Managerial and Decision Economics: Game Theory and Oligopoly's Pricing Strategies | Lecture notes Managerial Economics

Lecture 4

MANAGERIAL AND DECISION ECONOMICS

GAME THEORY AND OLIGOPOLY’S PRICING STRATEGIES

Game theory is the study of how interdependent decision makers make choices. It has many applications in

natural sciences, engineering, as well as in social sciences and economics.

SIMULTANEOUS GAME = A game in which all players choose their actions at the same time

(simultaneously), before knowing the actions chosen by other players.

•OLIGOPOLY MARKETS AND GAME THEORY

Use in industrial organisation: Game theory provides a useful framework to understand interactions between

competing oligopolists.

Interdependence of firms’ profits arises when the number of firms in a market is small enough that every

firm’s price and output decision affects the demand and marginal revenue conditions of every other firm in

the market.

Game theory is an analytical guide or tool for making decisions in situations involving interdependence.

PRISONER’S DILEMMA

A prisoner’s dilemma arises when all rivals possess dominant strategies, and, in dominant strategy

equilibrium, they are all worse off than if they had cooperated in making their decisions.

Players are the decision makers

Actions are all possible moves that a player can make

(steal or split)

Payoffs usually consist of profits or gains the players

receive after the game has been played out. (0 or 6800 or

13600)

Information structure defines how much each player knows at each point in the game

In a game with perfect information each player knows every move the other player has made

before taking any action.

All games in which players move simultaneously are games of imperfect information because

players do not know the move of the other player. (This case!)

A player’s strategy is a set of rules telling which action to choose as a response to opponent’s possible

actions. Each player aims to select the strategy that will maximise his/her own payoff.

1. If one knew for certain that Player 2 chooses “steal”, Player 1 is indifferent between steal and split. In

either case Player 1 gets zero. So, assuming that Player 2 chooses “steal”, Player 1 can choose either

“steal” or “split”.

2. If one knew for certain that Player 2 chooses “split”, then Player 1 is better off when he chooses “steal”.

3. Putting both scenarios together, we see that “steal” is a (weakly) dominant strategy for Player 1. Hence

Player 1 is bound to choose “steal”.The same holds for Player 2 as well, because he has exactly same

payoffs for the same actions.

Hence both players choosing “steal” is a Nash equilibrium of this game!

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Lecture 4 MANAGERIAL AND DECISION ECONOMICS GAME THEORY AND OLIGOPOLY’S PRICING STRATEGIES Game theory is the study of how interdependent decision makers make choices. It has many applications in natural sciences, engineering, as well as in social sciences and economics. SIMULTANEOUS GAME = A game in which all players choose their actions at the same time (simultaneously), before knowing the actions chosen by other players.

• OLIGOPOLY MARKETS AND GAME THEORY

Use in industrial organisation : Game theory provides a useful framework to understand interactions between competing oligopolists. Interdependence of firms’ profits arises when the number of firms in a market is small enough that every firm’s price and output decision affects the demand and marginal revenue conditions of every other firm in the market. Game theory is an analytical guide or tool for making decisions in situations involving interdependence. PRISONER’S DILEMMA A prisoner’s dilemma arises when all rivals possess dominant strategies, and, in dominant strategy equilibrium, they are all worse off than if they had cooperated in making their decisions. Players are the decision makers Actions are all possible moves that a player can make (steal or split) Payoffs usually consist of profits or gains the players receive after the game has been played out. (0 or 6800 or

Information structure defines how much each player knows at each point in the game In a game with perfect information each player knows every move the other player has made before taking any action. All games in which players move simultaneously are games of imperfect information because players do not know the move of the other player. (This case!) A player’s strategy is a set of rules telling which action to choose as a response to opponent’s possible actions. Each player aims to select the strategy that will maximise his/her own payoff.

If one knew for certain that Player 2 chooses “steal”, Player 1 is indifferent between steal and split. In either case Player 1 gets zero. So, assuming that Player 2 chooses “steal”, Player 1 can choose either “steal” or “split”.
If one knew for certain that Player 2 chooses “split”, then Player 1 is better off when he chooses “steal”.
Putting both scenarios together, we see that “steal” is a (weakly) dominant strategy for Player 1. Hence Player 1 is bound to choose “steal”.The same holds for Player 2 as well, because he has exactly same payoffs for the same actions. Hence both players choosing “steal” is a Nash equilibrium of this game!

NASH EQUILIBRIUM:

First formalised by John Nash in 1950s. In a Nash equilibrium no player has an incentive to change his/her action because his/her strategy yields the highest possible payoff given the other player sticks to his/her strategy. I. A dominant strategy is a strategy that outperforms any other strategy regardless of the strategy selected by an opponent. II. A dominated strategy is never employed and so can be eliminated, elimination of a dominated strategy may result in another being dominated: it also can be eliminated. SOCIAL OPTIMUM = it is the objectively good choice in all the payoff, but that rarely it is taking into account. Usually this choice is the role that an authority has to practice. SEQUENTIAL DECISIONS: One firm makes its decision first, then a rival firm observes this decision before making a response. For a sequential game, it is convenient to map the choices facing the players in the form of a game tree. EXAMPE: Suppose two breakfast cereal producers (Firm A and Firm B) consider launching one of two possible products: Crunchy : This product’s appeal is its crunchiness. Fruity : This product’s appeal is its fruitiness. 1.If A chooses “Crunchy”, then B will choose “Fruity”. 2.If A chooses “Fruity”, then B will choose “Crunchy”. 3.Hence, by induction, Firm A knows that only the above shown paths are actually relevant. 4.Firm A maximises its payoff by choosing “Crunchy”. Hence Firm A choosing “Crunchy” and Firm B responding to it by choosing “Fruity” is the Nash equilibrium of this sequential game.

Shows firms decisions as nodes with branches extending from the nodes
One branch for each action that can be taken at the node
Sequence of decisions proceeds from left to right until final payoffs are reached
Backward induction is a method of finding a Nash equilibrium by looking ahead to future decisions to reason back to the current best decision

PRICING STRATEGIES TO DETER ENTRY:

Pricing strategies to maintain a firm’s market power in the long run:

(^) Limit pricing : an established firm commits to setting price below the profit-maximising level to prevent entry
Predatory pricing : assumes that a monopolist expands output aggressively and cuts price so that the entrant sustains an economic loss, even if this requires the monopolist to sustain an economic loss as well.
The monopolist’s hope is that potential entrants would eventually get the message and assume that the monopolist would respond aggressively to all entry and future potential entrants would stay out. [GUARDA SLIDE 38] If the monopolist lowers its price to 50, the potential entrant’s residual demand curve is p=50-q which lies everywhere below the potential entrant’s marginal (MC) and average cost curves (AC). Therefore, if the monopolist is assumed to maintain its output after entry, the entrant will sustain an economic loss and hence entry is impossible. EXAMPLES: 1. 2. In the first Game Tree, the entry is deterred, because the LIMIT PRICING kept competitor out. In the second Game Tree, the entry is NOT deterred, because LIMIT PRICING is NOT a credible threat so that the competitors enters.

• LIMIT PRICE WITH ASYMMETRIC INFORMATIONS:

Information asymmetry lies in the fact that the potential entrant (PE) does NOT know if the nature assigned the incumbent monopolist (M) high or low production costs whereas the monopolist is very well aware of its own costs. [In other words: Nature flips a coin to determine if M is high cost or low cost. M is informed of the outcome, PE is not informed.] If there was no asymmetric information, PE would know if the game is at node M1 or M2 after nature’s coin flip. If the game is at node M2 (M is a low cost firm), PE won’t enter because low price is M’s dominant strategy after this node and PE is bound to make a loss, if M goes for low price. If the game is at node M1 (M is a high cost firm), PE will be interested in entering, because M will surely choose a high price, in which case PE will make a positive profit upon entering. Hence, if M is a low cost firm, then M has nothing to fear. BUT if M is a high cost firm, then M will pretend to be a low cost firm (by signaling that it will set a low price) and hope that PE won’t enter.

Managerial and Decision Economics: Game Theory and Oligopoly's Pricing Strategies, Lecture notes of Managerial Economics

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