies to mix actions probabilistically (a mixed strategy).
    • For example, “hit first serve down the T 50% of the time, out wide 50% of the time.”

Cross Effects

  • Many games are zero-sum (one player’s loss is another’s gain).
    • Poker, sports.
  • Sometimes payoff-increasing action hurts the other player, sometimes not. Games can have win-win or lose-lose outcomes.
    • More common in business situations.
  • Two-sided markets (video games—consoles and games) create complementarities. Producing and selling a lot of game consoles increases the gains to making more and better games, which increases the gains to selling consoles, etc. Recently, complements have come to be known as the “sixth force,” complementing a Porter analysis.
  • Price wars are destructive to all competitors.

Information

  • Who knows what?
  • Game theory assumes rules, player identities, contract enforceability, etc. are common knowledge. This ensures mutual awareness of strategic interdependence.
    • I know that you know, you know that I know that you know, …
  • It leaves room for private information about payoff-relevant variables.
    • I know how much oil my geologist estimates is in a tract to be bid upon, but not how much others estimate.
    • I do know the distribution of other players’ values…that is common knowledge.
  • Private information may be one-sided (market for lemons, health insurance) or multi-sided (oil auction case).

Enforceability

  • Non-cooperative game theory assumes away agreements that implement jointly optimal strategies.
  • Businesses are often forbidden from overt joint-profit maximizing agreements (collusion).
  • Breach of contract is common and may be good strategy (and even efficient!) in some circumstances.
  • Some things may be non-contractible (e.g. effort may be difficult to monitor or quantify).
  • In such settings, cooperation (win-win outcomes) will emerge only if it is in the participants’ separate and individual interests to continue to take the prescribed actions.
  • Alternatively, cooperative game theory can be a useful shorthand for thinking about certain aspects of bargaining.

The Prisoner’s Dilemma

  • The classic simultaneous-move game.
  • Two people collaborate in an armed robbery and are arrested by the police.
  • Police lack direct evidence but have evidence of weapons violations.
  • Each suspect is questioned separately and can “confess” or “deny,” not knowing the other’s choice.
    • If both confess, both get 5 years in jail.
    • If neither confesses, both get 2 years in jail.
    • If one confesses and the other denies, the confessor gets 1 year, the denier gets 10 years.

Prisoner’s Dilemma: Normal Form

  • The matrix representation of the game is called the normal form. This is the standard visual representation of a simultaneous-move game.
  • Person 1’s payoff is the first number of the pair, person 2’s payoff is the second.

Confess: A Dominant Strategy

  • Regardless of person 2’s choice, person 1 is better off choosing “Confess.” “Confess” is a best response to “Deny” and to “Confess.”
  • The same is true for person 2’s choice.
  • When a strategy is always a best-response, it is a dominant strategy.
  • In playing a game, if you have a dominant strategy, use it. If your opponent has a dominant strategy, expect her to use it.

Solving the Prisoner’s Dilemma

  • Each player finds it optimal to "Confess."
  • A Nash equilibrium is a set of strategies such that every player’s strategy is a best-response.
  • If two players have dominant strategies, then that forms a unique Nash equilibrium.

Lessons from the Prisoner’s Dilemma

  • The outcome is a lousy one for the players. They would both be better off if they both play their individually worst strategy (Deny).
  • This is not a good game to be a player in.
  • If it is possible to engineer a game where other players have dominant strategies, you can steer them toward your preferred outcome.
  • If is possible to change the rules (e.g. introducing alternative strategies), that could be worth trying.

Prisoner’s Dilemmas Everywhere

  • Prisoner’s Dilemmas are everywhere.
  • Tobacco companies and advertising bans.
    • Tobacco advertising not very effective in getting non-smokers to smoke, but is effective at getting existing smokers to switch brands.
    • Advertising is a best-response regardless of whether other firms advertise.
    • Advertising is also costly.
    • Equilibrium involves advertising by all firms, but advertising costs shrink the pie.
    • After 1970 ban on television ads, advertising expenditure fell 63million,profitsrose63 million, profits rose91 million.
  • Other Examples?