EC3312: Game Theory & Applications to Economics
AY2013/2014, Semester 2, Lecturer: Sun Yeneng
Course Coverage:
1. Static Games of Complete Information
2. Dynamic Games of Complete Information
3. Static Games of Incomplete Information
4. Dynamic Games of Incomplete Information
This is a very, I repeat, very mathematical course which precludes MA4264. It will, however, be very useful in EC4101. The introduction to this module would be gentler if EC3101 was taken before this module, however knowledge from EC3101 will not help much in this course.
First, understand the difference between perfect information and complete information. They are very different, and the difference is very important throughout the whole course, but to understand the difference, we need to know the information of the game and the strategy of each player. Each game has a particular set of information about the number of players, the action space, types, beliefs and utility/payoff functions of each player. This usually represented by G = {A1, ..., An; T1, ..., Tn; P1, ..., Pn; U1, ..., Un}. Actions and strategies are very different too, actions refer to the actions a player can take at any information set, or simply put, decision nodes(the points in time when player has to make a move) that can be differentiated by the player; whereas strategy profiles refer to the set of actions that player can follow throughout the whole game.
Now, if in a game, the game structure and payoff functions of each player are commonly known, then the game information is complete; whereas information is perfect if and only if all the moves are observable by other players. Thus, a game can be of complete information but not perfect, vice versa. In addition, the symmetric property of a game is also useful in deriving n player games, so it is really important to differentiate the terms properly.
The first segment of the course is on static games of complete information, famous examples of such games are Prisoner's Dilemma, Battle of the Sexes, Tragedy of the Commons, Cournot and Bertrand Duopoly. In this segment, you will formally learn about Nash Equilibria as well as finding the pure and mixed strategy Nash Equilibria. If you have done EC3101 prior to this course, just pay more attention to mixed strategy for more complicated games and you will do fine.
The next segment is the dynamic version. From this segment onwards, you will only be required to find pure strategy Nash Equilibria. Famous games include the Pirate Game, Take-away Coins, Hungry Lions and Stackelberg Duopoly. In this segment, you will learn about backward-induction. It is important to note that each backward induction outcome corresponds uniquely to a Subgame Perfect Nash Equilibrium. There may be more Nash Equilibria than backward induction outcome, and the non-Subgame Perfect equilibria are considered to be based on non-credible threats. As a result, there are considered bad equilibria and should be eliminated. The set of SPNE is alway the subset of the set of NE of the game, and might be identical in the case of static games of complete information. Significant topics in this segment are extensive form representation, SPNEs, discounting, multi/infinite-period bargaining and trigger strategies.
The third segment will introduce incomplete information which introduces heavily utilizes probability. It is a lot more complicated as the games vary greatly depending on the symmetries of the games. Nature will often choose a set of games with a fixed probability, some players will know which game is chose but some people might not. In some cases, all players don't know what has Nature chose, resulting in a symmetric game. It will also introduce the notion of Perfect Bayesian Equilibria, which is too complicated to be discussed on this post. Google it if you're interested.
The final segment is the dynamic version of the third segment, introducinga new genre of games called signaling games, and with it, pooling and separating equilibria. These topics were briefly covered in EC3101, but this module will cover it extensively, justifying the equilibria with mathematics and logical arguments. Drawing extensive form representation can be a chore, so do practice a lot on drawing the complicated game trees, especially the 4 information sets tree. We were lucky that Prof Sun always provide the tedious diagrams for us in all his tutorials, assignments and examinations.
I would say that this module can be difficult for most people, especially the proofs as they require extra research to understand why they work and how can they be modified for other similar problems. Only take it if you are mathematically-inclined, and I don't mean doing partial differentiation or matrix algebra because they are practically non-existent in this module. Familiarity with reading, writing and understanding mathematical proofs make a huge different, and a lot of brain power will be required for improvising proofs or solving decision games in exams. For me, a semester with MA2108, paid with the price of B-, makes writing proofs for this module a piece of cake.
Workload: Moderate
Difficulty: Difficult
Grade: A
Course Coverage:
1. Static Games of Complete Information
2. Dynamic Games of Complete Information
3. Static Games of Incomplete Information
4. Dynamic Games of Incomplete Information
This is a very, I repeat, very mathematical course which precludes MA4264. It will, however, be very useful in EC4101. The introduction to this module would be gentler if EC3101 was taken before this module, however knowledge from EC3101 will not help much in this course.
First, understand the difference between perfect information and complete information. They are very different, and the difference is very important throughout the whole course, but to understand the difference, we need to know the information of the game and the strategy of each player. Each game has a particular set of information about the number of players, the action space, types, beliefs and utility/payoff functions of each player. This usually represented by G = {A1, ..., An; T1, ..., Tn; P1, ..., Pn; U1, ..., Un}. Actions and strategies are very different too, actions refer to the actions a player can take at any information set, or simply put, decision nodes(the points in time when player has to make a move) that can be differentiated by the player; whereas strategy profiles refer to the set of actions that player can follow throughout the whole game.
Now, if in a game, the game structure and payoff functions of each player are commonly known, then the game information is complete; whereas information is perfect if and only if all the moves are observable by other players. Thus, a game can be of complete information but not perfect, vice versa. In addition, the symmetric property of a game is also useful in deriving n player games, so it is really important to differentiate the terms properly.
The first segment of the course is on static games of complete information, famous examples of such games are Prisoner's Dilemma, Battle of the Sexes, Tragedy of the Commons, Cournot and Bertrand Duopoly. In this segment, you will formally learn about Nash Equilibria as well as finding the pure and mixed strategy Nash Equilibria. If you have done EC3101 prior to this course, just pay more attention to mixed strategy for more complicated games and you will do fine.
The next segment is the dynamic version. From this segment onwards, you will only be required to find pure strategy Nash Equilibria. Famous games include the Pirate Game, Take-away Coins, Hungry Lions and Stackelberg Duopoly. In this segment, you will learn about backward-induction. It is important to note that each backward induction outcome corresponds uniquely to a Subgame Perfect Nash Equilibrium. There may be more Nash Equilibria than backward induction outcome, and the non-Subgame Perfect equilibria are considered to be based on non-credible threats. As a result, there are considered bad equilibria and should be eliminated. The set of SPNE is alway the subset of the set of NE of the game, and might be identical in the case of static games of complete information. Significant topics in this segment are extensive form representation, SPNEs, discounting, multi/infinite-period bargaining and trigger strategies.
The third segment will introduce incomplete information which introduces heavily utilizes probability. It is a lot more complicated as the games vary greatly depending on the symmetries of the games. Nature will often choose a set of games with a fixed probability, some players will know which game is chose but some people might not. In some cases, all players don't know what has Nature chose, resulting in a symmetric game. It will also introduce the notion of Perfect Bayesian Equilibria, which is too complicated to be discussed on this post. Google it if you're interested.
The final segment is the dynamic version of the third segment, introducinga new genre of games called signaling games, and with it, pooling and separating equilibria. These topics were briefly covered in EC3101, but this module will cover it extensively, justifying the equilibria with mathematics and logical arguments. Drawing extensive form representation can be a chore, so do practice a lot on drawing the complicated game trees, especially the 4 information sets tree. We were lucky that Prof Sun always provide the tedious diagrams for us in all his tutorials, assignments and examinations.
I would say that this module can be difficult for most people, especially the proofs as they require extra research to understand why they work and how can they be modified for other similar problems. Only take it if you are mathematically-inclined, and I don't mean doing partial differentiation or matrix algebra because they are practically non-existent in this module. Familiarity with reading, writing and understanding mathematical proofs make a huge different, and a lot of brain power will be required for improvising proofs or solving decision games in exams. For me, a semester with MA2108, paid with the price of B-, makes writing proofs for this module a piece of cake.
Workload: Moderate
Difficulty: Difficult
Grade: A