CLICK HERE TO DOWNLOAD PPT ON GAME THEORY
Game Theory Presentation Transcript
1.Game Theory
2.What is Game Theory?
Game Theory: The study of situations involving competing interests, modeled in terms of the strategies, probabilities, actions, gains, and losses of opposing players in a game. A general theory of strategic behavior with a common feature of Interdependence.
In other Words: The study of games to determine the probability of winning, given various strategies.
Example: Six people go to a restaurant.
- Each person pays for their own meal – a simple decision problem
- Before the meal, every person agrees to split the bill evenly among them – a game
Game Theory: The study of situations involving competing interests, modeled in terms of the strategies, probabilities, actions, gains, and losses of opposing players in a game. A general theory of strategic behavior with a common feature of Interdependence.
In other Words: The study of games to determine the probability of winning, given various strategies.
Example: Six people go to a restaurant.
- Each person pays for their own meal – a simple decision problem
- Before the meal, every person agrees to split the bill evenly among them – a game
3.Basic Concept
Players-Participants of a given game or games.
Rules-Are the guidelines and restrictions of who can do what and when they can do it within a given game or games.
Payoff-is the amount of utility (usually money) a player wins or loses at a specific stage of a game.
Strategy- A strategy defines a set of moves or actions a player will follow in a given game. A strategy must be complete, defining an action in every contingency, including those that may not be attainable in equilibrium
Dominant Strategy -A strategy is dominant if, regardless of what any other players do, the strategy earns a player a larger payoff than any other. Hence, a strategy is dominant if it is always better than any other strategy, regardless of what opponents may do.
Players-Participants of a given game or games.
Rules-Are the guidelines and restrictions of who can do what and when they can do it within a given game or games.
Payoff-is the amount of utility (usually money) a player wins or loses at a specific stage of a game.
Strategy- A strategy defines a set of moves or actions a player will follow in a given game. A strategy must be complete, defining an action in every contingency, including those that may not be attainable in equilibrium
Dominant Strategy -A strategy is dominant if, regardless of what any other players do, the strategy earns a player a larger payoff than any other. Hence, a strategy is dominant if it is always better than any other strategy, regardless of what opponents may do.
4.Five Assumptions Made to Understand Game Theory
5. Interdependence of Player Strategies
Sequential – Here the players move in sequence, knowing the other players’ previous moves.
- To look ahead and reason Back
2) Simultaneous – Here the players act at the same time, not knowing the other players’ moves.
- Use Nash Equilibrium to solve
6.Dominant Strategies
Sequential – Here the players move in sequence, knowing the other players’ previous moves.
- To look ahead and reason Back
2) Simultaneous – Here the players act at the same time, not knowing the other players’ moves.
- Use Nash Equilibrium to solve
6.Dominant Strategies
7.Dominated Strategies
8.Maximin Strategies
9.Pure and Mixed Strategies
A strategy that specifies one and the same specific action at each decision point is a pure strategy.
Many a times a player does not want to be predictable, therefore he/she randomizes among the actions at some or all decision points.
A strategy that specifies one and the same specific action at each decision point is a pure strategy.
Many a times a player does not want to be predictable, therefore he/she randomizes among the actions at some or all decision points.
10.Nash equilibrium
Each player’s predicted strategy is the best response to the predicted strategies of other players
No incentive to deviate unilaterally
Strategically stable or self-enforcing
Each player’s predicted strategy is the best response to the predicted strategies of other players
No incentive to deviate unilaterally
Strategically stable or self-enforcing
11.An Entry Game
12.Games of incomplete information
Prisoner’s Dilemma
No communication:
- Strategies must be undertaken without the full knowledge of what the other players (prisoners) willdo.
Players (prisoners) develop dominant strategies but are not necessarily the best one.
Prisoner’s Dilemma
No communication:
- Strategies must be undertaken without the full knowledge of what the other players (prisoners) willdo.
Players (prisoners) develop dominant strategies but are not necessarily the best one.
13.Payoff Matrix for Prisoner’s Dilemma
14.A game of incomplete information
If p is the probability that the incumbent’s cost are high and (1-p) is the probability that the incumbent’s cost are low, the profit earned on entry are:
p (4) + (1-p) (-3) = (7 p-3)
The numbers are expressed in lakh of Rupees. The profit earned by staying out are zero, therefore, the entrant will earn profits as long as p>3/7.
If p is the probability that the incumbent’s cost are high and (1-p) is the probability that the incumbent’s cost are low, the profit earned on entry are:
p (4) + (1-p) (-3) = (7 p-3)
The numbers are expressed in lakh of Rupees. The profit earned by staying out are zero, therefore, the entrant will earn profits as long as p>3/7.
15.Coke – Pepsi Repeated Game
Suppose the both agree to charge price P (Which is greater than the marginal cost) and to charge price Pc (Which is equal to marginal cost) if some cheating is detected. This is called the ‘grim-trigger’ strategy.
Profit to each firm = ½ (Market demand)(P-MC)Suppose Pepsi cheats it makes extra profit equal to profit of coke, but will be fined new price Pc on caught. Hence Pepsi will not be able to make that profit once again.
Suppose the both agree to charge price P (Which is greater than the marginal cost) and to charge price Pc (Which is equal to marginal cost) if some cheating is detected. This is called the ‘grim-trigger’ strategy.
Profit to each firm = ½ (Market demand)(P-MC)Suppose Pepsi cheats it makes extra profit equal to profit of coke, but will be fined new price Pc on caught. Hence Pepsi will not be able to make that profit once again.
Posts
0 comments