7. IMPEFRECT COMETITION - A GAME THEORY APPROACH

Game theory is the branch of microeconomics concerned with the analysis of optimal decision making in competitive situations, in which the actions of each decision maker have a significant impact on the fortunes of rival decision makers. Most of the theories of oligopoly are particular examples of game theory models.

Basic game theory concepts and tools

A game is any situation in which players (the participants) make strategic decisions - i.e. decisions that take into account each other's actions and responses. Examples of games include firms competing with each other by setting prices, or a group of consumers bidding against each other at an auction for a work of art.

Strategic decisions result in payoffs to the players: outcomes that generate rewards or benefits. For the price - setting firms, the payoffs are profits; for the bidders at the auction, the winner's payoff is her/his consumer surplus - i.e. the value the consumer places on the artwork less the amount she/ he must pay.

A strategy is a rule or plan of action for playing the game. For price - setting firms, a strategy might be: I'll keep my price high as long as my competitors do the same, but once a competitor lowers his price, I'll lower mine even more. For a bidder at an auction a strategy might be: I'll make a first bid of $200 to convince the other bidders that I'm serious about winning, but I'll drop out if other bidders push the price above $5000.

The optimal strategy for a player is the one that maximizes player's expected payoff.

In a cooperative game players can negotiate binding that allow them to plan joint strategies, and in a noncooperative game, negotiation and enforcement of binding contracts are not possible.

Basic assumptions:

1. games involving players who are rational, in the sense they think through the consequences of their actions. In essence we are concerning with the following question: if I believe that my competitors are rational and act to maximize their own payoffs, how should I take their behaviour into account when making my decisions?

2. complete symmetry a perfect information (i.e. competitors have the same cost structure and are fully informed about each others' costs, about demand, profits, etc.);

3. understanding your opponent's point of view, and deducing his or her likely responses to you actions

A ONE - SHOT, SIMULTANEOUS - MOVE GAME

(a single decision)

Late nineties in XX century, competition between Honda and Toyota in the North American automobile market. Each firm faced a decision of whether to build a new auto assembly plant in North America

The payoffs in the matrix show the extent to which the players in the game are interdependent: Toyota's payoff depends on what Honda does, and vice versa. In game theory, a player will very rarely control its own fate.

Game theory seeks to answer the question: What is the likely outcome of a game? To identify “likely outcomes” of games game theorists use a concept of a Nash equilibrium. At a Nash equilibrium, each player chooses a strategy, that gives it the highest payoff, given the strategies chosen by the other players in the game.

Dominant strategy - one that is optimal no matter what an opponent does.

The following example illustrates a duopoly; firms A and B sell competing products and are deciding whether to undertake advertising campaigns. Each firm will be affected by its competitor's decision. The possible outcomes of the game are illustrated by the payoff matrix.

F I R M B

Advertise Don't advertise

F I R M Advertise

A

Don't advertise

When every player has a dominant strategy, the outcome of the game is called an equilibrium in dominant strategies (outcome of a game in which each firm is doing the best it can regardless of what its competitors are doing).

Unfortunately, not every game has the dominant strategy for each player.

O r l e n	Lotos Group
		invest	invest	don't invest
				12 4	20 3
		don't invest	15 6	18 5

Comparing the concepts:

• dominant strategies - I'm doing the best I can no matter what you do.

You are doing the best you can no matter what I do.

• Nash equilibrium - I'm doing the best I can given what you are doing.

You're doing the best you can given what I am doing.

The dominant strategy is always leads always to the Nash equilibrium, but the latter is not always the result of the dominant strategy.

The prisoners' dilemma

The Nash equilibrium does not necessarily correspond to the outcome that maximizes the aggregate profit of the players. However, the rational pursuit of self- interest leads each party to take an action that is ultimately detrimental to their collective interest. The conflict between the collective interest and self - interest is often referred as the prisoners' dilemma.

R O N	D A V I D
		confess	confess	don't confess
				- 5 - 5	0 - 10
		don't confess	- 10 0	- 1 - 1

The prisoners' dilemma is widely studied throughout social sciences. Psychologists, political scientists, sociologists, and economists find a prisoners' dilemma a compelling idea because the tension it portrays between an individual player's self - interest and a group's collective interest shows up in many different ways in the world around us. For example, business firms start price wars, even though all firms in the industry get hurt as a result.

Tit - for - tat strategy - repeated game in which a player responds in kind to an opponent's previous play, cooperating with cooperative opponents and retaliating against uncooperative ones.

Electro World's

prices

0 Media Markt's prices

Games with more than one Nash equilibrium

A famous example of the game with more than one Nash equilibrium is Chicken.

L U K E	S L I C K
		swerve	swerve	stay
				0, 0	-10, 10
		stay	10, - 10	- 100, - 100

In economy the best example is a natural monopoly, where there is no room for another producer.

The business of satellite television involves high fixed costs and low marginal costs. This is because once a company launches a satellite and acquires the rights to programmes, the MC of adding one more household to its subscription base is relatively low.

S K Y	B S B
			In	Out
		In	- 118 - 747	673 0
		Out	0 137	0 0

Game theory by itself, cannot indicate which of these two Nash equilibriums is likely to arise. More details are needed about players and particular circumstances that they can face in order to make predictions about who will win.

SEQUENTIAL GAMES

Sequential game is a game in which players move in turn, responding to each other's actions and reactions.

potential competitor „Dziennik”

•

staying outside the market

entry

• • a firm existing in the market

“Gazeta Wyborcza”

price war adjustment

• •

Π_D - „Dziennik”'s payoff Π_G - “Gazeta”'s payoff

The Nash equilibrium sets after using the following strategies: entry the market (“Dziennik”) then adjustment to the circumstances (“Gazeta Wyborcza”).

Prof. Teresa Kamińska Microeconomics

45

Capacity expansion game between Toyota and Honda

H

O

N

D

A

T O Y O T A

build a new plant

build a new plant

do not build

do not build

16, 16 20, 15

15, 20 18, 18

payoffs are in millions of dollars per year

10, 5 15, 0

6, 8 10, 2

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