Game Theory

• Von Neuman and Morgenstern (The Theory of Games and Economic Behavior, 1944)

• Conceptual Framework– Game strategy– Components of a game

Two Person, Zero Sum Games

• Each person knows own and opponent’s alternatives

• All preferences are known

• Single period game

• Sum of payoffs zero

• Equilibrium reached when neither of the participants can improve payoff

Strategies

• Dominant strategy– Best regardless what others do

• Maximin strategy– Choice that maximizes across the set of

minimum possible payoffs– Best of the worst

Unstable Games

• No equilibrium found

• Strategy chosen leads to solution

• Each player then has incentive to switch

Two Person, Non-Zero Sum Games

• The Prisoner’s Dilemma

• Bonnie and Clyde are caught

• Dilemma: Confess or not

• 1 period game

• Non-cooperative solution: Both confess

• Cooperative solution: Both do not confess

• Off diagonal represents double cross

Duopoly as a Prisoner’s Dilemma

• Even if both agree to a cooperative solution, one may double cross

• Two firms: decision on amount of output {Small or Large}

• {L,L} represents normal profits

Repeated Games

• Single period game predicts competition, but there are likely to be multiple periods.

• Multiple periods allow for retribution, not found in single period games– Duopoly as a Multiperiod Game – More likely to collude

N-Person Games

• Extend to more than 2 players

• Complications:– Coalitions– Cooperation and duplicity

• Solutions can be difficult– Still gives insight into nature of conflict,

posturing, and resolution

Best Pricing Practices

• Shift attention to tactics and strategy to achieve competitive advantage

• Examine rival firm behavior as if it were a game– First-mover advantages– Credible threats to alter rival behavior– Stresses interdependency in oligopoly

Business Strategy Games

• When rivals alter products or pricing, react or adapt

• Anticipate actions; be proactive

• Sequential game--specific order of play– E.g.; One firm announces a price cut; decision

is to respond or not respond

• Simultaneous game--all players choose actions at same time

Business Rivalry as a Sequential Game

• The first to introduce a product, lower price, etc. often achieve recognition and advantage--first-mover advantage

• When games last several periods, actions can be rewarded or punished in subsequent periods– Entry of a new firm often discouraged by threat of

existing firms dropping prices to unprofitable levels.

First-Mover Games

• Game with military and civilian markets for Hum Vs.

Game Tree--Illustrating Sequential Games

• Game tree is like a decision tree

• Schematic diagram of decision nodes (or focal outcomes)

• Solutions parallel board games like chess

• One approach to solution--end-game reasoning--start with the final decision and use backward induction to find the best starting point.

1999 South-Western College Publishing

A Credible Threat

• A credible threat--an action perceived as a possible penalty in a noncooperative game. – Its existence sometimes induces cooperative

behavior.

• A credible commitment--a mechanism for establishing trust – Such as a reward for good behavior in a

noncooperative game.

1999 South-Western College Publishing

Mechanisms for Credible Threats and Commitments

• Contractual side payments, but these may violate antitrust laws.

• Use of nonredeployable assets such as reputation.

• Entering alliance relationships which may fall apart if any party violated their commitments.

• Using a "hostage mechanism”--irreversible and irrevocable can deter breaking commitments.

– Examples: "double your money back guarantees," and "most favored nation" clauses.

1999 South-Western College Publishing 1999 South-Western College Publishing

Hostage Mechanisms in Oligopoly

• Best Buy’s offer: If you find a lower advertised price, you’ll get the difference back

• This makes Best Buy cut prices whenever local stores cuts prices– Local stores realize they can’t undercut Best Buy– Customers realize it is unlikely to find lower prices– If potential entrants think they can get a foothold in area,

they know that Best Buy’s pricing is a credible commitment.

1999 South-Western College Publishing

Excess Capacity, Scale of Entry, and Entry Deterrence

• Building excess capacity can deter entry. Potential entrants know that the price can be driven down to unprofitable levels upon entry of new firms.

• The building of extra capacity is an action in a sequential game, often with the intent of forestalling entry. This is called a precommitment game.

Size Barriers

• Sometimes market entry requires large scale

• Incumbents may accommodate entrant, allowing a niche

• Incumbents may take entry deterring actions, such as cutting prices at the threat of entry

Sorting Rules

• Brand loyalty

• Efficient rationing

• Random rationing

• Inverse intensity rationing

Theory of Contestable Markets

• High prices encourage entry

• When barriers are low, even monopolist must be careful about raising prices too high.

• Contestable markets tend to have competitive prices and low or zero economic profits

• Potential entry matters more than actual number of firms

Simultaneous Games

• A sealed bid auction is a simultaneous game

• A dominant strategy is the best decision, no matter what anyone else does.

• When no Nash equilibrium exists, it is useful to hide one’s strategy by randomly changing strategies. Called a “mixed Nash equilibrium” strategy

Nash Equilibrium

• When all players make their best reply responses (so changing their choices cannot improve their situation) then the game is in Nash Equilibrium

• Since game trees have several branches, we can examine the concept in each part of the tree, called a subgame.

Repeated Games

• Escape from the prisoner’s dilemma

• If games are repeated, there is a greater expectation that firms will achieve a cooperative solution

• Firms signal by their behavior whether they want to cooperate or not

• Firms that expand output show that they do not want to cooperate

Repeated Game Strategies

• Grim trigger strategy--violations never forgotten– Alternatively, punishment can be short-lived– For multiperiod games, usually some period of

punishment that can induce cooperation

• Trembling hand trigger--when slight defections go unpunished– One non-cooperative act may be forgiven, but not

two