Dr. Adrian Teja
Issues to be discussed
Game Theory Game Theory Cases
Game Theory
Cooperative Game Theory Non Cooperative Game Theory
Seeks to predict the behavior of rational, intelligent firms competing independently.
Firms are rational if they make decisions by maximizing their subjective expected utility. Firms are intelligent if they recognize that other firms are rational. Intelligent firms can put themselves in the other firms’ positions and reasons from their points of view.
Applications of Game Theory
Product and price competition Coordination in channels of distribution Price war Implicit collusion First mover advantage Price as a signal of quality The “winner’s curse” in competitive bidding.
Games Consist of
Players or agents who make decisions. Planned actions of players, called strategies. Payoff of players under different strategy scenarios. A description of the order of play. A description of the frequency of play or interaction.
The Essence of Competition
Interdependence.
Interdependence means that the consequences to a firm of taking an action depend not just on that firm’s action.
Conflict of interest.
Firm must not be able to collude.
Rules of The Games Means Complete Descriptions of The Game
The number of firms Their feasible sets of actions at every juncture in the game Their utilities (profits) for each combination of moves The sequence of the moves The structure of information about moves (who knows what? When?).
Order of Decisions in Games
Simultaneous-move game
Game in which each player makes decisions without the knowledge of the other players’ decisions.
Sequential-move game
Game in which one player makes a move after observing the other player’s move.
Frequency of Interaction in Games
One-shot game
Game in which players interact to make decisions only once.
Repeated game
Game in which players interact to make decisions more than once.
Possible Strategies
Dominant strategy
Secure strategy
A strategy that results in the highest payoff to a player regardless of the opponent’s action. A strategy that guarantees the highest payoff given the worst possible scenario.
Nash equilibrium strategy
A condition describing a set of strategies in which no player can improve her payoff by unilaterally changing her own strategy, given the other players’ strategies.
Dominant Strategy Player B
Left B Player
Strategy Player A Player A
Strategy Up
Up Down Down
10, Left 20 10, 20 -10 , 7 -10 , 7
Player A has a dominant strategy: Up Player B has no dominant strategy
Right Right 15, 8 15, 8 10, 10 10, 10
Simu taneous-Move, One-S ot Games
Secure Strategy Player B
Left Player B
Strategy Player A
Strategy Up Player A
Up Down Down
Right
10, 20Left
15, 8 Right
10, 20 -10 , 7 -10 , 7
15, 8 10, 10 10, 10
Player A’s secure strategy: Up … guarantees at least a $10 payoff Player B’s secure strategy: Right … guarantees at least an $8 payoff
Simu taneous-Move, One-S ot Games
Nash Equilibrium Strategy Prisoners’ Dilemma
A Game of Complete Information Vs A Game of Incomplete Information
A game of complete information is one in which the rules of the game are common knowledge among the firms.
Every firm knows the rules, Every firm knows that every other firm knows the rule, Every firm knows that the other firms know that it knows the rules, etc.
A game of incomplete information is one in which the rules of the game are not common knowledge among the firms.
There is some asymmetry in the information at the start of the game.
Most real-world games are games of incomplete information Firms often do not know the motivations of their competitors – they do not know their costs and hence their profits from various actions, nor even whether they are guided by profits or some other objective. 2. Firms often do not know the technological capabilities of their competitors, that is, they do not know the feasible sets of actions of their competitors. 3. Firms differ in their knowledge of the world, i.e. one firm may know more about the commercial potential of a new drug than its competitors because it has done more product development than others. 1.
Pricing Game
Two Airlines, A and B, serve a given route A is the price leader – it moves first - and choose between 2 moves, the ticket prices $200 and $300 B is the follower, observes A’s move, then choose between $200 and $300 A have 2 strategy and 2 moves B have 4 strategy and 2 moves
Extensive Form Representation of a Pricing Game
Strategic Form Representation of A Pricing Game
Advertising Decision (1) Firm B
Firm A
Strategy
Advertise
Don't Advertise
Advertise
$4K, $4K
$20K,$1K
Don't Advertise
$1K,$20K
$10K,$10K
Advertising Decision (2) Leader's Strategies
Challenger's Strategies
Strategy
Advertise in Medium 1
Advertise in Medium 2
Advertise in Medium 1
1,0
0,1
Advertise in Medium 2
0,1
1,0
Monitoring Employee Worker Strategy Manager
Monitor
Don’t Monitor
-1, 1
1, -1
1, -1
-1, 1
Monitor
Don’t Monitor
Coordination Game Firm B Strategy
120-Volt Outlets
90-Volt Outlets
120-Volt Outlets
$100, $100
$0, $0
90-Volt Outlets
$0 , $0
$100, $100
Firm A
Entry Game (1)
Entry Game (2)
Conclusion
When there are multiple equilibria in a game, the Nash Equilibrium loses some of its predictive power. When multiple perfect equilibria exist, the firm must pick what it sees as the more promising equilibrium. To do so, the firm must necessarily bring into play considerations that were not part of the formal game (e.g. personality, history, culture). Several iteration game is not the same as one iteration game.